Bill Robertie’s Backgammon Lesson 1: Early

game … which point to make?

Take a look at Position 1. Black has a 4-2 to play. What should he do?

White – Pips 161

Black – Pips 160

Black to Play 4-2

There are two clear candidates here; make your own 4-point, or your opponent’s 5-point (your 20-
point). Anything else is a waste of a great shot. But which point should we pick?

Early game problems where you have a choice of good points to make can usually be solved by
asking yourself three key questions.

First, which point is intrinsically more important?

Second, how do the particular circumstances of the position affect the absolute value of the point?

Third, what’s the degree of difficulty for making each point?

Part 1. We’ll start with the intrinsic value of the points. This is pretty easy to determine. The most
valuable points in the early going are the two 5-points, closely followed by the 4-points and the bar-
points, which are about equal. Other points are much weaker than these key blocking points. Only
considering intrinsic value, the White 5-point (your 20-point) is the top choice.
Part 2. Now we have to look and see how the actual position we’re in affects the value of the
points. This part requires more judgment.

On Black’s side of the board, not much has changed from the starting position. Black has moved a
builder from the 13-point to the 8-point, giving him a little better diversification than he had before.
White is still anchored on Black’s 1-point. All in all, Black’s 4-point is just about as valuable as on
the opening roll.

But on White’s side of the board, the position has changed a lot. First, White has actually made an
inner board point. That means an anchor, any anchor, is more important than it used to be, because
any attack that White launches is now more likely to be successful.

In addition, however, the point White has made is his 4-point. With the 4-point made, White’s 5-
point becomes even more valuable (for both sides) because of the strength of the 4-5-6 structure.
Back in the 1970s, Paul Magriel, in his classic book Backgammon, labeled the 5-point the “Golden
Point”, signifying its importance in the opening. While the 5-point is the best point to have in the
early going, its power can be mostly neutralized if the opponent then makes the 4-point anchor. But
the combination of the 4-point, 5-point, and 6-point, which I like to call the Golden Structure, is a
real game-changer. Whoever makes that structure in the early game is on the verge of a powerful
double. Even anchoring on the 3-point in front of the structure merely allows the defender to hang
on in a clearly inferior position. The only road to equality is hopping the structure entirely and
anchoring on the bar-point, and that will be hard to do.

Conclusion: White’s 5-point has risen in importance, while Black’s 4-point hasn’t changed much.
Making the anchor with 24/20 22/20 now gets the edge.

Part 3. Finally, we have to consider degree of difficulty. How hard is it to make a good anchor,
compared to the difficulty of making blocking points? This question almost always favors making
the anchor.

Right now Black has one non-double (4-2) that makes the 20-point, and another one (6-4) that
makes the almost equally valuable bar-point. On Black’s side of the board, he currently has six rolls
(3-1, 4-2, and 6-1) that make a good blocking point. But that number will grow dramatically as soon
as he adds even a single builder in his outfield. Pull a checker from the midpoint to the 9-point, for
example, and Black will suddenly have nine non-doubles working on those points (6-1, 6-2, 2-1, 3-
1, 4-1, 4-3, 4-2, 5-2, and 5-4). Add in his doubles, and Black becomes a favorite to make a key
blocking point, each turn!

Meanwhile, his chances of making a good anchor won’t get bigger, because unless he gets hit, he
can’t add any new checkers to his anchor-making list. Upshot: good anchors are much harder to
make than good blocking points, so your desire to make them is greater.

All three considerations point clearly to 24/20 22/20 as the best play with a 4-2. When in doubt
between an anchor and a blocking point, make the anchor!
Bill Robertie’s Backgammon Lesson 2: Run or
Anchor?
In Position 2, Black has a 6-2 to play. What’s the right idea here?

White – Pips 161

Black – Pips 160

Black to Play 6-2

Black has a few reasonable choices in Position 2. If he wants an anchor at all cost, he can button up
with 24/22, after which he has to choose between 13/7 and 8/2 for his six. If he wants to stay
flexible and run a checker out, he can try either 22/14 or 22/16 13/11. All the plays have some
merit, and there’s no obvious standout. What’s the right idea?

Here’s a key principle that will guide you through a lot of early positions: Points are good, and
points that are anchors are especially good. Period.

Now it’s true that the 22-point is not the best anchor to have. Given a choice, you’d rather be on the
20-point or the 18-point. But right now it’s the only anchor available. As we discussed in Lesson 1,
the 20-point and bar-point anchors are hard to get, so when you’re under pressure you should be
happy to take what’s available.

After playing 24/22, the best six is obviously 13/7. The bar-point is much stronger than the 2-point,
so you slot the bar even though you give White a few more shots. Now that you have an anchor,
being hit isn’t a potential disaster.

Of the running plays, the best is 22/16 13/11, simply because it moves a checker into the outfield
and tries to stay out of trouble, a very good idea when your opponent has a better home board and
you don’t have an anchor. Black has a few too many blots after this play, but White has to throw a
four to really hurt him.
Several plays here are outright blunders: 13/5, 24/18 22/20, and 24/18 13/11.

The first play (13/5) violates a good general rule: Don’t slot while your back checkers are split.
When you slot a point, you’re hoping for your opponent to miss so you can cover next turn. If your
back checkers are split, your opponent will attack you there if he doesn’t hit your slot, and you’ll
have to get in from the bar before you can try to cover.

The other two plays (24/18 24/22 and 24/18 13/11) violate a different rule: Don’t leave your back
checkers sitting on points your opponent really wants to make. Violate this rule and your opponent
will just start hitting everything in sight, while you scramble to survive. The exception (sort of) to
this rule is the split on the opening roll with a play like 24/20 or 24/18. If your opponent is in the
starting position, he doesn’t have quite enough ammunition in place to really hurt you. But once he
starts making points, you’re in danger. Either keep your blots safely tucked away back on the 24,
23, or 22-points, or run for safety in the outfield, but don’t dawdle on the target range.
Bill Robertie’s Backgammon Lesson 3:
Making the 5-Point
Here are two early game positions where Black has not much and White has an inner point and
some pressure.

Position (a):

White – Pips 152

Black – Pips 160

Black to Play 3-1
Position (b):
White – Pips 150
 Black – Pips 160
Black to Play 4-2

When Paul Magriel wrote his seminal book Backgammon in 1976, one chapter that was particularly
noteworthy was entitled “The Golden Point”. There he described the importance of the 5-point, both
for offensive and defensive purposes, and showed how making the 5-point was a key goal of early
game play.

Over the years, theory regarding the 5-point has never really changed much. We’ve found a few
exceptions, and certainly expanded our knowledge of when to break the 5-point later in the game,
but the 5-point remains a key opening goal in most positions.

The two examples given above are very typical cases. In each position, Black has a chance to make
either the offensive 5-point (Position (a)) or the defensive 5-point (Position (b)). In each position,
there are alternatives that seem to have strong merit. In Position (a), Black’s rear checkers are under
some pressure and seem to require a defensive anchor, which he can grab with 24/21 22/21. In
Position (b), Black can actually hit while making a somewhat inferior anchor with 13/9* 24/22.

But in each case, simply making one of the 5-points is better. In Position (a), making his own 5-
points smooths Black’s distribution while starting to put White under some pressure. In Position
(b), grabbing the defensive 5-point with 24/20 22/20 prevents White from ever building a priming
position, after which Black can start to build points on his side of the board.

It’s incredibly hard to go wrong by making one of the 5-points at an early stage. The exceptions are
rare and tend to be exceptions by only small amounts. When in doubt, go for the 5-point.
Bill Robertie’s Backgammon Lesson 4: Using
Benchmark Positions
A key idea in understanding the proper use of the doubling cube on a practical level is that of the
“benchmark” position. A benchmark cube situation is a position where one of the decisions
(doubling or taking) is a toss-up, while the other is completely clear. Properly understanding a
benchmark position is very useful since it unlocks the key to many related positions. Just compare
your actual position to the benchmark, spot what the relevant differences, and you should be able to
make a good cube decision over the board.

White – Pips 168

Black – Pips 151

Black on roll. Cube action?

This early cube decision shows an excellent benchmark position. White started the game with a 5-1,
splitting his back men, and Black responded with a 4-4, making two inner-board points. (Not best,
by the way; making the 20-point and the 9-point is better, with a more enduring positional edge.)
White then danced, and Black is now contemplating a double.

An analysis by the Extreme Gammon program (highly recommended, by the way) showed that the
double/no double decision was completely marginal, with only a tiny difference between the two
plays. If doubling is theoretically marginal, then taking is, of course, hugely correct. Dropping is a
mistake costing almost one-third of a point. (As a practical matter, this means that doubling is
mandatory, since it theoretically costs nothing and might prompt a huge blunder on your opponent’s
part.)

Better players are aware of hundreds of good benchmarks, so they can make their over-the-board
decisions quickly and accurately.
Bill Robertie’s Backgammon Lesson 5: Split or
Slot?
Slotting to make a key point and splitting your back checkers are two tactical ideas that dominate
early-game play when more obvious choices like hitting blots and making points aren’t available.
The 1970s and 1980s were the heyday of slotting. The preferred method of winning a game was to
build an imposing prime (often by slotting points, then covering) and follow it with a crushing
double. The older method, taking the points you were given and looking for a chance to escape your
back checkers, was seen as antiquated and wimpy, a game plan only suited for geezers playing in
the park.

This all changed in the 1990s with the arrival of the bots, first Jellyfish, then Snowie, and then in
2010 Extreme Gammon, the current top bot. The early bots didn’t slot their 5-point with an opening
roll of 2-1, 4-1, or 5-1, as had been customary; instead, they split their back men with an ace. (The
latest version of Extreme Gammon now prefers slotting with the 2-1 roll, and rollouts back up that
decision.) These results swept the backgammon world, and soon almost everyone was splitting
rather than slotting with opening aces.

While there was nothing wrong with copying the bot’s plays with the opening rolls, players soon
began making serious mistakes in other parts of the game. Since these opening rolls were the most
obvious examples of slotting, they “learned” that slotting was simply an error except in a few
bizarre circumstances. As a result, they started missing strong slotting plays in all sorts of opening
and middle-game situations. They’d discarded a key tactical idea on the basis of a tiny set of
opening positions.

So when is slotting to be preferred to splitting? In general you’re looking for a combination of

factors, some of which argue against splitting, others of which argue in favor of slotting. The next
position illustrates these ideas pretty clearly.
Cash game, Black on roll, Black owns the cube.

White – Pips 129

Black – Pips 152

Black to Play 2-1

Here Black finds himself in a weak position with stacks and stripped points, while facing a strong
White board. With the 2-1 roll, Black can try various things. He can play very safe with 13/10, split
his back men with 24/21, split and build with 13/11 24/23, or purely build with 13/11 6/5. At first
glance, no play leaps out as clearly right. Let’s see if we can whittle down the possibilities.

The problem with the splits is that White’s game has become just a little too powerful to abandon
the anchor. White doesn’t actually have a lot of rolls to fill in the gaps in his prime, but he’ll be
happy to launch a blitz if he can, and splitting gives him that opportunity. In fact, either split boosts
Black’s chances of losing a gammon enormously – from about 20% after the non-split plays to
around 28% after the split plays. Such high gammon chances would require the split plays to win at
least 4% more games than the non-splits to be contenders. There’s nothing in the position to suggest
that could happen, so let’s toss out the splits.

Absent the splits, we’re now down to a choice between the aggressive 13/11 6/5 and the quieter
13/10. The key here is to remember that Black doesn’t want to split anymore. But if splitting is too
dangerous, then Black will need to build a front position quickly to stay in the game. There’s no
guarantee that 13/10 will give him a position anytime soon. That play, after all, leaves five shots but
still doesn’t give Black a lot of good point-making numbers. 13/11 6/5, on the other hand, leaves 13
shots but gives Black a ton of point-makers if it works. Slotting with 6/5 is right by a wide margin,
and it’s right whether the cube is centered or Black already owns it.

One footnote to this position: you might reasonably think that duplication plays a role in this
decision. When Black slots his 5-point, White needs fours to hit, but 4-2 and 6-4 already make good
points in his board. But in fact the play is structurally correct and the duplication is irrelevant. If we
move White’s inner-board points to the 4-point and the 2-point, so that fours don’t build any new
points, then the slot is still correct, and by almost as wide a margin.
Bill Robertie’s Backgammon Lesson 6:
Volunteering a Shot
Backgammon is basically a race, and losing ground in a race is usually a bad idea, to be avoided if
at all possible. Safe, constructive plays are generally good. Constructive plays which leave a few
indirect shots aren’t bad, and are often necessary to make progress.

But sometimes there aren’t any safe plays, or even moderately risky plays, that make progress.
What if the safe plays all hurt your position in some way? Then you may start looking at plays that
leave a direct shot. These plays may be costly if your opponent hits, but they may improve your
position if your opponent misses (which he’s generally favored to do.)

Let’s look at a few criteria for volunteering a direct shot. Since we’ve been talking about high
anchor positions in the last few articles, we’ll start with a high anchor problem. Consider Position 1.

White – Pips 133

Black – Pips 111

Black to Play 6-2
Black leads in the pip count by 22 pips, 111 to 133. He’s already doubled, and now he’s trying to
bear his checkers home against White’s high anchor on his 5-point. He’s a favorite to win, but not
an enormous favorite; on roll, he’s just about 2-to-1 to win the game.

His 6-2 roll, however, is one of his worst. There’s only one safe play: 8/2 8/6, clearing the 8-point.
The strength of the play is solely that it leaves no blots. The downside is pretty obvious. By clearing
the 8-point, Black removes a crucial landing spot that he’ll need later when he tries to clear the 11-
point and the 13-point.

There’s another play to consider, however. It’s 13/7 4/2. Black leaves a blot on his bar-point which
White can hit with a deuce. If White misses, however, Black’s game is better in every respect. He’s
kept the 8-point as a landing spot, and next turn he’ll have several rolls, like 6-5 and 4-3, which
make the 7-point while clearing one of his troublesome outer points.
13/7 4/2 is what we call a “pure” play. Pure play simply means putting your checkers where they
belong, assuming they don’t get hit. Slotting the 7-point certainly qualifies as a pure play, since if
White doesn’t roll a deuce, Black will be much better off in all future variations.

Are pure plays right? That depends. Basically, when considering a pure play which volunteers a
direct shot, you need to balance the upside (ease of future play) versus the downside (the cost of
getting hit). That’s often not an easy choice. Here are some of the issues you should consider:

Arguments against volunteering a shot:

> If your opponent’s position on the other side of the board is strong (closed board, solid prime, or
some of both), you probably don’t want to leave a shot.

> If your position is good and your future rolls will play easily (at least for awhile), you probably
don’t want to leave a shot.

> If your opponent’s position is stretched, so that he may have to concede a crucial point before you
do, you probably want to wait and play safe.

Arguments for volunteering a shot:

> If your opponent’s position is weak (open points or blots in the home board), you may not mind
leaving a shot.

> If the point is crucial to winning the game, you may want to leave a shot.

> If your opponent is vulnerable after being hit, you may want to leave a shot.

Let’s apply these arguments to Position 1 and see what they tell us.

How strong is my opponent’s home board? It’s actually very strong. This is a powerful argument
against leaving a shot. White is very close to completing a prime, so a hit will probably win the
game for him. At the very least, he’ll be a solid favorite.

How easily do my future rolls play? This is ambiguous. If you clear the 8-point, you still have a
spare on the midpoint, which probably represents one free roll. You may be able to shift some of the
checkers in your home board, which might represent another roll or two. All in all, you might have
two or three rolls to play before you have to break a key point.

Will my opponent have to concede a key point (his 20-point or midpoint) before me? No.

How crucial is the 7-point to winning the game? It’s certainly helpful. Actually, by slotting the 7-
point you get to keep the 8-point as a bonus, and the two points together are very useful.

Is my opponent vulnerable after hitting? He’s somewhat vulnerable. He’ll have a couple of blots
floating around, which might allow you to reenter and attack, but you’ll still be a big underdog after
getting hit.

The biggest consideration here is the strength of White’s home board. Hitting is probably a winner
for him. If all the other arguments came out in favor of slotting, then slotting might be correct, but
here they’re collectively ambiguous. So play safe with 8/6 8/2 and wait. Leaving a shot is a blunder.
To see when leaving a shot is right, take a look at Position 2.

White – Pips 137

Black – Pips 111

Black to Play 6-2
Now White’s home board is not impressive at all, and Black doesn’t need to be afraid of being hit,
so 13/7 4/2 is the best play. White will hit if he can, but in the resulting positions, White will be a
long way from winning.
Bill Robertie’s Backgammon Lesson 7 –
Duplication
Duplication is a cute tactical idea which can lead you to make the right play in a wide variety of
situations. The basic idea is pretty simple. You find yourself in a vulnerable position. You roll an
awkward number. No matter what move you make, your opponent will have some bad things he can
do to you next turn. You want to minimize the number of his rolls that can hurt you. What do you
do?

The answer? Duplication! Try to play your number in such a way that your opponent needs the
same number to accomplish his goals everywhere on the board, rather than different numbers in
different places. In this way, you reduce his effective numbers to a minimum, giving yourself the
best possible chance to survive.

Let’s start with a very simple example.

White – Pips 113

Black – Pips 76
Black to Play 6-1

Black owns the cube, and leads by 37 pips in the race. That’s the good news. The bad news is that
his 6-1 roll forces him to break the 16-point, leaving two blots.

Where should he leave his two outside blots? Duplication gives the answer. If he foolishly plays
16/10 16/15, White can hit with any 5, any 3, and a few more combination numbers (2-1, 1-1, 4-1,
and 6-4), a grand total of 27 shots. That means a full 75% of White’s possible throws will hit a blot
and almost certainly win the game (or even a gammon).

But suppose Black alertly plays 16/10/9. Now he’s duplicated White’s fours! White needs a four to
hit on the 16-point, and another four to hit on the 9-point. Needing a four in both places means that
White’s total shot numbers are greatly reduced. He can hit with any four, plus the combination
numbers of 1-1, 2-2, 3-1, and 6-5, for a total of only 17 shots. Less that half of White’s numbers
now hit, and that’s a big improvement over the first play. (Of course, Black may leave another shot
next turn, but that’s a separate problem. He might also have left a shot next turn after the other
play.)

This was actually a pretty easy example of duplication. Black had to leave a shot in two different
places, so he arranged his checkers so that the same number hit in both cases. Other examples of
duplication are more subtle. See if you can find the duplication in the next problem.

White – Pips 139

Black – Pips 117

Black to Play 2-1
In this murky position, Black has already doubled but is now trying to rescue his two loose checkers
and get them to the safety of his prime. White’s game is choppy, but if he can keep hitting Black’s
blots, he may develop solid winning chances.

With the 2-1 roll, Black will obviously enter with the ace and then look around for the best deuce.
He has only two choices: 16/14, which leaves White twos to hit, and 7/5, which creates better
development but leaves White fours to hit. So two questions arise:

> What’s the right play?, and

> What does duplication have to do with this problem?

The right play is actually 16/14. This seems strange since at first glance it doesn’t seem to matter
whether Black leaves White twos or fours to hit, whereas it’s obvious that 7/5 improves Black’s
distribution. To see why 16/14 is the best play, we have to look deeper and see what White will
actually do with his various rolls.

Suppose Black plays 16/14 and gives White deuces to hit. Now imagine the position without the
loose Black checker on the 14-point, and take a look at how White’s deuces would otherwise play.

> 62 would be played 24/16, escaping a checker.

> 52 would be played 6/1* 3/1, making the ace-point, putting Black’s rear checker on the bar, and
activating the partly-dead checker on the 3-point.

> 42 would be played 8/4 6/4, making the 4-point.

> 32 would be played 24/21 3/1*, moving a spare to the edge of the prime and hitting loose.

> 21, the worst roll, can still be played 24/21, reaching the edge of the prime.

What’s important to notice here is that each of White’s rolls containing a deuce is already
constructive. If Black leaves the blot on the 14-point, White will elect to hit with a deuce, but his
relative gain is not very great since he could have played the deuce effectively in any event.

Now let’s imagine the loose Black checker off the board and see how White would play his fours.

> 64 is awkward; White has a choice between 21/11 and 13/3, both of which are bad.

> 54 would be played 13/8 13/9. White surrenders control of the outfield.

> 43 would be played 24/21 13/9. A reasonable roll.

> 42 makes the 4-point as before. A constructive roll.

> 41 is played 13/8.

As we look at the individual rolls, it’s clear that White’s fours, as a group, are much less effective
than his deuces. Leaving White a four to hit turns his fours into good numbers rather than mediocre
numbers.

Now we can see why this is a duplication problem. Playing 16/14 duplicates White’s twos, but in a
non-obvious way. White’s deuces were all playing effectively, but they were doing different things
on different parts of the board; it takes some real effort to see that deuces were the number to be
duplicated.
Bill Robertie’s Backgammon Lesson 8: More
on Duplication
In my last post, I introduced the concept of duplication. It’s a powerful idea, one of the crucial
tactical ideas in backgammon. Look for your opponent’s numbers that already play well, and
remember that plays which expose blots to those very same numbers elsewhere on the board
become stronger than they at first appear. Here’s another good example.

White – Pips 128

Black – Pips 155

Black to Play 6-1

Black’s not crushed yet, but his game is starting to deteriorate. His back men haven’t moved yet,
and White has a ton of attackers in play in case Black decides to split. Up front, Black’s made his
bar-point but doesn’t have a lot of numbers to extend his little prime. Meanwhile, White’s checkers
are poised to escape, and he’s got nice diversification, with small numbers building his 5-point, and
large numbers hopping into Black’s outfield.

At first, 61 doesn’t look like a particularly good shot for Black. Splitting in back with 24/23 13/7
isn’t inviting. White’s few remaining awkward numbers, like 66, 55, and 44, now become crushers,
while everything else continues to play well. Playing two men down with 13/7 13/12 looks
constructive, but contains a subtle flaw. It’s not the immediate danger – only 63 and 64 hit for
White. But if White hops into the outfield next turn without hitting – 61, 62, 51, and 53, for instance
– Black has to deal with this blot rather than build his board. The longer Black goes without
building his board, the more danger he faces. The simple 13/7 8/7 eliminates the outfield danger, at
the cost of leaving even fewer point-making numbers.

The solution is hard to find: it’s 13/7 6/5! Slotting into a double shot is a rare play. The
circumstances have to be just right, and here they are. First, there’s some duplication involved. The
small number combinations now give White the choice of hitting or making the 5-point. He will
choose to hit, but it’s only clear with the 32 roll. With 21 and 31, hitting gets the nod only because
of the extra gammon chances generated by a third man back. (At double match point, White should
build his 5-prime with these two rolls.) As for the other hitting numbers, Black is worse off for
having slotted, but not by much. White still only has a two-point board, and Black’s checkers are
suddenly well-developed and in play. And of course if White misses altogether, Black is delighted.
After some rolls like 55 and 44, Black is already the favorite, while mediocre rolls like 54 and 41
leave the game even money!

One reason that backgammon is a tough game is because a long series of completely routine and
easy moves can be punctuated by the need to make a sudden, crucial and decisive play. Get it right,
and the game can move quickly in your direction. Get it wrong, and the game will slip away from
you.
Bill Robertie’s Backgammon Lesson 9: High
Anchor Holding Games
Next to races, the most common type of position in backgammon is what we call the holding game.
Holding games occur when one side escapes his back checkers to the safety of the midpoint or
beyond, but the other side (the “defender”) does not. Instead, the defender manages to anchor his
two back checkers somewhere in his opponent’s home board.

Take a look at this pretty typical position.

White – Pips 136

Black – Pips 116

Black on roll. Cube action?

An anchor on the 4-point, 5-point, or bar-point (7-point) is considered a high anchor. An anchor on
the 2-point or the 1-point is a low anchor. The 3-point constitutes a separate case, with
characteristics of both high and low anchor games.

The side who has escaped his back checkers (Black in Position 1) is almost always the favorite in a
high anchor holding game. Here Black has a 20-pip lead in the pip count (116 to 136), and that’s
enough to make him almost a 3-to-1 favorite in the game. If he doubles (which he should), White
has a clear take. Then Black will try to bring his checkers home without being hit. Sometimes he’ll
succeed, occasionally he won’t. Most of White’s wins come when Black leaves a shot somewhere
(often when trying to clear the midpoint or the 8-point) and White hits. Very occasionally, White
will roll a couple of big sets of doubles and actually win the race. But mostly, White’s hoping to get
a shot and hit it.
Clear a Point, or Wait and Build?

Since clearing points is very important when bearing home against an anchor, many players tend to
make point-clearing plays automatically. But in backgammon, no play is ever really automatic.
Let’s look at some of the issues involved. Consider Position 2, for example.

White – Pips 114

Black – Pips 93
Black to Play 5-3

Black is on roll and leads in the race by 21 pips, 93 to 114. He’s already doubled. He has one
outside point, the 11-point, left to clear. One way for Black to lose this game is to eventually leave a
shot on the 11-point, and then get hit by a subsequent 5-2 or 6-1 from White. With his roll of 5-3,
he can eliminate that danger by simply clearing the 11-point now, with 11/6 and 11/8. It’s clearly
the right play, leaving Black an enormous favorite. Now he’s only concerned with clearing his
remaining outside points successfully.
 White – Pips 80

Black – Pips 93
Black to Play 5-3

Although Black’s pip count is the same (97 pips) as in the previous position, White’s has changed
dramatically. Instead of trailing by 21 pips, White now leads by 13 pips! As a result, Black’s
strategy has to change completely.

The danger of Black’s getting hit on the 11-point at some later time is now relatively
inconsequential. White’s real threat is much more direct: he simply wants to win the race. At some
point (perhaps next roll) White will run off the anchor with a 6 or a 5. Black will then need to attack
the checker that remains and attempt to fill in his 3-point and 4-point, completing a prime. The best
plan is to fill in the 3-point now, then attack the 4-point as soon as White leaves. This plan has more
risk than Black would like, since a single 4 from the bar may win for White, but it’s all Black has.
He should just play 8/3 6/3 and await developments.

The moral here is pretty simple. When playing against a high anchor, knowing the pip count is
crucial. With a big lead (which is usually the case) look to bring your checkers home with minimum
risk. If the race is close or you are trailing (as in Problem 3), White may have to leave his anchor
before you can come home. In that case, being well-placed to attack is crucial.
Backgammon Lesson 10 – Holding Game
Doubles
Last article, we talked about some of the tricky play problems that arise in high anchor positions.
This time, we’ll start to look at doubling strategy in these common situations. (Remember, a high
anchor game is one where one player has escaped all his back checkers, while his opponent has
managed to secure an anchor on the 4-point or 5-point.)

Take a look at Position 1.

White – Pips 131

Black – Pips 119

Black on roll. Cube action?

In Position 1, Black has escaped his back checkers and White is holding the 5-point anchor. Black’s
trying to bring his checkers on the midpoint home without leaving a shot. White hopes to hit any
blot that Black is forced to leave, or, alternatively, win the race by outrolling Black later on. Black
has the advantage, but White is not without resources. Should Black double?

Before we answer that question, let’s look at the most important feature of the position: the pip
count.

Black’s pip count is 119. (To calculate a pip count, just multiply the number of checkers on a point
by the value of the point, and calculate the sum for all your points. Four checkers on the midpoint,
for example, contribute 4 * 13 = 52 to your pip count.) White’s pip count is 131, so Black has a 12-
pip lead, which represents about 10% of his pip count of 119.

If this were a straight race, where both sides had disengaged and there was no possibility of hitting a
shot, a 10% lead in the race would be enough to double. Straight races have been extensively
analyzed by computer since the 1970s, and an 8% lead is usually enough to offer a good initial
double. (The trailer need to be down no more than 12% to have a take.)
Here, however, White has more ways to win than just throwing bigger numbers in the race. There’s
a very real chance that he could hit a shot, and that possibility adds a few percent to his winning
chances. In addition, he usually has a better bearoff position than Black when the race actually
starts, since he has the luxury of filling his board smoothly, while Black may be left with a gap on
his 5-point.

The net result of all these factors is that Black’s winning chances are actually under 70%, and he
doesn’t quite have a double yet.

Clearly, Black needs more than just a minimal racing lead to double in these high anchor holding
positions. Just how big a lead does he need? Take a look at Position 2.

White – Pips 139

Black – Pips 119

Black on roll. Cube action?

The pip count is now 119 for Black and 139 for White. Black’s lead is now 20 pips, about 16% of
his pip count. In a straight race, that lead would mean a double for Black and a clear pass for White.
Here, Black just has enough to double. White, however, still has an clear take. His combination of
racing chances and hitting chances enable him to win slightly more than 25% of the time. As an
added bonus, he’ll almost never be gammoned from this position, so as long as his winning chances
stay above 25%, he can take.

How big a lead does Black need to have before White will have to pass? Let’s move on to Position
3.
 White – Pips 139

Black – Pips 99
Black on roll. Cube action?

Position 3 is similar to Position 2, but I’ve moved two of Black’s checkers from the 13-point to the
3-point, a distance of 10 pips each. The pip count is now 99 for Black and 139 for White, a lead of
40 pips. This must be a pass for White, right?

Wrong! It’s still a take. In fact, Black’s winning chances are only about 1% better in Position 3 than
Position 2. How can this be??

What’s happening is that Black is gaining one asset (racing chances) but losing another asset
(timing) simultaneously. If we compare Position 3 to Position 2, Black is now much less likely to
lose a race, but much more likely to get hit as he tries to clear the 13-point. The two assets (racing
chances and timing) are moving in opposite directions at about the same rate. Black’s double is
solid in both positions, but White has a clear take in both cases, although for different reasons.

In almost all normal 5-point holding games like the ones shown here, White has a pretty take. Black
needs about a 15% lead in the pip count to have a good double. Remember those rules, and you
won’t make many cube errors in these common positions.
Backgammon Lesson 11 – Position or Race?
In this position, with Black on roll, who is a favorite?

White – Pips 161

Black – Pips 140

Black on roll. Who’s a favorite?

This is a good problem for two reasons.

(1) Many players look at this position and think the answer is almost too obvious to even require a
discussion. At the same time, they often can’t quite agree on what the obvious answer is.

(2) It’s a position which illustrates in stark terms the relationship between a racing lead and a
positional edge, and as such it has some real historical significance.

Back in the period 1977-1982, the elite backgammon world was ruled by what was then known as
the ‘pure style’. The Bible of the pure style was Barclay Cooke’s Paradoxes and Probabilities, a
collection of 168 checker and cube problems, which was published in 1978 and which became
wildly popular among the tournament set. The essence of the pure style was that backgammon was
a game of key points and primes. The race had some relevance, but not nearly as much as had been
thought by the simpler players of an earlier generation. Playing for the race too early caused players
to sacrifice positional assets, to their later detriment.

The theory of the pure style led naturally to a basic game plan: Grab both 5-points, slotting if you
needed to, control all four quadrants, build a prime, and finally hit and trap a checker, with an easy
win. If your blots got hit, just fall into a well-timed back game and turn things around later. It was a
seductive plan, leading to beautiful-looking positions with powerful primes, high anchors, all
checkers working, and a complete absence of stacks.

The pure style was very attractive to the new wave of former chess players who were moving into
the backgammon world in large numbers. It offered a view of backgammon that made the game
similar to chess: strong points, control of the center, good development of the pieces, all leading to
victory in the end.

Most successful tournament players tried to play some version of this style, and the style seemed to
work. The players who were winning big tournaments were (with a couple of exceptions) playing
just this way. I tried to model my own game on this approach, and by 1981 I was having some
success. I’d won a couple of big tournaments, as well as many smaller ones, and I was doing well in
chouettes around Boston. Life was good.

Then I met Alex.

Alex was probably in his mid-70s when I met him. His location and date of birth were a little hazy,
but according to his stories he’d bounced around the world a lot, spending most of his time in the
Middle East and Eastern Europe. He’d played backgammon for a long time in a lot of different
places. He never played for high stakes ($5 a point was his limit) and he didn’t like tournaments
because they took too long. He liked to hang around the Cavendish Club in Boston and watch the
$20 chouette (the big game in those days) and occasionally play heads-up for $2, $3, or $5 a point.

On Sundays the big game was a bit of a hit-or-miss affair, so sometimes I’d find myself at the club
with nothing to do. Alex and I would get to chatting about his travels, and we started playing heads-
up to pass the time until a chouette would start. I figured Alex played an old-fashioned game and
would be pretty easy pickings for a veteran like myself, schooled in all the latest tricks.

I was right about Alex’s style. It was old-fashioned. He split his back men with most opening plays,
and never ever slotted. His goal was to get into a race or a holding game as quickly as possible. He
handled blitzes reasonably well, and never seemed to get into a back game. His cube action seemed
a little weak – he was slow to double in positions where he had strong threats, and I thought he was
too quick to drop some interesting positions.

I had faced opponents in tournaments who just tried to play a racing game, but they were beginners
or intermediates who made lots and lots of obvious mistakes and were easy to beat. Alex was
different; he wasn’t easy to beat. As the days passed and the count of games climbed to 200 and
then 300 and then 400, I realized to my shock that I was just breaking even. As far as I could tell, I
was supposed to be winning big. My cube action was clearly better, I saw Alex making technical
errors in positions that I had rolled out and understood well, and to top it all he was playing this
passive style that should have been cannon fodder for my state-of-the-art hyper-aggression. Had I
just hit a really unlucky streak?

I doggedly pressed on over the next few weeks, and the game count mounted to 500 and 600 and
700. My luck finally changed. It got worse. Alex was now up 30 points or so in our long session. At
last he quit, as he was going on a long trip to see friends and relatives. I paid up and now had plenty
of time to ponder just what had happened.

I was tempted to shrug and conclude that our sessions had just been an aberration, in which I had an
extended run of bad luck against a much weaker player. But that just didn’t feel right. I really didn’t
believe that I had been all that terribly unlucky. As I thought about the session, I realized that the
mix of our two styles had led to a lot of holding games, where I had some nice holding position like
the 5-point plus an extra man back, while Alex had escaped his back checkers and led in the race,
but with little or no structure. According to the theory of the time, I was supposed to be better in
those positions. But now I started to wonder about that.
As an experiment, I created the position at the start of this post, which is an extreme case of the sort
of situation I was remembering. Black has a racing lead but absolutely no structure, and White is
beautifully placed with both 5-points and control of all quadrants. I thought White had to be a solid
favorite here. If I had taken this position to a tournament and shown it to a bunch of good players, I
was certain they would concur unanimously. But I got a lot of these positions against Alex, and
didn’t seem to win as often as I thought I should.

I decided to roll the position out 300 times, with no cube, and see what happened. I also decided to
play Black’s position just as Alex had played it, never leaving a shot unless I had to. (Conventional
wisdom of the day was that Black should slot points quickly, before White’s board got too strong.)
The rollout took a few days (this was 1981, remember – no bots) and when it was finished Black
had won 58% cubeless.

I was startled, but also excited. I understood why I had been losing to Alex. Whatever edge I had in
complex positions and cube handling had been overcome by the number of times I had taken too
many chances in the opening and been swept into playable but inferior holding games. Clearly, my
early game play needed some serious adjustment, and I had some hard work ahead. On the bright
side, I’d stumbled on an idea that would certainly improve my game a lot, and I couldn’t wait to
refine it into a real weapon.
Now suppose you were Black in this position. How would you play these rolls?

(a) 5-2
(b) 4-1
(c) 2-1
(d) 6-5

Solutions:

First note that Black is a favorite. White might get a shot and then hit it, but Black has a lot of safe
rolls, and a lot of rolls that leave only a single shot. Note also that just being hit isn’t the end of the
game. A cubeless Extreme Gammon rollout puts Black at 56%, close to the 58% from my manual
rollout many years ago.

(a and b) The right idea for Black is not to leave a shot unless he has to. With 5-2, he should just
play squat with 13/6, while 4-1 should be played 13/8 rather than hitting on the 1-point. Alex
understood that Black had time to wait, while most players of that era would have tried to clarify
the position quickly with 13/8 6/4 or 6/1*.

(c) If you have to leave a shot, the outfield is usually the right place, since White will have to make
a concession to hit by breaking his anchor. With 2-1, play 13/10.

(d) Occasionally a roll arises which is potentially so strong that it’s right to play big. With 6-5, the
right play (but only by a little bit) is 13/7 6/1*. White hits with 20 shots, but Black becomes a very
solid favorite when White misses because of the slotted bar-point. Contrast that with the 4-1 play,
where Black still has a ton of work to do if he plays 6/1* and White misses.
Backgammon Lesson 12 – Holding Game
Doubles, Part 2
In some earlier posts we talked about doubling in high anchor games, and looked at some typical
positions where White held an anchor on the 5-point and Black was trying to cash in on his racing
advantage and bring his last checkers home to victory. All of those positions turned out to be takes.

From those examples, you might conclude that almost any 5-point game was a take, regardless of
the race. But it’s not quite that simple. In this article we’ll look at some examples where small
modifications to the position can produce big changes in the evaluation.

Let’s begin by looking once more at one of our previous problems.

White – Pips 139

Black – Pips 99
Black on roll. Cube action?

Black has a whopping 40-pip lead in the race (99-139), but White has an easy take, based on his
chances of getting and hitting a shot as Black tries to clear both the 13-point and the 8-point.

With that position in mind, take a look at this one:

 White – Pips 148

Black – Pips 108

Black on roll. Cube action?

Black has a 40-pip lead just as before (108-148), but the position is a little different. Black owns his
7-point in this example, and he has a big pile of checkers on his 6-point and 7-point. Is that enough
to change the evaluation?

Indeed it is! In Diagram 2, Black should double and White has a big pass. There are two reasons:

* Black now has 7 rolls each turn that clear the 13-point without leaving a shot: 22, 33, 44, 55, 66,
and 65.

* The many spares on the 6-point and 7-point mean that Black will have several turns to move
without disturbing his position, while he waits to throw a number that clears the midpoint.

Seven rolls may not seem like a lot, but the cumulative effect is substantial. If he has four rolls to
try to throw one of his seven numbers, his chances of success are higher than you might think:
about 60%! And even after he leaves a shot, White still has to hit it, and then win the game after
hitting. White’s winning chances in Diagram 2 are only about 17%, and he has to pass.

Now try this position:

 White – Pips 127

Black – Pips 98
Black on roll. Cube action?

Here Black leads by 29 pips. Certainly he has a double, and at first glance you might think that
White can take here. But White has a big problem. Unlike the previous positions, White’s home
board is no longer in such good shape. In those positions, White was on the verge of completing a
full prime, which would win the game if he could hit a shot. But here, White’s home board is
ragged, with the 3, 4, and 5-points still to be made. Because White has made the 1 and 2-points first,
he can’t hope to make an outside prime and roll it home. Instead, he has to fill in all three home
board points before he can claim the game after hitting. That’s a tall order, and it will give Black
many extra opportunities to save the game even if he gets hit. The weak home board gives White a
clear pass.

Remember: if your game plan depends on hitting an eventual shot, three separate events must occur:

1. Your opponent must leave a shot.

2. You must hit the shot.

3. You must win after hitting.

If the best you can hope for is to get a single shot, then event (2) is never more than about 40%. To
have a take, the probability of event (1) needs to be around 50%, and event (3) needs to be almost a
certainty. Check all the features of a position before taking a cube in these situations.

Backgammon Lesson 13: Make a point or hit?

 White – Pips 150

Black – Pips 161

Black to Play 3-1
(a) Black to play 3-1.

(b) Black to play 3-2.

Here’s a typical early game position where neither side has made much progress yet. White has
played a 5-3 and a 6-3, making his 3-point and running a checker into the outfield. Black has rolled
a 5-1, balancing his builders and splitting his back men.

The 3-1 and 3-2 rolls give Black a choice between hitting and making a good point. Lots of players
hit automatically in these positions, not really believing that any non-hitting play can be good. But
that’s not right. Constructive positional plays are often better than hitting, especially in the early
game when boards are weak. Not always, however; sometimes hitting is, in fact, correct. Before we
address the particulars of the position, let’s take a general look at the rules that guide this sort of
choice. I’ll list a bunch of features of the position, and which choice each favors:

> A strong home board favors hitting; a weak home board favors building a point.

> A big disadvantage in the race favors hitting; a close race is neutral.

> The more ground you can gain in the race by hitting, the more correct it’s likely to be. Hitting
a blot in your opponent’s inner or outer boards is usually correct; hitting a blot in your own outer
board is sometimes a mistake.

> Strong threats for your opponent favor hitting as a tempo play or making a defensive anchor;
few threats favor making an offensive point.

> Stacks of checkers favor making a point; no stacks imply plenty of points already, which favors
hitting.
With those principles in mind, let’s start with the first roll, 3-1. Here everything points to making
the 5-point as the best play. Black has no home board and big stacks, and making the 5-point fixes
both problems. The race is close, hence relatively neutral. The blot to be hit is in Black’s outer
board, only a modest argument for hitting. The stacks strongly favor unstacking and make the 5-
point. White has only weak threats, which is an argument for structure.

The weight is strongly in favor of 8/5 6/5, which is in fact the best play with a 3-1.

Playing a 3-2 is a different sort of problem. Now the choice is between hitting or making a good
anchor, so a lot of those arguments disappear, since Black can’t do anything about his stacks. Here
the real question is: how badly does Black need an anchor? And the answer is: not much. White
doesn’t have a strong attacking formation, and Black’s rear checkers are already well-placed.
Hitting also works now as a tempo play, taking away half of White’s roll and reducing his offensive
chances still further. The best hitting play is just 13/10* 23/21, keeping a spare on the midpoint and
preparing to make a good anchor later.

One more point before we leave this position. Players who go on long losing streaks often feel they
are rolling incredibly badly for long periods of time. In fact, what’s often happening is that they are
steaming and making mistakes in just these sorts of positions, taking the first play they see instead
of thinking the position through. Thus they tend to drift into bad positions more often than they
should.

Backgammon Lesson 14: Which point to

make?
Although the first roll of the game is pretty well understood, backgammon gets much more
complicated as we get a little deeper into the game and positions get more complex. Both positions
in this article occur at the third move, after Black wins the opening roll and White responds. Try
your hand at these commonplace and apparently simple situations, and see how you do.

Position 1.
 White – Pips 161

Black – Pips 162

Black to Play 4-3

When you have a choice between an offensive or a defensive point in the opening, you need to ask
yourself two questions:

> Which point do I need more? If your home board is stronger than your opponent’s, your need to
be defensive is minimized and you want instead to build on your advantage by making another
offensive point. If his home board is stronger, you need defense and will make a defensive point.

>Which play leaves me with a better structure? Good structure, meaning strong points and a
smooth distribution of builders, is an important consideration. If one play leaves substantially better
structure than the other play, factor that into your decision.

In Position 1, both questions point in the same direction. White’s home board is stronger, so Black
prefers making the defensive 20-point to the offensive 5-point. Also, making the 5-point leaves
Black with a weaker structure – the 8-point is stripped, and there are no builders remaining in the
outfield to make new points in conjunction with the stack on the 6-point. By making the 20-point
instead, the spare on the 8-point and the builder on the 9-point give Black a lot of rolls to make an
offensive inner point next turn.

Position 2.
 White – Pips 162

Black – Pips 164

Black to Play 4-2

Here’s the position after Black opens with a 2-1, aggressively slotting his 5-point, and White
responds with a 3-2, splitting and bringing a builder down.

This position hinges on a cute tactical idea that’s common to a number of opening situations. In
general, it’s better for Black to have the 4-point made with the 5-point slotted than just to have the
5-point itself. The reason is that the formation with the 6, 5, and 4-points all made, while the
opponent has no development, is so powerful that it’s worth taking considerable risks to achieve it.
So here the right play is the cute 8/4* 6/4 rather than the solid 11/5.

For a related position, suppose that White opens the game with 43 and choose the Middle Eastern
split – 24/20 24/21. Now, if Black rolls 44, the right play is not 13/5*(2) but 13/5* 8/4*(2).

The merit of the play just depends on the positional structure, not on potential cube turns or
gammon possibilities. It’s true that if Black makes the 4-point and White fans, he has an initial
double, whereas there are no upcoming doubles after 11/5. However, that’s not what is driving the
play. It’s also the right idea at double match point, and by a lot.

Back in the 1970s, Paul Magriel made this play, but although he was the strongest player of his
time, he couldn’t convince anyone else of its correctness. Even in that wild era, simply making the
5-point just looked too strong with no immediate risk. Much later, the play caught on and eventually
the bots proved that it was in fact the best play.

Backgammon Lesson 15: Hit or Not?

Many backgammon problems boil down to a simple question: hit, or don’t hit. In essence,
backgammon is a pretty simple game. In general, you want to make points, and in general, you want
to hit.
When you can hit a checker on the other side of the board, gaining both time and racing equity, you
almost always want to do so. (The only exceptions occur when the alternative is to make a very
strong priming or blocking point on your side.) But when the only possible hit is to hit a blot in your
inner board, the choice is more difficult. Now you’re risking a significant loss of race equity if you
get hit back, so the hit is rarely automatic. For a hit in your inner board to be correct, one of these
two reasons usually applies:

(1) You’re hitting on a key blocking or priming point, which you very much need to make.

(2) Your opponent has so many threats that a tempo play is necessary; that is, you’re hitting to
prevent your opponent from attacking with his entire roll.

Keep these ideas in mind as you evaluate Black’s choices in the following problem.

Position 1.

White – Pips 156

Black – Pips 166

Black to Play 5-3
This problem is best solved by a process of elimination. Black will enter with his three, Bar/22, and
choose among four fives, none of which stands out as an excellent play. Try discarding the
obviously worst choices first until you’ve narrowed the field, then see which looks most appealing
between the survivors.

> 6/1*. Hitting loose on the ace-point in the early game is a tantalizing play. It often looks
necessary, it’s almost always wrong, but on the occasions when it’s correct, it’s usually correct by a
lot. The hit is a tempo play (designed to take away half of the opponent’s roll), but to be correct, the
need for a tempo play must be huge. That means that your opponent needs plenty of builders ready
to pounce, and you absolutely must put him on the bar. Here the play is wrong because White
doesn’t have enough serious threats. True, White has some pointing numbers. But to make his 3-
point, he’ll have to break his 7-point or 8-point. He’ll do that if he can, but it’s not a threat you need
to guard against because of the broken points and the return shots. Meanwhile, 6/1* just dumps a
checker out of play and risks losing plenty of ground in the race.

> 8/3*. The same idea as 6/1*, but even worse. Black strips the important spare off the 8-point,
while leaving almost twice as many shots as 6/1*.

> 11/6. Better than the first two choices by a lot, but look at that hideous stack on the 6-point. In the
absence of crushing threats, the idea in the early game is to unwind stacks, not make them worse.

> 13/8. Doesn’t do anything great, but doesn’t damage the position either. Here it’s the winner by
default, as the other choices are all ruinous.

In our position, White’s threats weren’t all that serious, so a quiet play made sense. If White had a
more dangerous collection of builders, 6/1* might have become the best play.

Backgammon Lesson 16 – More on Hitting

In the last blog post we looked at some hitting problems in the early game. In this post we’ll look at
a couple of more examples where hitting is one possibility.

When you have a chance to hit on your opponent’s side of the board in the early game, it’s usually a
pretty easy choice. Gaining a lot of ground in the race, advancing your back checkers, and taking
away at least half your opponent’s roll are so important that such hits are usually routinely correct,
and even when wrong are rarely wrong by much.

Hitting on your own side of the board is more problematic. Merely hitting is no longer enough of a
rationale. Here are some of the other questions you need to ask:

Am I hitting on a key point? The key points are the 5-point, the 4-point, and the bar-point. Both
you and your opponent want to make these points quickly. Fighting for these points is crucial. If he
makes one of these points, he gets an anchor and doesn’t have to worry about being primed. If you
make the points, you lock in his back checkers.

Am I unstacking when I hit? Hitting and unstacking an overloaded point is good, bringing your
checkers into play. Hitting while breaking an already made point is much weaker.

Do I already have a good anchor? Hitting after you’ve made a good anchor on his side of the
board isn’t very risky. You won’t like being hit back, but your game won’t collapse. Hitting without
a good anchor is more dangerous. Now a return hit could be awkward.

Consider these salient ideas while we look at the next two problems.
 White – Pips 145

Black – Pips 152

Black to Play 2-1
Position 1: Black to play 2-1.

White has advanced his back checkers quickly, and Black has an opportunity to hit on either the 4-
point or the 5-point. Let’s check our hitting criteria and see if a hit here is recommended.

Are these key points? Certainly.

Can we hit while unstacking? Yes. The big stack on the 6-point cries out to be unstacked.

Do we have an anchor, for defensive insurance? Yes. The 21-point represents a good, solid
advanced anchor. We certainly don’t want to be hit back, but we can easily survive.

But — if you have a choice between attacking on the 5-point and attacking on the 4-point, which
should you choose?

Why choose? Hit both! The best play is 6/5* 6/4*. No other play is close.

Now let’s look at a second example.

 White – Pips 150

Black – Pips 149

Black to Play 4-3
Position 2: Black to play 43.

Many players assume that hitting in the outfield is a routine play in the early game, and hit without
thinking. Position 2 is a good example, where all but the best players would play 13/9 13/10* in a
flash.

It’s true that hitting is mostly right, but it can be wrong, so in particularly difficult situations, learn
to pay careful attention to the merits and demerits of hitting. At the beginning of this article, we
listed three key criteria for hitting. Here are some other factors that bear on a hitting question. When
in doubt, check for them as well:

How much ground do I gain in the race by hitting? The more, the better. Hits on your
opponent’s side of the board are more likely to be clearly right than hits on your side of the board.

Does hitting cost me a valuable point? Hitting with a spare checker is much more likely to be
right than a hit which concedes a point in the process. Hitting from a big stack is even more likely
to be correct.

Is my home board strong? The more points you have in your home board, the more likely any hit
is to be correct.

Am I vulnerable after the hit? The biggest hitting errors occur when the hit leaves you with a
bunch of vulnerable blots around, while your opponent’s game remains pretty solid.

Do I have a good alternative? As always, the strength of the alternative plays is key. Question
anything obvious if the alternatives are solid and strong.
In Position 2, every criteria argues against the hit. The 10-point isn’t a crucial point, Black gains
minimal ground in the race by hitting, it costs him the midpoint and doesn’t unstack, his home
board is weak, he doesn’t have an anchor, he’s very vulnerable after the hit, and he has a great
alternative, 20/13, which leaves him in a fine position. While 20/13 is the top choice (because it
saves the exposed and now useless blot on the 20-point, the hit is so bad that even 7/3 6/3 is to be
preferred.

2017 Boston Quiz Contest, Part 1

The backgammon boom continues apace, with new tournaments popping up on the calendar on a
regular basis. Two new tournaments appeared in just the past month: the Boston Open (Feb. 23-26)
and the Viking Classic in Bloomington, MN (Mar. 9-12). Both were well attended, with 82 players
in Boston and 83 players in Minnesota, very strong numbers for first-time events.

To help kick off the Boston tournament, I created a quiz contest for Sunday morning, with no entry
fee and a $100 prize to the winner. Marty Storer of New Hampshire took first place with an
outstanding score of 17/20, closely followed by Dennis Culpepper of Virginia with 16/20.

The collection of problems in the quiz is a little unusual. There aren’t any weird, tricky positions or
difficult cube decisions based on match score considerations. It’s just a group of pretty normal
positions where the choice is between two or three reasonable-looking plays. The idea here is to
understand where you want to put your checkers when there’s nothing decisive to do this turn.

This blog post contains the first five problems of the quiz. Over the next couple of weeks, I’ll post
the remaining 15 problems, five at a time. Enjoy!

Problem 1: Black to play 4-3

 White – Pips 160

Black – Pips 167

Black to Play 4-3

White opened with a 5-2, splitting, and now Black rolls 4-3. In the little world of ‘Replies to the
Opening Roll’, this is one of the most often misplayed. Let’s see why.

As a general rule, when our opponent splits on the opening roll, we want to split as well. But 24/21
13/9 leaves White a direct shot, so most players settle on 24/20 13/10 as their play.

But this move has a problem as well. When your opponent splits with a deuce, you shouldn’t be
eager to leave a blot on your 10-point. If you do, White has 10 hitting numbers: 6-1, 5-2, 4-3, 6-3,
and 5-4. Except for 6-1, these are all rolls that don’t do much right now. Leave a checker on the 10-
point, however, and these rolls jump from mediocre to very strong. In effect, by playing 13/10
you’ve diversified your opponent’s numbers very nicely.

But if we rule out the two split-and down plays, what’s left? The Middle Eastern split with 24/20
24/21 is rarely right; it puts two vulnerable checkers on the very points where White is eager to
attack. Even worse is 13/6, a play you just can’t make when your opponent has no board.

What’s left are the hitting plays: 6/3* combined with either 13/9 or 24/20. They put White on the
bar, giving him bad sixes. Playing 13/9 has the advantage of unstacking both stacked points, while
playing 24/20 starts the best anchor. Fighting for the 3-point isn’t a great play, just one that’s less
bad than the alternatives here.

Rollouts indicate that 13/9 is better than 24/20 by a tiny amount, but let’s not quibble; we’ll score
either play as correct.

Problem 2: Black to play 3-2

 White – Pips 152

Black – Pips 163

Black to Play 3-2

Once your opponent has made an advanced anchor in the opening, splitting and going for an anchor
yourself becomes top priority. Which split? Playing 24/21 is riskier, coming under fire from three
builders. On the other hand, it starts a better anchor, which balances out the extra builder to a
certain extent. But the real clue comes from our answer to Problem 1. There we saw that we don’t
want a checker on the 10-point if our opponent has split with a two. Here our opponent already has
a checker on his 10-point, so let’s use our split to make him uncomfortable with 24/22!

If we use our two to split, the right three must be 13/10, unstacking and duplicating our opponent’s
threes. Slotting with 6/3 isn’t very effective because we won’t break the 8-point to cover.

Problem 3: Black to play 5-1

 White – Pips 149

Black – Pips 162

Black to Play 5-1

Apparently unconstructive numbers in the very early game can often be put to good use with a little
extra thought. Remember that when your opponent has no board, you can get away with plays that
you couldn’t attempt later in the game.

The simple-minded approach here leads you to plays like 21/15 or 21/16 11/10, which seem to be
relatively safe. Both however, are blunders! Instead, Black should look at a few key features of the
position: (1) White has no board, (2) Black will have to leave some blots no matter how he plays,
(3) his 6-point still has an ugly stack, and (4) duplication is a powerful idea.

Put them all together and the play 21/16 6/5! Should jump out. White’s fours are strong but nothing
else does much, and if White doesn’t hit all Black’s numbers are working.

Problem 4: Black to play 2-1

 White – Pips 162

Black – Pips 160

Black to Play 2-1

The early game position after making your bar-point with a 6-1 is especially awkward. You still
have the big stack on the 6-point, while the 7-point and 8-point are both stripped. If you try to
preserve the position as it stands, you may be caught between the need to bring down builders from
the midpoint and the need to split and move the back checkers.

A better approach is to take any opportunity to create a better position by making inner points, even
at the cost of a shot. Here’s an extreme example of that idea. The obvious 13/11 24/23 is only third-
best here. Better is 6/3*, unstacking and attacking. But best of all is 7/5 6/5! Black unstacks and
builds his best point, even at the cost of 25 shots. If White misses Black is in charge, but even when
White hits Black has plenty of compensation in the form of a better board and a more playable
position.

Problem 5: Black to play 3-1

 White – Pips 157

Black – Pips 157

Black to Play 3-1

After the discussion of Problem 4, you might well conclude that Problem 5 is easy; if making the 5-
point in the face of a double shot was right in Problem 4, then surely making the 5-point in Problem
5, in the face of only a single shot, must be correct. But backgammon is a tough game, and in fact
that play isn’t right. Here Black should keep the 8-point and just play 13/10 11/10. Why?

There are four main reasons which all bear on the solution.

(1) White is now anchored on Black’s 3-point. Black’s 8-point now has some real blocking value,
more than it had in Problem 4.

(2) In Problem 4, Black had only one blot after making his 5-point. If he makes the 5-point in this
position, however, he’s got four blots around the board. While most of them are hard to attack for
the moment, there will still be sequences where the blots are a liability.

(3) The alternatives to making the 5-point in Position 4 were a loose hit and a modest build-and-
split play. The alternative here is actually making a point. While it’s not a blocking point, the 10-
point bears on both the 4-point and 5-point in complete safety. It’s a very good asset for now, much
more than just having some useful blots.

(4) by locking down the 10-point, Black is now completely secure on his side of the board, meaning
he can devote all his energy to escaping his back checkers. After 8/5 6/5, Black’s game is in flux on
both sides, and the looseness of his position may stop him from making more progress.

No one of these four reasons is decisive in itself, but the combination of the four indicates that
making the 10-point is best by a solid margin.
2017 Boston Quiz Contest, Part 2
Last time we looked at Quiz positions 1 through 5 from the quiz contest at last month’s Boston
Open. This week we’ll move on and look at positions 6 through 10.
Good luck!

Problem 6: Black to play 6-5

White – Pips 142

Black – Pips 153

Black to Play 6-5

With his rear checker blocked, Black only needs to arrange his builders in the most efficient way for
next turn. Playing 14/8 11/6 is totally safe but too stacked. Playing 14/8 13/8 is even more stacked
and not even totally safe! The best play is 11/5 14/9, which gives an excellent distribution at the
cost of only four shots.

Problem 7: Black to play 6-5

 White – Pips 129

Black – Pips 124

Black to Play 6-5

Things change a little when Black doesn’t have any checkers back. With all his checkers escaped
and a 16 pip lead in the race after moving, even leaving only two shots with the pretty-looking 11/5
13/8 is too risky if a good alternative is available. A better play is 11/5 9/4, which is totally safe and
has the added merit of giving Black more pointing numbers, which boost his gammon chances a bit.

Note that in a match at DMP, the priming play (11/5 13/8) would be slightly better.

Problem 8: Black to play 4-2

White – Pips 145

Black – Pips 156

Black to Play 4-2
Black can enter from the bar on either the 21-point or the 23-point. Entering on the 21-point gives
him a couple of ways to safety a blot, and also gives him a better chance to escape his back checker
at some point. But is safety what Black wants here? Let’s look a little deeper.

How’s the race? Black trails by 11 before the roll. After he plays his 4-2, he’ll trail by six. That’s
not indicative one way or the other, so let’s look elsewhere.

The odd feature of the position is White’s huge stack on his 8-point, probably the result of an
awkward 5-5 earlier. The easiest way for White to repair this flaw is to dump checkers into his inner
board and cover them later. Black can counter that plan by entering on the 23-point and guarding
White’s inner board.

If Black wants to play Bar/23, then what’s his four? Stacking with 10/6 is silly given White’s weak
board, so how about 15/11? That looks a little loose with White’s rear checkers already split, but
notice that many of White’s hits contain a six (6-1, 6-2, 6-3, and 6-4). White would like to use sixes
to hit loose on his 2-point, both to attack and to push Black forward in his board. So 15/11 benefits
from a lot of duplication.

Given his racing deficit, of course, getting a second checker hit isn’t a disaster for Black, and
playing Bar/23 15/11 puts all his checkers where they’d like to be. It’s the right play.

Problem 9: Black to play 3-3

White – Pips 120

Black – Pips 136

Black to Play 3-3

Bar/22 is forced, after which Black has a nice safe play available: 12/6 and 8/5. It leaves him with a
good distribution of builders and no problems playing his next roll. That’s an easy play to make if
you’re playing quickly.

However, Black has a better move available: Bar/22, followed by switching with 4/1*(2) and finally
adding a builder with 8/5. When you throw a small-to-medium double and your opponent has one
or more loose men in your inner board, be sure to check out the switching plays. They take away
part of your opponent’s roll, give him some awkward shots from the bar, and set up a possible blitz.
The switch is especially strong when your opponent has a combination of stacks and stripped
points, since being able to play only half his roll may be awkward. In this position Black doesn’t
have a double if White fans, but he’s then only one good sequence away from a cube.

Problem 10: Black to play 3-1

White – Pips 126

Black – Pips 145

Black to Play 3-1

Black can’t move his back checker with a 3-1, but since he’ll trail by 15 in the race after he plays,
the checker is fine just where it is. What Black needs to decide here is the best way to keep building
his inner board while awaiting developments.

Beginners tend to play 8/4 here. It’s safe and starts the next point in the board. But it has two
drawbacks which outweigh any safety: the 8-point becomes stripped, and the midpoint remains with
a huge stack. Much better is 13/10 6/5, which unstacks the midpoint and keeps a spare on the 8-
point. If Black doesn’t get hit almost all his rolls play well. If he does get hit he should have plenty
of return shots, and even if he doesn’t hit anything he may be able to anchor and cause White more
problems down the road.

When plays like this start to look obvious, it’s a sign that you’re making the transition from an
intermediate to an open player.

2017 Boston Quiz Contest, Part 3

So far we’ve looked at Quiz positions 1 through 10 from the quiz contest at last month’s Boston
Open. In this post you can test yourself on positions 11 through 15.
Stay focused!

Problem 11: Black to play 6-5

White – Pips 145

Black – Pips 137

Black to Play 6-5

Here’s an easy one.

When you’re in a holding position, the basic rule is to keep your spares moving from the back to the
front. If you leave a spare on a rear point and then can’t move the spare safely later, you might have
to give up an intermediate point that you’d rather keep.

In this position Black’s rearmost spare is the checker on his 13-point, so that’s the checker he wants
to move if he can. The right play is just 13/2. Playing 8/2 6/1, on the other hand, leaves the 8-point
stripped and might cause Black to have to abandon the point prematurely.

Problem 12: Black to play 6-2

 White – Pips 117

Black – Pips 138

Black to Play 6-2

Black trails by 21 pips before the roll. He can hit and get almost all the racing deficit back in one
fell swoop, and that’s what he should do: 20/12* is the move.

While the play abandons the anchor and leaves plenty of blots around, the upside is too great to
ignore. Black has the better board and lots of builders to improve it quickly, while White’s 4s, 5s,
and 6s all play badly from the bar. Yes, a small double by White could be devastating, but that’s
backgammon. White’s inner board is too weak for Black to play tight.

Problem 13: Black to play 6-1

White – Pips 147

Black – Pips 130

Black to Play 6-1
When deciding on a safe play or a somewhat risky play, look at your opponent’s inner board first.
That will usually give you most of the information you need.

Here Black already leads by 17 pips (130-147) and once he plays his 6-1 he’ll bump his lead up to
24. Moreover, he has a safe and reasonably constructive play available: the simple 15/8, putting a
new builder in position.

But White’s inner board is very weak right now – no new points, a big stack on the 6-point (and the
8-point as well) and another loose blot on his 9-point. Clearly White won’t be enthusiastic about
hitting some indirect shot that might be lying around next turn.

Does Black have a constructive play that only leaves indirect shots? Yes – he can play 13/7 13/12!
He unstacks the big midpoint stack that might spell trouble down the road while leaving two
indirect shots. (After that play, White should only hit with 5-5; hitting with any other number would
be a blunder.)

Problem 14: Black to play 6-3

White – Pips 136

Black – Pips 110

Black to Play 6-3

Black and White are locked in a mutual holding game. Black will lead by 35 pips after he plays his
roll, making him a solid favorite. Still, he has problems to solve. The 6-3 roll gives him a choice
between making his 1-point (7/1 4/1) or clearing the 10-point (10/7 10/4). What’s right?

Many players would make their ace-point here, keeping the 10-point to maintain communication
between the checkers on the 15-point and the home board. Here, however, the “communication” is
an illusion. Black needs to throw doubles to clear the 15-point without leaving a shot, whether he
owns the 10-point or not. It’s true that keeping the 10-point will give Black some numbers (fives)
that let him clear the 15-point while leaving only a single shot. This advantage is balanced,
however, by the need to clear the 10-point later.
The right idea here just clearing the 10-point with 10/7 10/4, abandoning the communication and
buying as much time as possible to throw a set of doubles. After clearing the 10-point Black will
have plenty of checkers to move while he waits for the set that brings him home.

Problem 15: Black to play 4-4

White – Pips 152

Black – Pips 146

Black to Play 4-4

Double-fours is a great shot but, like most doubles in the early part of the game, it’s easy to
misplay.

Both 13/9(2) 13/5 or 13/9(2) 8/4(2) create very good structures. But Black can do better by focusing
on the key element in the position — White’s blot on his 5-point. If White can cover that blot, he’s
got a reasonable position. If Black can hit the blot, White’s toast. Since Black can’t hit this turn, he
has to look at a tempo play that will keep White busy so Black has another shot next turn.

With that in mind, Black’s play becomes clear: 8/4(2), strengthening the board, 6/2*, the tempo hit,
and finally 13/9, the best four available. White now needs ones, twos, and threes to enter and ones
and twos to cover, so Black has some duplication working. Finally, if White dances the tempo hit
could turn into a full-fledged blitz, and with the cube already turned gammons will be in the air.

2017 Boston Quiz Contest Part 4

So far we’ve looked at Quiz positions 1 through 15 from the quiz contest at February’s Boston
Open. In this post you can test yourself on positions 16 through 20.

Good luck!

Problem 16: Black to play 5-1

 White – Pips 150

Black – Pips 107

Black to Play 5-1

Black has a perfectly safe play available – 23/22 6/1. But he can’t play it, because he’s 49 pips
ahead after he plays his roll. In one or perhaps two rolls he’ll have to run into the outfield anyway,
and then White’s game will be much stronger because he’ll have released the spare checkers on
Black’s 5-point into the outfield.

With a huge race lead and a deteriorating position, you can’t try to play a holding game. Instead you
have to try to run before your opponent’s game gets better and yours gets worse. Hence the five is
clear: Black has to make his move with 23/18, then figure out the best ace.

He has two plausible aces: 4/3, giving no extra shots on his side of the board, or 8/7, giving White a
3-shot but preserving his 4-point board. To see which is right, consider these two features of the
position.

(1) A lot of hitting is about to happen. Black is trying to run his checkers into the outfield, and
White will be hitting pretty much any shot he sees, even if he has to leave shots in return. In a
slugfest, you need a good home board, which is a strong argument for keeping the 4-point and
playing 8/7.

(2) After Black moves 23/18, White’s best hitting number is a 3. Playing 8/7 duplicates threes.
True, White will hit with 20/17* rather than 10/7*, but the duplication reduces the cost of being hit
on the 17-point, since White had an acceptably good hit elsewhere.

Put those two ideas together, and it’s clear that 23/18 8/7 is the play.

Position 17: Black to play 3-2

 White – Pips 151

Black – Pips 138

Black to Play 3-2

“Points are good.”

“Stacking is bad.”

“Take small risks to improve your position.”

These are all good rules of thumb, which apply in many positions. Here are some others that are
also useful:

“Play safely to protect a big racing lead.”

“Your opponent’s inner board strength will tell you how aggressively to play.”

And finally, one more:

“Weight possible gains against possible losses when deciding how much risk to take.”

Now let’s look at Position 17. Black has stacks everywhere, and the only safe play (11/6) creates an
even bigger stack. He does however, have a play that unstacks and makes a new point – 13/11 6/3,
leaving only 12 shots. (13/11/ 13/10 leaves 18 shots – too many). What’s right?

First, let’s note that Black has one major asset in this position – his racing lead. After he plays his 3-
2, he’ll be up 18 pips. Other than that he doesn’t have much, so he’s got a very strong incentive to
protect that lead.

Next question: How risky, really, is 11/6? Sure, it’s ugly as sin, but how likely is it to leave a shot
next turn? After all, the logic behind 13/11 6/3 is that Black is taking a small risk this turn to build a
position that will be safer down the road. Let’s compare 11/6 and 13/11 6/3 in terms of how likely
they are to get hit on both the first and second turn, assuming White can hold his position.
On the first turn, 11/6 is obviously totally safe, whereas 6/3 gets hit with 12/36 numbers (33%). A
clear safety advantage to 11/6, of course.

Now on to the second turn. After 11/6, Black will leave a shot with a total of 14 numbers (6-5, 6-3,
6-2, 5-4, 5-1, 3-1, and 2-1). Assuming White hits on average about 40% of the time, depending on
where Black’s blot ends up, White will get about 5.6 hits in 36 rolls, a bit under 16%.

How much safer is 13/11 6/3 on the second roll (assuming the blot got missed on the first roll)?

After 13/11 6/3, Black will leave a shot next turn (again, assuming White holds his position) with a
total of 19 (!) numbers: 6-5, 6-3, 6-2, 5-4, 5-1, 4-3, 4-2, 3-1, 1-1, 2-2, and 6-6.

Oops.

The ‘flexible’ play is not only riskier on the first roll, it’s also riskier on the second roll if White
missed the shot on the first roll! That’s not what you might expect, but it makes sense when you
think about it. Black has to cover the blot with half his roll, then look around for how to play the
other half of his roll. He won’t have a lot of choices there, so it’s not so surprising that he’ll have to
leave a lot of shots. (In addition, the existing blot prevents some of his doubles from playing safely,
whereas doubles are always safe if you didn’t have any blots to start with.)

Under the circumstances, 11/6 starts to look better and better. It’s actually much safer than it first
appears, and that’s enough to make it the right play.

Problem 18: Black to play 6-1

White – Pips 161

Black – Pips 115

Black to Play 6-1

When you have the best possible 5-point board (2-point to 6-point) and your opponent has a blot on
your ace-point, you nearly always want to hit unless your opponent has a very strong board or
prime. Most players know to hit when they have a cover number or two already in place. In fact,
you should hit even if you’re not likely to cover for two or three turns.

In Position 18, for instance, the right play is 7/1* 21/20, not 13/7 21/20. Simply making a prime
gives White a direct shot to make an ace-point game. He may make that anyway, but at least you’ve
given yourself a better chance at a closeout.

Look at it another way: if you knew White wasn’t going to throw an ace next turn (which he’s 70%
not to do) which position would you rather have? Clearly you’d want the position with two men on
the bar. So go for it now. Hitting with 7/1* actually wins more gammons and more games.

Problem 19: Black to play 5-4

White – Pips 111

Black – Pips 77
Black to Play 5-4

Most players would make the right play here but for the wrong reason.

The best play is 18/14 9/4, giving White a 5-4 shot to hit (which is not necessarily winning for him
because of his weak board). This looks like a sort of ‘pay now or later’ problem, giving one indirect
shot now to avoid leaving a direct shot clearing the 9-point later on.

But that’s not what’s happening here. At double match point, for instance, 18/9 is actually correct!
(By a tiny bit.) The idea of playing 9/4 now is that Black is playing for the gammon and wants to
start his bearoff with plenty of spares on the 6-point and 4-point. Sticking a spare on the 4-point and
keeping his two other checkers on different points gives him the best chance to keep those spares on
his 4-point and 6-point.

After 18/9, Black’s fours are blocked, so as he tries to clear the 9-point he may have to put spares
on his low points. If White enters on the first or second turn, Black may have to move more
checkers down to his low points as he waits to clear the 9.
The net effect is that keeping his outfield checkers split boosts Black’s gammon chances by more
than 5%, while costing him a little more than 0.5% in losses. So go for the gammon, but be aware
that safety isn’t the issue here.

Problem 20: Black to play 2-2

White – Pips 104

Black – Pips 82
Black to Play 2-2

Bearing in can be tricky.

Black can clear his 8-point right now with 8/6(3) 6/4, but that leaves a lot of men (eight) on the 6-
point. Combined with the gaps on the 1-point and 3-point, Black might have trouble playing 5s and
3s in the future.

Looking more carefully, 65, 54, and 52 would leave shots, as well as 63, 43, and 32. That’s 12 blot
numbers out of 36 rolls. There must be a better play.

Since Black rolled a double, he can look at switching with 5/3(2), then either 6/4(2) or 8/4. By
making the 3-point, Black has a landing spot for his 5s and 3s, as well as all his other numbers. So
the switch must be for sure, then Black just needs to decide on his last two deuces.

The race is pretty much a lock (Black’s up 30 after the roll), so he has no need to rush a checker in
unless it’s actually the safest play. Notice that if Black plays 8/4 with the last two deuces and White
rolls a five, Black would leave a direct shot with 61 or 63. He can avoid that sequence by keeping a
spare on the 8, so he should play 6/4(2) with his last two deuces and be pretty safe for the next turn.
At most White will get an indirect shot.

Some positions are like this — you can’t rely on general principles. You just have to get down in
the weeds and see what’s actually happening.
Backgammon Lesson 17: Bearing Off to Win a
Gammon

Consider the following problem, which arose in a recent chouette:

White – Pips 118

Black – Pips 60
Black to Play 4-4

As the captain, I had a 4-4 to play. Three plays were possible.

1. 9/5 6/2(2) 4/off. This is clearly the safest play. Black is even with spares on the high point, and
White has the opportunity to enter with a 6.

2. 9/1 5/1 4/off. Legal, but this seemed the clearly worst of the three. Black is stripped, and so more
likely to leave a shot than with choice (1), while the two extra checkers on the ace-point clearly
reduce his gammon chances.

3. 9/5 4/off(3). The gusto play, going full blast for the gammon, at the cost of leaving more potential
shots than choice (1) or choice (2).

This is a problem of balancing extra losing chances with extra gammon chances. In backgammon,
it’s correct to trade extra losing chances for extra gammon chances if the number of extra gammons
is at least twice the number of extra losses. To see why this is so, remember that winning a simple
game will net you two points. Winning a gammon increases your net gain to four points, (a gain of
two points), but turning a win into a loss takes you from plus-two to minus-two, a net loss of four
points. When you turn a win into a loss, you lose twice as much as you gain when you turn a win
into a gammon, so you must win at least twice as many gammons before the aggressive play
(whatever that may be) becomes correct.

Over the board, my teammates and I could only guess at these numbers. Clearly, our losing chances
are small in any case. After play (1), they’re almost non-existent. Even after the risky play, (3), we
might easily have six or seven men off when we get hit, so a hit won’t necessarily win for White.
On the other hand, White needs 13 crossovers to get off the gammon. [This is computed by seeing
that the White checker on the bar needs four crossovers to enter and reach White’s home board, the
checkers on the midpoint add another four, and the checkers on White’s 7-point and 8-point require
another four, plus a final crossover to actually bear off a checker, a total of 13.] This implies that
our gammon chances are fairly good, certainly in the 40%-50% range, so extra checkers off should
add to those chances substantially. (We thought.) So we took three men off. We eventually won the
game but not the gammon.

Was our play correct? Extreme Gammon’s rollouts actually yield an interesting answer and some
intriguing insights.

First, let’s take a look at our losing chances after all three plays. As you might expect, they are low.
But let’s see just how low.

Losing Chances after Each Play:

After Play (1) 9/5 6/2(2) 4/off: 1.0%

After Play (2) 9/1 5/1 4/off: 3.0%

After Play (3) 9/5 4/off(3): 5.2%

No real surprises here. The “safe” play of clearing the 6-point and staying even on top is indeed the
safest. The unusual play of dumping the spares on the ace-point while keeping a closed board is
certainly riskier, raising the losing chances from 1% to 3%. And the bold play of taking off three
checkers while leaving a gap is riskiest of all, with losing chances over 5%.

These numbers, however, don’t answer the problem for us. To get an answer, we need to combine
these numbers with the gammon chances for each play. And here some real surprises await.

Gammon Chances after Each Play:

After Play (1) 9/5 6/2(2) 4/off: 45.3%

After Play (2) 9/1 5/1 4/off: 54.4%

After Play (3) 9/5 4/off(3): 48.7%

As you can see, Black is winning a gammon roughly half the time in this position. The safe play (1)
wins the fewest gammons, which is not unexpected. But the “aggressive” play (3) isn’t really so
aggressive after all. It wins only slightly more gammons than play (1). The real surprise is the
awkward-looking play of putting both spares on the ace-point (2), which wins far more gammons
than either of the other two plays!
It’s not hard, given these figures, to see what the right play is. Compared to the safe play (1), the
aggressive play (3) wins 3.4% more gammons at a cost of 4.2% more losses. Since we need to see
twice as many extra gammons as extra losses to make an aggressive play superior, play (3) is
clearly inferior to play (1). The two checkers that Black bears off are more than offset by the
awkwardness of the open 4-point, which requires Black to waste full rolls and half rolls later on to
avoid leaving a shot.

However, the awkward-looking play (2) is somehow the real deal. It wins 9.1% more gammons
than (1), at a cost of just 2% more losses. The 2-to-1 ratio of extra gammons to extra losses is easily
satisfied, so (2) is better than (1), and (1), as we saw, was better than (3).

Now we know the proper ranking of our three plays, but how can we explain it succinctly? The
lesson of this problem (and it’s a very counter-intuitive lesson) is this: the real strength of play (2) is
that it keeps a 6-point board, even if only for one turn. When White can enter on the first turn in
plays (1) and (3), he eliminates much of the gammon danger. Keeping White on the bar, even at the
cost of an awkward position with both spares on the ace-point, is worth it. But this is a very hard
play to find, and few players would find the right play in this sort of position.

Backgammon Lesson 18 – Consider All

Possibilities

A lot of backgammon positions are pretty simple: the right play is either forced or completely
obvious. Many others involve a clear decision between two very different alternatives. These
problems may be hard to solve, but at least the choices are clear.

Some positions, however, involve a lot of possible plays, all of which are somewhat reasonable.
These positions can be very tricky, and one of the dangers is overlooking the best play altogether
while sorting through the wealth of possibilities. Be alert, and try to enumerate all the plays before
starting to rank them.
 White – Pips 89

Black – Pips 123

Black to Play 5-3

Here’s a choppy-looking prime against prime game, in which neither side is particularly satisfied
with their position. White’s not likely to fill in his 4-point, while Black has big gaps on his 4-point
and 5-point. 53 is not an especially good shot, although Black can try a few things. What to do?

Let’s consider some of the plays that come to mind.

> 24/16 is a really bad idea. Black’s 34 pips down in the race, so trying to disengage isn’t a super
plan to begin with. And suddenly, some really bad shots become great attacking numbers – 51, 65
and the like. Throw this idea out.

> 9/6 8/3 is safe, but that’s about all. Black’s still way behind in the race, and now his front game
looks like it will never come together.

> 9/4 7/4 is better – Black swaps the 7-point for the more valuable 4-point, and his position
becomes a lot less awkward. But filling in the 5-point or the 7-point is now quite unlikely, so
Black’s game is probably as good as it gets.

If Black stops his analysis here, he’ll likely play 9/4 7/4. Not bad, but he won’t even have
considered the best play!

The right idea is 9/4 8/5, the hyper-aggressive double-slot! Black seizes his last chance to get a
really strong position. Suddenly the pressure is on White to throw a three or a four immediately. If
not, Black’s position will suddenly improve to a 5-prime or even a 6-prime, and White will be
squeezed and crumbling. Even if White does hit, Black now has a pretty-good ace-point game with
reasonable timing. The double-slot loses a few extra gammons, but picks up a new win for every
gammon it loses. It’s the clearly best play.
Backgammon Lesson 19 – The Tempo Hit

In backgammon, most hits are done for one of two reasons: to gain ground in the race, or to attack a
key point. A rarer, but still important use of the hit, is a defensive idea called the tempo play. Here
the plan is to prevent your opponent from using his whole roll to do something good. By hitting
(usually in your home board), you force him to spend half his roll coming in from the bar, so he’s
not in position to do something devastating elsewhere on the board.

Let’s first take a look at a common situation where beginners make a tempo hit incorrectly.

White – Pips 158

Black – Pips 167

Black to Play 5-2

White won the opening roll with a 6-3 and ran a back checker to the outfield. Black now rolls an
innocuous 5-2. Many beginners will go astray here and play 6/1* 24/22. Since it’s a hit, this looks
somewhat active and aggressive, but it actually doesn’t accomplish anything. White had no
powerful threats that Black needed to stop, and the checker left on the one-point is both
immediately vulnerable and a long-term liability. A better play is the simple 24/22 13/8. It does a
few good things (unstacks the midpoint, adds another builder to the 8-point, and splits the back
checkers), but most important, it doesn’t do any bad things.

Now let’s look at a very different situation.

 White – Pips 124

Black – Pips 109

Black to Play 4-2

Black is ahead in the race and hence has less timing than White. As a result Black will actually have
to escape White’s prime: waiting for it to collapse is not an option. If Black is going to escape, he’ll
need to throw a two at some point, and – guess what – he’s just thrown one. So there’s a really
strong case for playing 23/21 with the deuce.

Once the checker gets to the 21-point, White will point on it or at the very least hit loose. Black
needs a diversion to keep the dogs at bay, and 5/1* fits the bill perfectly. It has an added bonus
(don’t miss this) of winning more gammons for Black than any other play. It’s true that shoving
what was a nice builder down to the ace-point weakens Black’s chances for a full prime, but
changing a priming game into a sudden blitz is often the right strategy, especially when neither side
has an anchor.

The difference between these two positions is simply the amount of immediate danger that Black
faces. You don’t like to hit loose deep in your home board, both because getting hit back is usually
costly, and because the checker can become a future liability even if it isn’t hit. So to make the hit
correct, you need to be facing very serious threats. In Position 2, White has those threats; in Position
1, he doesn’t.

Backgammon Lesson 20 – Evaluating Early

Doubles
When contemplating a middle game double, don’t make the mistake of looking only at your
position. Remember to look just as carefully at the weaknesses in your opponent’s position. It may
be his weakness, rather than your strength, that gives you a good double.
 White – Pips 163 (+34)

Black – Pips 129 (-34)

Problem 1. Black on roll. Cube action?

Problem 1 is a perfect case in point. Black has escaped his back checkers and built a little structure,
while White has grabbed Black’s 5-point. In most positions of this general type, Black’s advantages
wouldn’t even add up to an initial double. But now look at White’s position:

> His back men are split and vulnerable to potential blitzing rolls like 66, 55, and 44, both now and
on subsequent rolls. If his two back checkers were anchored on the 23-point or the 22-point, the
position wouldn’t be a double.

> His front position is still chaotic and will be for a couple of turns. If he had a small 4-prime or
even a good board with, say, the 4-point and 5-point made, he’d have a threat to contain any
checker hit on the next couple of turns, and Black wouldn’t have a double.

But with both these weaknesses, White’s game is toothless enough so that Black has a very solid
double. White still has a clear take of course.
 White – Pips 159 (+28)

Black – Pips 131 (-28)

Problem 2. Black on roll. Cube action?

Black is off to a decent start in Problem 2. He’s got a good defensive anchor, while on the offensive
side he has – well – something. He’s got great points slotted, and next turn he might actually cover
one or two of them.

The key to the position is not Black’s game but White’s. While Black has something, White has a
bit less than nothing. No points, just blots. Something versus nothing is a good prescription for an
early double, especially if the defender doesn’t have an anchor. Without an anchor, there will
always be variations where things go terribly wrong and Black’s messy position turns into a
powerful blitz. Did you stop to guess what Black’s cubeless gammon chances were in Problem 2? If
you did, did you realize they’re over 25%? Numbers like that almost always guarantee not just an
initial double, but a strong and mandatory initial double. Black’s checkers aren’t just passive slots.
They’re also potential attackers, which can be activated by a single good sequence. Couple that with
a rock-solid defensive anchor, and Black has a great double.

Clear take, of course. There are plenty of variations where things don’t go so well and White
recovers quickly.

Backgammon Lesson 21: Fighting Stacked

Positions
One common dilemma that players routinely face is that of hitting a tasty blot or making a strong
blocking point. In very general terms, hitting the blot is most likely right. Hitting both gains ground
in the race and prevents your opponent from improving his structure, which in normal positions will
outweigh other choices.
As your opponent’s position becomes stacked and stripped, however, hitting blots recedes in
importance while building blocking points grows. The reason has to do with timing. A stacked
position can be repaired, but typically some time is required. A game with hitting and recirculating
of checkers provides exactly that sort of time. A prime, however, tends to shorten the game, as a
single bad roll can destroy the weaker player’s position in an instant. By building a prime, the
aggressor can accelerate the crisis point to his advantage.

Consider the military analogy. Two armies meet in the field. One is in peak form, the other consists
of raw recruits. Proper strategy for the untrained army is to give ground gradually, fighting only
small skirmishes while protecting the main body of troops until they are fully prepared for battle.
Proper strategy for the superior side is to pursue vigorously and try to force a full-scale engagement
at the first opportunity. (This was more or less the scenario for Washington’s successful retreat from
New York in 1776.)

White – Pips 164 (-3)

Black – Pips 167 (+3)

Problem 1. Black to play 3-1.

Problem 1 shows the position after White slots with an opening 21. With a follow-up of 31, Black
can hit or make his own 5-point. As has been known for a long time, hitting is right by a wide
margin. It gives Black a clear edge by gaining 20 pips in the race. After making the 5-point instead,
the game is equal, since White will follow by making his own 5-point.
 White – Pips 141 (-13)

Black – Pips 154 (+13)

Problem 2. Black to play 3-1.

At first glance this looks like a similar position, and in the actual game, in fact, Black played 24/20*
without much thought. But it’s actually a serious error. After 8/5 6/5 White is horribly squeezed,
and the combination of his stack on the 6-point and his stripped midpoint tears his position apart
very quickly. Take a look at how rolls like 65, 63, 61, 42, and 54 play, and you can see how
allowing White to move seals his doom.

Note that routinely counting the race could mislead Black into the wrong play. Black trails in the
race before the roll, 154-141. Many players would read that as a strong argument for hitting. But
seeing how upcoming rolls play provides an even stronger argument for not hitting.
 White – Pips 123 (-30)

Black – Pips 153 (+30)

Problem 3. Black to play 6-1.

Another illustration of the same theme. The right play is to make the 5-point while leaving the blot
on the midpoint alone, putting White in a quick and powerful squeeze. Playing 13/12* 13/7, by
contrast, gives Black not much of anything. White will enter and anchor or enter and float into the
outfield. If Black has to start a hitting contest, White’s better board will be a big asset. In fact, after
hitting, Black will be praying he can make his 5-point as soon as possible. Better, then, to just make
it now.

Backgammon Lesson 22 – Evaluating

Candidate Plays
While many plays in backgammon are virtually forced, other situations may leave you with five or
more reasonable alternatives. This is especially true of doubles, where the number of possibilities
may be even higher.

In such situations, you need a systematic approach to finding the best play. Most players react
haphazardly in these situations. They look for a good play, think about it for a few moments, and
only look for a second or third play if the first play doesn’t look appealing. If the second play
doesn’t look good after a moment or two, they may bounce back to their first play, or cast around
for another. The result is a chaotic decision process that may well overlook the best play.

A better approach is to spend a little time at the beginning to list, in your head, all the candidate
moves: those moves that are at least plausible. Only after you’re sure that you’ve listed all the
candidates do you proceed with the process of winnowing the list. In this way you can be sure that
you’ve at least seen the best play. Remember: If you don’t see a play, you can’t make it.
 White – Pips 156 (+0)

Black – Pips 156 (+0)

Black to Play 4-2

Black has so many possibilities here that our first job is just to list the candidate plays. So let’s see
what they might be.

First, we have our old standbys, 8/4 6/4, making the 4-point, and 24/20 22/20, making the 20-point.
We also have the plays where Black hits on the 5-point and follows with one of several reasonable
deuces: 22/20, 24/22, or 13/11. Finally, Black can elect to make the 9-point and play either 24/22 or
22/20. That’s a total of seven plausible candidates. Now let’s use what we know about the position
(and backgammon in general) to try and prune the list.

* 13/9 22/20 – Splitting the back checkers always involves some risk. Your goal is to improve the
connectivity of your checkers and prepare to escape the back men. You’re willing to pay some price
for connecting your men, but the price mustn’t be too high. The more builders White has in the
general area of your back men, the higher the price of leaving your men loose. Here White has eight
active attackers bearing on Black’s rear blots: three on the 6-point, plus all the men in the outer
board. So 24/22 is going to dominate 22/20 when that’s the choice of deuce. Shifting with 13/9
22/20 thus gets eliminated.

* 9/5* 22/20 – This play gets eliminated because a loose hit on the 5-point, while useful, is
thoroughly dominated by plays that make a great point.

* 9/5* 13/11 – The checker on the 11-point doesn’t add enough cover numbers to justify stripping
the midpoint and leaving four blots around the board. “Too loose, Lautrec”, as the late Chuck
Papazian was fond of saying.

* 9/5* 24/22 – Not a bad play, since it fights for the 5-point and leaves no extra blots around. Black
is likely to get hit back, however, while the 22-point could become a trap.
Even though we’ve eliminated these four, choosing among the remaining three is still a tough
decision. Here’s a summary of their strengths and weaknesses.

* 13/9 24/22 – Reasonable, since it leaves no blots and makes two points. The problem here is that
the midpoint is stripped, so Black’s upcoming sixes and fives could be quite awkward.

* 8/4 6/4 – This makes a nice point and smooths out Black’s distribution. Of all the choices, it gets
the most work out of Black’s checkers. If White couldn’t move, this would rank very high on the
efficiency scale. Unfortunately, White can move, and that’s the problem. He has plenty of builders
and lots of targets. Too dangerous.

* 24/20 22/20 – Defensive, but the play leaves a very nicely balanced position. Black secures the
best anchor and can’t be blocked in the future. The spare on the midpoint increases his flexibility.
Best of all, the cost of being hit with a four is minimized since fours would make White’s 20-point
anyway. Although making the 20-point with a 42 is occasionally too passive, here it offers the best
chances compared to the alternatives.

Backgammon Lesson 23 – Playing Efficiently

White – Pips 137 (-13)

Black – Pips 150 (+13)

Black to Play 4-1

Here’s a problem of a familiar sort. Black has been steadily building his front position, while White
has tossed in a 5-3 and a 6-5. White’s last roll of 6-5 completes the escape of his back checkers, but
leaves him with a huge stack on his midpoint. Now that White has escaped entirely, Black has to
leave his front position alone and start mobilizing the back men. He has two choices: 24/20 11/10,
or 24/23 13/9. (24/23 11/7 is all right as well, but 13/9 yields a slightly more active distribution.)
Which is best?
Years ago, most strong players would have played 24/20 in a shot. White must start moving the
checkers on the midpoint, and this play guards the outer board. It also prepares to anchor on the 20-
point, which is key since the race isn’t hopeless yet (Black trails by 8 after the roll.) And the play
has no obvious downside. True, there’s nothing really wrong with 24/23, but the play doesn’t guard
the outer board and doesn’t prepare to make an anchor, so there’s no real reason to choose it. Or is
there?

The bots play 24/23 13/9. Rollouts support this choice and in fact indicate that plays involving
24/20 are not just mistakes, but blunders! How can we explain this?

Most middle game backgammon problems can be solved by resorting to a small set of relatively
simple ideas: if you can’t do something big like making points or hitting blots or building a prime,
try to arrange your checkers efficiently so that you’re preparing to do something good next turn at
minimum risk. Here playing 24/20 prepares to make the 20-point while guarding the outfield. At the
same time, White has only a handful of numbers that point on Black’s head. So 24/20 11/10 would
seem to fit the bill perfectly.

But there are a few positions that just aren’t that simple. Sometimes we actually have to consider
how our opponent’s rolls play. This sort of concrete analysis can yield some very surprising results.

In this case, the difference between 24/20 11/10 and 24/23 13/9 comes from three groups of swing
rolls.

* Playing 24/20 11/10 gains strongly after two of White’s replies: 5-4 and 4-2. White will play 13/8
13/9 with a 5-4 after either play, but splitting to the 20-point gets Black a direct shot instead of an
indirect. 4-2 is a little different. After 24/23. White will play 13/9 13/11 with a 4-2, yielding some
indirects. After 24/20, White will revert to making the 4-point, but Black will get a direct shot
again. In each case, the blot on the 20-point forces a direct shot, as the play was designed to do.

* Playing 24/23 gains modestly on the doubles. Black doesn’t get pointed on after 1-1, 3-3, and 4-4,
which is a solid plus. After the big doubles (6-6 and 5-5), the race goes in the crapper, so it’s an
advantage to be able to anchor back on the 23-point rather than up on the 20-point.

* The key non-doubles that favor 24/23 are 6-3, 6-2, 5-1, and 3-1. After 6-3, played 13/4 in either
case, Black gets a double shot rather than a single. After 6-2 and 5-1, Black gets a double shot
without being hit. And 3-1 obviously favors not being on the 20-point.

Other than these swing numbers, the remaining rolls are pretty much a wash. Splitting to the 20-
point may force White to alter his play, but without any real gain.

This is in essence a problem in efficiency. Splitting to the 23-point does as much work in getting a
shot as the more obvious 24/20, for less risk. But finding such a play over the board, for the right
reasons, would be extremely difficult. After all, no one is standing by your side ringing a bell to
alert you that this position doesn’t conform to general principles.

Backgammon Lesson 24 – Handling 6-Primes

A full six-prime is the most powerful formation in backgammon. A checker trapped behind a six-
point prime can’t escape. To win, the trapped player has to somehow force his opponent to break
his prime.
Although building a full prime is the strategic goal in many positions, we don’t actually see too
many six-primes over the board. Often, the mere threat of making a six-prime will force a double
and a drop. Although six-primes aren’t common, they are governed by their own set of strategic
principles. Let’s take a look at a few.

White – Pips 99 (-8)

Black – Pips 107 (+8)

Problem 1: Black to play 41.

I’ve given this position to all of my pupils over the years, and, despite its apparent simplicity, it’s
proven to be one of the most difficult. Black has a 41 to play. He can keep a stripped six-prime in
two different ways: by playing 6/5/1, not hitting, or 6/2*/1, hitting. Or he can avoid a stripped
position and create more spares by playing 9/5 9/8. What’s the right idea?

The trap here is breaking the 9-point. It’s an appealing play because it looks “flexible”. But
flexibility is one of those slippery concepts, like “duplication”, that’s easy to misuse if you forget
what it’s for. The purpose of flexibility is to produce a position that can result in a six-prime. Once
you actually have a six-prime, the main idea is not to continue to be flexible, but to maintain the
asset you’ve got. Rule: Don’t break a six-prime unless you absolutely have to.

The right idea in Problem 1 is to just keep the prime and make the 1-point. Both the hitting and non-
hitting plays have arguments in their favor, but the hitting play is a little better because it prevents
White from fighting for his 3-point, which sometimes has the effect of driving Black’s checker back
to White’s ace-point, making escape more difficult. By playing 6/2*/1, Black will mostly remain on
White’s 3-point, letting him escape with his first six.
 White – Pips 55 (-40)

Black – Pips 95 (+40)

Problem 2: Black to play 54.

Problem 2 is just a trickier-than-usual application of our rule. All the reasonable looking plays that
break the six-prime (making the 2-point, or clearing the 9-point) are inferior. Once you break up a
six-prime, you’ll always be an underdog to get it back. As long as you keep the prime, you’re
guaranteed to have it for at least one more roll, and perhaps longer. That’s a big advantage.

Here the right play is a little hard to find even if you know what you’re looking for. It’s just 6/1
6/2*. Black has gotten ahead of himself as he tried to roll his prime home, so this is an attempt to
recirculate his checkers while his prime holds. He’d like White to enter with an ace or a deuce.
While Black brings the checker around the board, he might be able to slot and cover his 3-point,
rolling his prime forward in an orderly fashion.

In the vast majority of positions, ruthlessly maintaining the six-prime is correct. Backgammon
wouldn’t be backgammon, however, if there weren’t a few exceptions to this rule. Mostly these
occur when the winning side can break his prime to attack, typically picking up some extra
gammons to compensate for the extra losing chances caused by a broken prime. Look at Problem 3:
 White – Pips 76 (-21)

Black – Pips 97 (+21)

Problem 3: Black to play 62.

The routine move to win the game is the straightforward 11/3, slotting the front of the prime and
preparing to expend it next turn. But Black can do a bit better by abandoning the pure priming plan
and playing for a blitz with 8/2 8/6! If White doesn’t anchor, Black will launch a strong attack next
turn, while keeping losing chances acceptably small. (8/2 6/4 and 8/2 11/9 are also fine. Making the
2-point and playing for a blitz is the key idea.)

Backgammon Lesson 25 – Bearing in Against

the Ace-Point
When bearing in against an ace-point or other low anchor game, you generally have two goals in
mind. The first is safety; you want to create formations that are less likely to leave blots as you bear
off. The second is winning a gammon; you’d like to maximize your gammon chances if you can.

It’s usually good practice to look at the gammon chances first. If your gammon chances are either
very large or very small, then it’s not likely that any play you make will affect them enough to
matter. In those situations, you just make the long-run safe play, whatever that might be. But if the
gammon is up for grabs (which in practice means gammon chances in the 15% to 40% range) then
you may need to look for riskier plays which win more gammons at the cost of some extra losing
chances. Typically, these plays involve piling checkers on the 6-point and 5-point, hoping to hold
the prime as long as possible, or bearing off checkers rather than clearing a point.
 White – Pips 177 (+101)

Black – Pips 76 (-101)

Black to Play 5-1

So what’s happening in this position? Here it’s pretty obvious that Black is going to win a gammon
unless he gets hit. White has one checker to enter from the bar, then four checkers to extract from
the ace-point, and several checkers in the outfield as well. In total, White needs 20 crossovers to get
his checkers home, even after he manages to enter. Any reasonable play leaves Black with gammon
chances in the 58% to 60% range, which is so large that Black can forget about the gammon as an
issue and just concentrate on safety. So now we can ask the interesting question: What’s the long-
run safest play?

When playing strictly for safety, Black has four goals. Here they are, arranged in order of
importance:

(1) Don’t volunteer shots. Here this simply means that Black won’t slot the 7-point with his ace.
Giving White even a single indirect from the bar means giving him an extra 5.5% to hit, which
could easily be a game-winner.

(2) Try to ensure that 6-6 and 5-5 don’t leave shots. This won’t always be possible, and even when
it is possible you may decide to leave one of these numbers in order to secure better distribution.

(3) Strip the 6-point for quick clearance later. In general, you want to place your spare checkers on
the 3, 4, and 5-points, preparing to clear the 6-point when you get all your men in.

(4) Avoid phantom interior gaps. A real interior gap occurs when an interior point like the 3-point
or 4-point is actually open when the bearoff starts. Interior gaps are very weak and those formations
will leave many more shots than a completely made board. Less weak (but still a serious flaw) are
what I like to call “phantom gaps”, where you have all the points made but some points lack spares.
For example, if you have spares on the 6, 5, and 3-points, but no spare on the 4-point, you have a
phantom gap. Most players ignore this situation, but it’s actually more serious than it appears,
leading to awkward formations later and more shots.

Note that some phantom gaps are worse then others. The 2-point and the 5-point are the least
serious. The 2-point is so deep that it generally gets filled later, and the 5-point isn’t too important
because it’s sometimes an advantage to clear the 5-point before clearing the 6-point. The serious
phantom gaps occur on the 3-point and the 4-point.

If we now put all these ideas to work, we can find a clear winner with the 5-1, namely 8/3 6/5! All
criteria are met: no shot volunteered, 6-6 and 5-5 are both safe, the 6-point is stripped, and no
phantom gaps.

Other plays don’t work as well. 10/5 4/3 blots on both 6-6 and 5-5 and leaves a phantom gap on the
4-point. 10/5 6/5 doesn’t blot but also doesn’t put a spare on the 3-point, which may prove useful.

Backgammon Lesson 25 – Bearing in Against

the Ace-Point
When bearing in against an ace-point or other low anchor game, you generally have two goals in
mind. The first is safety; you want to create formations that are less likely to leave blots as you bear
off. The second is winning a gammon; you’d like to maximize your gammon chances if you can.

It’s usually good practice to look at the gammon chances first. If your gammon chances are either
very large or very small, then it’s not likely that any play you make will affect them enough to
matter. In those situations, you just make the long-run safe play, whatever that might be. But if the
gammon is up for grabs (which in practice means gammon chances in the 15% to 40% range) then
you may need to look for riskier plays which win more gammons at the cost of some extra losing
chances. Typically, these plays involve piling checkers on the 6-point and 5-point, hoping to hold
the prime as long as possible, or bearing off checkers rather than clearing a point.
 White – Pips 177 (+101)

Black – Pips 76 (-101)

Black to Play 5-1

So what’s happening in this position? Here it’s pretty obvious that Black is going to win a gammon
unless he gets hit. White has one checker to enter from the bar, then four checkers to extract from
the ace-point, and several checkers in the outfield as well. In total, White needs 20 crossovers to get
his checkers home, even after he manages to enter. Any reasonable play leaves Black with gammon
chances in the 58% to 60% range, which is so large that Black can forget about the gammon as an
issue and just concentrate on safety. So now we can ask the interesting question: What’s the long-
run safest play?

When playing strictly for safety, Black has four goals. Here they are, arranged in order of
importance:

(1) Don’t volunteer shots. Here this simply means that Black won’t slot the 7-point with his ace.
Giving White even a single indirect from the bar means giving him an extra 5.5% to hit, which
could easily be a game-winner.

(2) Try to ensure that 6-6 and 5-5 don’t leave shots. This won’t always be possible, and even when
it is possible you may decide to leave one of these numbers in order to secure better distribution.

(3) Strip the 6-point for quick clearance later. In general, you want to place your spare checkers on
the 3, 4, and 5-points, preparing to clear the 6-point when you get all your men in.

(4) Avoid phantom interior gaps. A real interior gap occurs when an interior point like the 3-point
or 4-point is actually open when the bearoff starts. Interior gaps are very weak and those formations
will leave many more shots than a completely made board. Less weak (but still a serious flaw) are
what I like to call “phantom gaps”, where you have all the points made but some points lack spares.
For example, if you have spares on the 6, 5, and 3-points, but no spare on the 4-point, you have a
phantom gap. Most players ignore this situation, but it’s actually more serious than it appears,
leading to awkward formations later and more shots.

Note that some phantom gaps are worse then others. The 2-point and the 5-point are the least
serious. The 2-point is so deep that it generally gets filled later, and the 5-point isn’t too important
because it’s sometimes an advantage to clear the 5-point before clearing the 6-point. The serious
phantom gaps occur on the 3-point and the 4-point.

If we now put all these ideas to work, we can find a clear winner with the 5-1, namely 8/3 6/5! All
criteria are met: no shot volunteered, 6-6 and 5-5 are both safe, the 6-point is stripped, and no
phantom gaps.

Other plays don’t work as well. 10/5 4/3 blots on both 6-6 and 5-5 and leaves a phantom gap on the
4-point. 10/5 6/5 doesn’t blot but also doesn’t put a spare on the 3-point, which may prove useful.

Backgammon Lesson 26: Leave Your Anchor

or Not?
White – Pips 105 (+6)

Black – Pips 99 (-6)

Black to Play 5-2

Here we see a position from the tail end of a mutual holding game. These positions typically arise
as follows:

> Both sides make an advanced anchor in the opening.

> Both sides bring down some builders from the midpoint and make a few blockading points.
> Neither side ever rolls a big double that would allow it to escape the back men safely.

> Both sides slowly dismantle their blocking points and build inner board points behind the
opponent’s anchor.

> Crunch time! Both sides start to face tricky decisions about when to leave the anchor.

In this position we’ve reached crunch time. Black has a small lead in the race (99 to 105 before the
roll), but it’s not hugely significant. If he runs with 21/14, White can attack the checker he leaves
behind on the 21-point. If he doesn’t run, he has to either dismantle his last blocking point (9/4 9/7)
or kill some builders in his inner board (6/1 3/1 or 6/1 4/2). At crunch time, you’re usually faced
with a bunch of unappealing choices, and you’re looking for the least-bad play. It’s dirty work, but
you have to do it.

Let’s list a few general guidelines for this sort of position, and see if they point us in any clear
direction. Sometimes they do, but often they don’t.

(1) If you can escape your back checkers cleanly, do it. This is the easiest case. If Black rolled 6-
5, for instance, it’s massively correct to play 21/15 21/16. Nothing else is close.

(2) Being way ahead in the race is an argument for running. This is a pretty obvious point, but
you need to be way ahead for this point to matter much. Here Black will lead by 13 pips if he runs –
not enough to be decisive.

(3) The better your opponent’s attacking position, the more you want to keep the anchor as
long as you can. The is usually the crucial factor. A “bad” attacking position has stacked points or a
weak inner board with blots. A “good” attacking position has many pointing numbers plus an
absence of inner board blots. Here White’s attacking position is very good. If Black runs, White has
10 immediate pointing numbers (4-3, 4-1, 3-1, 4-4, 3-3, 2-2, and 1-1) plus four more hits in the
outfield (6-3 and 5-4). In addition, all the rest of his ones, threes, and fours hit loose, putting Black
in an immediately critical position. White’s only bad numbers are 6-5, 6-2, and 5-2, and even these
aren’t disasters.

(4) Having useful waiting moves is a strong argument for staying. What makes this a good
problem is that Black is actually out of useful waiting moves. If he doesn’t run, he’s got to either
kill checkers or break his last outfield point, leaving a shot.

(5) If the only alternative is breaking your home board, running is likely to be right. This idea
is important but doesn’t come into play here.

(6) When in doubt, keep the anchor. If running is a mistake, it’s liable to be a big mistake.
Staying, however, is rarely a big error.

The key consideration here is (3). White’s attacking structure is ideal. He has no stacks and no blots
in his inner board. If Black doesn’t expose himself this turn, White will almost certainly have to
weaken his structure in some way next turn, after which Black can run to better effect. For now, we
have to discard 21/14.

We also have to discard 9/4 9/7. The 9-point is a great asset, leaving a blot is a bad idea, and leaving
a blot exposed to a deuce is especially bad since deuces don’t play well for White on his side.
With those two plays out of the way, we’re reduced to 6/1 3/1 or 6/1 4/2. Here 4/2 is the right
deuce, leaving the 3-point slotted. This gives Black a chance to make a 5-point board with a
subsequent six, and a stronger board will be a big asset in the later stages of this game.

A final point in favor of our play is that it holds off the cube! White has a strong double after 21/14
(but it’s still a take), a slightly correct double after 9/4 9/7, and no double after either 6/1 3/1 or 6/1
4/2.

Backgammon Lesson 27 – Which Point to

Make?
Here are two early game positions where Black doesn’t have much and White has an inner point
and some pressure.

Problem 1:

White – Pips 152 (-8)

Black – Pips 160 (+8)

Black to Play 3-1

Problem 2:
 White – Pips 150 (-10)

Black – Pips 160 (+10)

Black to Play 4-2

When Paul Magriel wrote his seminal book Backgammon in 1976, one chapter that was particularly
noteworthy was entitled “The Golden Point”. There he described the importance of the 5-point, both
for offensive and defensive purposes, and showed how making the 5-point was a key goal of early
game play.

Over the years, theory has never really changed much on this point. We’ve found some exceptions,
and certainly expanded our knowledge of when to break the 5-point later in the game, but the 5-
point remains a key opening goal in most positions.

The two examples show both a typical case and one of the exceptions. In each position, Black has a
chance to make a great point: either the offensive 5-point (Position 1) or the defensive 20-point
(Position 2). In each position, there are alternatives that seem to have strong merit. In Position 1,
Black’s rear checkers are under some pressure and seem to require a defensive anchor, which he
can grab with 24/21 22/21. In Position 2, Black can unstack and make his 4-point with 8/4 6/4.

In one of these positions, making the offensive or defensive 5-point is better. In the other it’s not.
Can you spot which is which?

In Position 1, making the 5-point smooths Black’s distribution and grabs the best point in his board,
a point which will be hard to get in the near future. Making the 21-point grabs a great anchor, but
leaves Black with many difficulties developing his front position. Right now Black’s rear checkers
aren’t under too much pressure, so he should leave them alone for now and just play 8/5 6/5.

In Position 2, Black can make the 20-point or the 4-point. The 4-point is a nice point, but it’s not as
valuable as the 5-point in Position 1. At the same time, Black’s 20-point has gone up in value now
that White has made his 4-point. If White hadn’t grabbed a new point, making the 20-point would
be stronger than making the 4-point. Here it’s stronger yet, and making the 4-point is actually a
blunder!

Are we done?

Well, not quite. I forgot to mention there might be a third play in Problem 2, better than either the 4-
point or the 20-point! It’s 24/22 13/9*, hitting and making the 22-point. Hitting a blot generally
takes second place to making the 5-point or 4-point, and making the 22-point also falls short of
making one of those two great points. But backgammon players have a reliable adage:

Doing two good things is usually better than doing one great thing.

That’s the case here. Neither the 22-point or the hit would be sufficient in themselves, but taken
together they trump making the 20-point.

Backgammon Lesson 28 – Which Point to

Make (2)
Problem 1.

White – Pips 156 (-6)

Black – Pips 162 (+6)

Black to Play 6-4
Problem 2.
 White – Pips 136 (-14)

Black – Pips 150 (+14)

Black to Play 6-4

These positions look very similar, but in fact Black should play 6-4 differently in each case. What
are the right plays and why?

In backgammon, a key skill is anticipating the flow of the game. You look at the board, you see
what each side is trying to do, and you formulate a plan that fits the requirements of the position.

Later in the game, this kind of anticipation is often easy. When your opponent has a five-point
prime, you know that priority number one is to get your back checkers to the edge of the prime and
anchor there. Priority number two will be to jump the prime if you roll a big number. Most of your
plays will be easy. You’ll have a tough decision only if your roll lets you do something crucial on
both sides of the board, like hopping the prime or building a prime of your own. But most of the
classic position types come with their own set of requirements, which are easy to understand.

Early game plays are more difficult, however, because the position generally hasn’t solidified, so
the flow of the game is harder to anticipate. Harder, however, doesn’t mean impossible. Let’s take a
look at these two positions and see what’s happening.

We’ll start with Problem 1. However Black plays his 6-4 this roll, it’s easy to see what his future
game plan looks like. On any roll where he can’t make a new blocking point, he’ll be splitting his
back men and trying to either build an anchor or run into the outfield. White will be trying to hit
those men, and Black will be trying to hit back. In many variations, a fair amount of hitting will
ensue. In a hitting contest, inner-board points are vital, to keep your opponent on the bar as much as
possible. So 10/4 8/4 is the right 6-4. By building inner points quickly, Black caters to the hitting
contest which is likely to start soon.

Now let’s look at Problem 2 and contrast the two situations. Here Black has a great anchor on the
18-point. He’s not leaving that point anytime soon, unless he rolls a nice double that lets him swing
around the board. Instead, he’ll go to work building a blockade and trying to trap White’s last
checker.

White, for his part, won’t be moving up much, unless he can jump into the outfield and hit a blot.
His proper game plan is to stay back with the last checker for a while, instead building his board in
preparation for a later hit. Both sides are waiting; neither side is looking to get hit. With fewer
hitting variations in the near future, Black needs a blockade and good distribution more than he
needs an inner point. So making the bar-point is his play now.

Backgammon Lesson 29 – Hit or Make the 20-

point?
We are in the very early part of the game and neither player has much structure. White has,
however, made his 4-point.

White – Pips 155 (-5)

Black – Pips 160 (+5)

Black to Play 4-2

Some players, new to the game and principally learning from books, get the impression that
advanced, creative backgammon requires leaving blots and shots at all opportunities. Not true.
While there are lots and lots of positions where weirdly aggressive plays are justified, there are
plenty of other positions where battening the hatches is the right idea. This position is a case in
point.

Black’s best play is to make an anchor with the ultra-safe 24/20 and 10/8, leaving no blots; the
runner-up play is 24/20 13/11, still making an anchor but leaving two outfield blots. The hitting
play 20/16* 24/22 is third-best by a wide margin.
This result will take many readers by surprise. “Why not hit and gain ground in the race? Looks
pretty safe. White is on the bar and I’ve gained 16 pips. Sure I don’t have any board yet, but White
isn’t very strong either.”

What’s wrong with this reasoning? Well, in actuality not very much. Hitting isn’t a bad play; Black
in fact improves his winning chances by hitting. What’s worth noting, however, is that, because he
has no board, Black improves his winning chances very little by hitting.

Let’s look at the numbers. Before Black rolls, he’s a very slight underdog, only about 49.3% to win
according to rollouts. After hitting with 20/16* 24/22 (the best way to hit, connecting his two rear
blots) Black’s winning chances increase, but only to 49.4%! Hitting has taken him from a small
underdog to an slightly smaller underdog.

Making the anchor does somewhat better. After anchoring and buttoning up with 10/8. Black moves
to 50.8% to win. Again just a small increase (only 1.5%) but now at least he has become a favorite.
This makes sense, since he’s now ahead in the race (although only by a pip) and he’s made the best
point on the board. Why wouldn’t he be a favorite?

After 20/16* 24/22, however, Black is swimming. True, he’s a little farther ahead in the race, but he
has no points anywhere and three blots that can be attacked, while White is still the only player with
a point. Although White is on the bar, he has a full 21 numbers that enter and hit. Under the
circumstances, it’s not really a surprise that Black is still a small underdog.

The general principle operating here is that structure supports blots. The more structure you have,
the more blots you can tolerate and the more likely it is that a hitting play is correct. Structure, in
the form of home board points, operates both offensively and defensively. Offensively, it makes hits
stronger by increasing the chance that your opponent fans when you hit and reducing the number of
enter-and-hit numbers. Defensively, structure allows you to tolerate a loose hit by preventing your
opponent from taking too many chances; he has to respect your structure and play more
conservatively.

Look at the next position to see the contrast:

 White – Pips 155 (+4)

Black – Pips 151 (-4)

Black to Play 4-2

Position A. Same as before except Black has made his 5-point.

With the extra structure provided by his 5-point, Black is correct to hit with 4-2. White is both more
likely to fan and less likely to hit back if he enters.

When you have no board at all, a play that makes one of the best anchors, either the 20-point or the
18-point, is likely to be better than a loose hit, even hits that appear relatively safe. An anchor may
be a conservative asset, but it’s one that exerts its power for most of the game.

Backgammon Lesson 30 – Make the 20-point

or the 4-point?
 White – Pips 161 (+1)

Black – Pips 160 (-1)

Black to Play 4-2

There are two clear candidates here; make your own 4-point, or your opponent’s 5-point (your 20-
point). Anything else is a waste of a great shot. But which point should we pick?

These early game point versus point problems can usually be solved by asking yourself three key
questions.

First – Which point is intrinsically more important?

Second – How do the particular circumstances of the position affect the absolute value of the
point?

Third – What’s the degree of difficulty for making each point?

Part 1. We’ll start with the intrinsic value of the points. This is pretty easy to determine. The most
valuable points in the early going are the two 5-points, closely followed by the 4-points and the bar-
points, which are about equal. Other points are much weaker than these key blocking points. Only
considering intrinsic value, the White 5-point (your 20-point) is the top choice.

Part 2. Now we have to look and see how the actual position we’re in affects the value of the
points. This part requires more judgment.

On Black’s side of the board, not much has changed from the starting position. Black has moved a
builder from the 13-point to the 8-point, giving him a little better diversification than he had before.
White is still anchored on Black’s 1-point. All in all, Black’s 4-point is just about as valuable as on
the opening roll.
But on White’s side of the board, the position has changed a lot. First, White has actually made an
inner board point. That means an anchor, any anchor, is more important than it used to be, because
any attack that White launches is now more likely to be successful.

In addition, however, the point White has made is his 4-point. With the 4-point made, White’s 5-
point becomes even more valuable (for both sides) because of the strength of the 4-5-6 structure.
Back in the 1970s, Paul Magriel, in his classic book Backgammon, labeled the 5-point the “Golden
Point”, signifying its importance in the opening. While the 5-point is the best point to have in the
early going, its power can be mostly neutralized if the opponent then makes the 4-point anchor. But
the combination of the 4-point, 5-point, and 6-point is a real game-changer. Whoever makes that
structure in the early game is on the verge of a powerful double. Even anchoring on the 3-point in
front of the structure merely allows the defender to hang on in a clearly inferior position. The only
road to equality is hopping the structure entirely and anchoring on the bar-point, and that will be
hard to do.

Conclusion: White’s 5-point has risen in important, while Black’s 4-point hasn’t changed much.
Edge to making the anchor with 24/20 22/20.

Part 3. Finally, we have to consider degree of difficulty. How hard is it to make a good anchor,
compared to the difficulty of making blocking points? This question almost always favors making
the anchor.

Right now Black has one non-double (4-2) that makes the 20-point, and another one (6-4) that
makes the almost equally valuable bar-point. On his side of the board, he currently has eight non-
double rolls (3-1, 4-2, 5-3, and 6-1) that make a good blocking point. But that number will grow
dramatically as soon as he adds even a single builder in his outfield. Pull a checker from the
midpoint to the 9-point, for example, and Black becomes a strong favorite to make a good point.

Meanwhile, his chances of making a good anchor won’t get bigger, because unless he gets hit, he
can’t add any new checkers to his anchor-making list. Upshot: good anchors are much harder to
make than good blocking points, so your desire to make them is greater.

All three considerations point clearly to 24/20 22/20 as the best play with a 4-2. When in doubt
between an anchor and a blocking point, make the anchor!

Backgammon Lesson 31 – Where to Leave a

Blot?
 White – Pips 150 (+2)

Black – Pips 148 (-2)

Black to Play 2-1

Black survived the first stage of an early 5-5 blitz and has established an anchor. Now he has to find
the right way to get home. With the 2-1 roll Black has to drop a blot somewhere. The only serious
contenders are 6/3, 8/5, and 13/10. How does he decide?

When forced to leave a somewhat awkward shot, there are four criteria we examine. In no particular
order, they are the following:

(1) How many shots do we leave?

(2) How good is the point that we’re starting?

(3) How stacked is the point we’re moving from?

(4) Does hitting cost our opponent anything?

Let’s take a look at just how these issues apply to our current position.

(1) How many shots do we leave? The winner here is 6/3, which leaves only 11 shots. Playing 8/5
instead gives White 14 shots, while 13/10 leaves 15 shots. How much weight we give to this factor
really depends on just how much it hurts to be hit. Here it’s annoying, but it’s far from the end of
the game. White has only a 3-point board, and no builders in position. Defensively, we have a good
anchor on the 17-point. We don’t want to lose ground in the race, but we won’t be too badly hurt if
we do. So while leaving the fewest shots favors 6/3, it’s not an important factor in our decision. (If
White had a 5-point board, it might be the most important factor.)

(2) How good is the point that we’re starting? Hands-down winner here is 8/5. The 5-point is
obviously much better than either the 3-point or the 10-point.
(3) How stacked is the point we’re moving from? Slight edge here to moving off the bigger stack on
the 6-point, but since all these points have at least two spares, this consideration isn’t a big deal.

(4) Does hitting cost our opponent anything? This last criterion is decisive. White is delighted to hit
with the blot on his 23-point, but breaking his 18-point anchor to hit on Black’s 10-point is a big
price to pay. Not only does White break a great defensive point, but he may leave two more blots in
the process. Breaking the anchor to hit is enough of a price for White to pay that it outweighs the
value to Black of starting the better 5-point, making 13/10 a narrow winner.

When forced to leave shots, pay attention to your opponent’s stacks and stripped points.
You’re relatively happy to leave a blot in front of a point with no spares, since you can force your
opponent to make a concession in order to hit. Be less eager to leave a blot in front of either a blot
or a severely stacked point, since your opponent will be eager to hit.

Backgammon Lesson 32 – Playing Proto-

Backgames
White – Pips 147 (-37)

Black – Pips 184 (+37)

Black to Play 4-1

Things went badly for Black in the early part of the game, and after getting a couple of men hit, he
wound up making his 20-point. White has made some progress, securing his own 10-point to make
the start of a blockade. Now it’s Black’s turn, and he has a 4-1 to play.

I call these positions proto-backgames. A proto-backgame is a position where one side (Black in
this case) has had several men hit and sent back, but the opponent (White) hasn’t yet been able to
make a prime to contain the checkers.
These positions are very difficult to play because they can branch off in so many directions. One
branch leads to a genuine backgame, in which White manages to build a real prime while Black
maintains a couple of points in White’s board. Another branch leads to a standard holding game,
where White gets hit a few times and builds an anchor in Black’s board, while Black keeps the 20-
point and releases his rear checkers. Sometimes both sides build an assortment of holding points
throughout the opponent’s position.

Proto-backgames are governed by two key strategic considerations.

Key idea #1: In these very long games, the value of key points rises. In typical holding/racing
games, your 20-point is a good defensive anchor, but with the game moving along rapidly, you may
be able to hold that point for only 10-15 moves. In a proto-backgame, however, you may be able to
keep the 20-point for 30-40 moves. During that whole stretch, the 20-point is working hard to keep
your opponent from building a prime, making the point even more valuable than usual. In this
position, for example, Black will not yield the 20-point unless he’s forced to, or unless he’s
managed to prime some White checkers and is now looking to disengage.

Key idea #2: As in true backgames, Black is currently so far behind in the race that he doesn’t
really mind falling a little further behind, as long as he’s battling for key points. Right now Black
has no board, so White can take chances with little risk. As soon as Black makes a board, White’s
play becomes much more constrained. So Black will vigorously fight for his 4-point, 5-point, and
bar-point, and he won’t mind slotting those points if he can.

With these ideas in mind, our 4-1 roll plays pretty easily.

Since Black has no fear of being hit, 6/5 is the best play with an ace. Black unstacks and starts a
great point. The four can be played in several ways. He can slot with 11/7 or 13/9, which are both
good. But if you’re happy leaving extra shots (which is perfectly OK in this position) just play 8/4*!
Compared to 11/7 or 13/9, it has the merit of knocking out White’s point-making numbers like 4-2,
5-3, or 6-1.

Plays like 8/4* 6/5 are routine in positions where you’re way behind in the race, have at least two
anchors, and your opponent has no board. However, you must have these conditions present for the
‘pure’ plays to work. (‘Pure’ was what we called these plays in the 1970s and 80s – it just means
putting your checkers where you’d like them to go and ignoring the chance your opponent might
hit.)
Backgammon Lesson 33: Slotting in a Back
Game
White – Pips 190 (+68)

Black – Pips 122 (-68)

Black to Play 5-2

In this position Black has established a solid grip on the position. He’s escaped all his back
checkers, built his 4-point and his 7-point, and leads the race by 68 pips (122-190) before rolling.

If Black has accomplished all that, then White probably hasn’t done nearly as well, and in fact he’s
stuck in what’s called a 2-5 game with an as yet undeveloped front game. Some players refer to the
2-5 as a back game, but I think of it more as a hybrid between a back game and a holding game. The
2-5 game can’t really be primed, so White never has any trouble recirculating checkers, effectively
eliminating the main strategy for busting a back game. The flip side for Black is that the 2-5 game
won’t generate nearly as many shots as a pure back game, so Black’s in less danger of being hit.

Did Black miss a chance to double before his roll? No, not at all. While he has an edge, he still has
plenty of work to do: he needs to fill in the 3-point and clear his midpoint for starters. While he’s
doing all that, White will be filling in his home board. Although White’s position looks weak now,
it will be much more formidable when the crisis comes a few moves down the road. But the
simplest way to see this isn’t a double is to note that Black doesn’t have any market losers. No
matter what he throws (5-3 is probably his best shot) White will still have a take next turn. If your
opponent is always taking next turn, there’s no need to double this turn.

So what should Black do with his 5-2 roll? The obvious play is 13/8 6/4. It leaves no blots,
continues the process of clearing the midpoint, and creates a third builder for the 3-point. Black’s
ongoing plan will be to bring down more spares, make the 3-point naturally over the next few rolls,
clear the midpoint, and find a good spot to double. Most players would choose this route, and it’s
perfectly sound.

A better choice, however, is the slotting play: 8/3 6/4! Black needs the 3-point badly, and while he
might make it naturally over the course of the next few moves, there’s a good chance he may not.
Slotting gives him by far the best overall chance to make the point. It’s also much safer than it
looks, since White should only hit if he rolls 1-1. With any other ace (even 3-1) White should just
make his 5-point and keep building, because hitting leaves him too exposed at a time when his front
position is still very weak.

It’s easy to overlook plays like this because it appears that Black will make the point naturally at
some time in the future. That’s never guaranteed, however, and if your opponent’s position is weak
enough right now then slotting the needed point will often be the right play.

Backgammon Lesson 34 – Prime or Slot?

White – Pips 175 (+65)

Black – Pips 110 (-65)

Black to Play 3-2

The lesson of this problem is pretty simple: don’t make blocking points against a back game unless
there’s some chance of actually blocking your opponent.

The obvious play is 13/8, filling in the last blocking point in Black’s prime. The blot left on the 13-
point is of no consequence in view of White’s weak board. However, Black has no need for the 8-
point. White has plenty of time to maneuver and build his board with the four spare checkers on his
13-point and 8-point, plus the spare on the 20-point which can be released with any five or six. If he
makes the 8-point now, Black will find himself needing to clear it in a few rolls, at a time when
White’s board is much stronger than it is now.
Instead, Black has a chance to address the real problem in his position – his open 3-point. It’s true
that Black has several builders bearing on the 3-point, and each turn he’s a little less than even
money to make the point naturally. But it’s a disaster for him if he never makes the point – then
White is in effect playing a 2-3-5 back game, and Black will be leaving plenty of shots when
White’s board may be strong enough to win.

The right play is to go ahead and slot now with 8/3! Not only is White unlikely to hit, but most of
his possible hits are too dangerous for him in light of his weak board. If he throws a hitting number,
he’ll mostly be better off passing on the hit and just building his position. In effect, the 3-2 roll
gives Black a free shot to build the most critical point available.

A Backgame Tactic 35
White – Pips 77 (-109)

Black – Pips 186 (+109)

Black to Play 6-2

In this position, Black finds himself at the tail end of an ace-deuce back game. Things seemed
promising for a while, then not so good, then downright awful. Now, with seven men trapped
behind a full prime and his board almost completely shot, Black has a 6-2 to play.

As problems go, this one is pretty easy. The correct answer is just 3/1, building a three-point board,
leaving a fourth point slotted, and remaining with just one completely dead checker. White will
probably break his prime next turn, and if Black can roll a six before he rolls a three, he’ll release a
checker and have a reasonable chance to play the rest of the game with just one man out of play.
His idea will be to build his board from the back, making his 4-point and bringing builders to his
11-point and 12-point, bearing on the 5-point and 6-point. With some luck, he’ll hit a checker, and
with some more luck, he’ll actually close it out, saving the gammon and perhaps winning the game.
The 4/2 play has a different idea. Black wants to leave his 1-point open but slotted. He plans to fill
in the high points in his board, while leaving the blot on the ace-point permanently uncovered.
Hopefully he’ll hit White and White will roll some aces as he reenters, allowing Black to recirculate
the extra checkers on the 2-point and 3-point. Eventually, Black will build a prime, White will enter
and expose a second checker, and Black will hit it and double White out.

It should be pretty easy to see that Plan 2 is very farfetched compared to Plan 1. We have a name
for this: FPS, or ‘Fancy Play Syndrome’. FPS can get you gammoned a lot, so avoid it when you
can. Black doesn’t need to catch a second checker to win; with some luck, one checker will be
enough. True, it may be an ugly win, but ugly is OK. When you win ugly, they still have to pay you
the prize money.

Although the position may seem trivial, it yields several worthwhile ideas to note.

Idea #1: Although Black’s game looks hopeless, rollouts indicate that his winning chances after 3/1
are about 15%. That’s a non-trivial number, so even if you find yourself in such a position, you
need to keep playing hard and try to extract all the value you can.

Idea #2: In the absence of objective data, groupthink can overwhelm reason, even among a
collection of highly-skilled experts.

If you had presented this position as a problem to a roomful of tournament players back in the early
1980s, you would have gotten an interesting reaction. The beginners and intermediates would all
have played 3/1. Why not? It’s obvious, right? But all the world-class players (myself included)
would have played 4/2. The idea that Plan 2 was both sophisticated and correct was so ingrained at
that point that no top player questioned it. (The position actually comes from a match of that period,
in which one of the best players in the world played 4/2, his opponent agreed with the play, and the
transcriber, who later wrote a book about the match, thought 4/2 was so clear that in the manuscript
he didn’t even consider it worthy of a comment!)

Idea #3: Rollouts can’t solve this problem. I now think Plan 1 is the correct plan, and XG agrees.
Setting up a rollout won’t help, however, because when you force the bot to play 4/2 on its first
move, it will subsequently cover the 1-point as soon as it can with any ace or deuce. So even if Plan
2 had merit, a rollout couldn’t find it. For more on this idea of positions requiring long-range plans
that might not be solvable by the bots, see Mike Corbett’s interesting book Backgammon Problems.
Attacking a Back Game
White – Pips 206 (+83)

Black – Pips 123 (-83)

Black to Play 6-5

This problem is taken from a game in the Athens finals between Billy Horan and I in 1994. (Billy
was White, I was Black.) The game was early in the match and the score wasn’t relevant, so I’ve
recast it as a cash game position.

If you’ve taken up the game recently you may not be familiar with the name, but Billy Horan was
one of the top three or four players in the world for a ten-year stretch, from the late 1980s to the late
1990s. During that time, he won several international tournaments, as well as two of the six World
Cups.

Horan’s style was deep and complex. He actually liked playing back games, but his command of
middle-game maneuvering was so good that it was very rare to see him in a game that was poorly
timed. He had a well-developed knack for sensing when a back game was becoming difficult to
play, and switching into some other formation before his game got critical.
Billy and I played a lot of matches in those years, and since he liked back games and I liked
defending against them, our matches were often lively and complicated. This position is a case in
point.

After I rolled 6-5, it was time to stop and assess things more closely. The obvious play, of course,
was just 16/10 11/6. If White’s game were poorly-timed, I’d make this play without much thought.
Here, however, White’s game is pretty well timed. If I make the obvious play and White rolls a 6,
he’s in great shape. It will take me several moves to move my checkers to the inner board, and in
that time White will be releasing checkers from his 20-point and taking control of the outfield. Even
if White rolls a poor shot at first, he should be able to remake his board by the time the crisis comes.

During this period, I was experimenting with a new idea for attacking massive back games
(positions where the back game player has more than two points), involving breaking the front
points of the prime rather than clearing from the back. The idea was to block the high points of the
back game while allowing the deep points to move. This method frequently worked by forcing the
back game player into more of a holding game formation that was easier to play against.

After I realized that I didn’t like 16/10 11/6 much, I started looking at 16/11 7/1. This keeps the
stack of checkers on the 20-point cooped up for a bit, while allowing the checkers on the 22 and 23-
points to move. Now the rolls of 4-6 and 5-6 immediately force White to break a key point, while
other fours and fives give him a choice between moving off one of his points or breaking his board.
This move had a good feel, so I played it and went on to win the game. (Billy eventually won the
match, though.)

The play doesn’t really involve any specific calculation. It’s based more on the idea that with
White’s army split into two distinct and widely-separated chunks (seven checkers in his home
board, eight in mine, and no one in the middle quadrants), it’s hard for White to handle a prolonged
game. Since I’ve only killed one checker, I should be able to handle a long game pretty well.

Over the years, I checked this position against the bots as they evolved. The early bots, Jellyfish and
the first iterations of Snowie, didn’t like this play either in their evaluations or their rollouts. Snowie
4 still evaluated the play as a big error, but its 3-ply rollout moved the play to the top of the list.
XG’s results were almost identical. These results still aren’t conclusive because nobody really
knows what correct play looks like in these complicated games, but it’s indicative that 16/11 7/1
might be on the right track.

Play Safe or Play for the Gammon?

 White – Pips 78 (+19)

Black – Pips 59 (-19)

Black to Play 4-1

Back at World Cup VI, in 1998, Kent Goulding and I introduced a ‘Quizgammon’ contest,
consisting of a set of 30 problems taken from all phases of the game. Everyone who was interested
paid an entry fee of $20 and sat down for an hour with their problems and answer sheet. After
everyone handed in their solutions, Kent and I went over the answers and announced the winners.
The event was an instant success. Players really liked the idea of matching wits, with the luck of the
dice finally and thoroughly removed.

The idea caught on and Quizgammons and their variants are seen at a lot of tournaments nowadays.
This position is taken from a Quizgammon contest in Boston in 2003 (won by Falafel, well ahead of
the field). It was the hardest problem in that quiz, the only one that no one was able to solve over
the board.

Here Black is bearing off against a busted deuce-point game. His bearoff position is all right but not
great. The pile of checkers on the 6-point combined with the stripped 4-point indicates that Black
may have trouble with shots and awkwardness somewhere down the road. Getting hit isn’t likely to
cost Black the game, but it might spell the difference between winning a single game and winning a
gammon.

At first glance, the position seems to offer a choice between a “safe” play, 6/1, which stays nicely
even-ended, and a “bold(er)” play, 5/off, which gets a checker off but leaves the 4-point and 5-point
stripped. On closer examination, another play pops up: 4/off 4/3, which gets a checker off and
clears the 4-point, leaving spares on all the other points. This starts to look appealing because all the
spares might let Black rip off a lot of checkers over the next few turns.

Most players stop their analysis at this point. Those are the only plays that don’t volunteer a shot,
and volunteering a shot in the bearoff when you have many reasonable alternatives is –
unthinkable?
Well, not quite unthinkable. It’s just very rare. But here’s a good example of when the rare becomes
possible. Here are some of the features that argue for an unusual play:

(1) White has no board, so getting hit won’t lose the game.

(2) The gammon is a bit of a long shot, so Black wants to bear off in a hurry.

(3) His position is just awkward enough so that bearing off both quickly and safely will be hard to
do.

Put all these factors together and a fourth play comes to mind: 4/off 1/off! This looks super-
aggressive at first (volunteering a shot just to get another checker off), but if White hits he’s in a
vulnerable position, with at least three and maybe four blots strung around the board. On reflection,
this must be the best play to win a gammon, and that in turn raises another question. If Blacks rips
two off, will White even hit with his deuces?

The answer to that question is – sometimes. White should hit with 2-1 and 2-2, because those
numbers pick up the blot in his board, eliminating the direct shots. He should also hit with 2-6 and
2-5, because those numbers get the blot on the 23-point into the outfield, where it’s a little safe. The
intermediate deuces, 2-3 and 2-4, neither safety the blot on White’s 3-point nor move the blot on
White’s 23-point, and with those numbers White should pass up the hit and just move the checker
on his 12-point.

Note also that when hitting is right, it’s mostly right by a tiny amount. Only with 2-2, which leaves
only one blot around, is the hit massively correct.

Compared to the best double match point play, 5/off, taking two off with 4/off 1/off costs about 1%
winning chances in exchange for 5% more gammons, a very favorable trade. It’s a cute play, and a
strong argument for looking carefully to make sure you’ve seen all the plausible plays. You can’t
make a play that you never see.

Offering Early Doubles

When should you double in the very early part of the game? How soon is too soon? Let’s take a
look.
 White – Pips 170 (+17)

Black – Pips 153 (-17)

Black on roll. Cube action?

The diagram shows a common sort of early game position. Black made his 5-point early on while
White countered with his 4-point. Some hitting occurred and White just fanned. The dance gives
Black a chance to think about turning the cube. Should he? Let’s see.

I like to evaluate these early doubles with Joe Sylvester’s old Race – Position – Threat (RPT)
method. Evaluate who’s ahead in each category, and if Black has an edge in two out of three, he
probably has a double and White probably has a take. If Black leads in all three, Black has a sure
double and White often has to pass.

The race here is pretty easy: White has a checker in the air, and Black has a solid lead of 17 pips,
153 to 170.

The position and the threat categories actually merge in this problem. If Black covers his 4-point,
then he has a solid edge in position. But his only real threat in the position is to cover the 4-point,
which he’s likely to do. We can say that he either has a positional edge with no threat, or a big
threat but not much of a current edge. (Note that White’s blot on his 10-point is pretty safe, as
almost all the numbers that hit would be properly used to cover the 4-point. Black’s only hitting
number is actually 5-3.)

With the positional edge hinging on the execution of the threat, we can’t really give Black a 3 on
the RPT score. Scoring him a solid 2 looks more like it, in which case White most likely has a take
and Black probably has a double. Actually White’s take is pretty easy here. Mostly Black covers his
4-point and White enters, after which the game goes on. White has the worst of it but his game is
solid with no actual positional weaknesses. Black will have two checkers to escape, and he’ll be
unlikely to make his bar-point anytime soon, so White should be able to generate plenty of
counterplay for the rest of the game.
How strong is Black’s double? That’s actually the more interesting question. A good double
requires some market losing sequences, and Black has a few here. If he covers, say with a 6-3, and
White then fans, the position will be double and drop. He’s got a total of 26 cover numbers, after
which White fans 25% of the time, making a total of about 18% market-losing sequences. That
might sound like a lot, but it’s not really that impressive because no sequence leads to a huge
market loss. After Black covers with a 6-3 and White fans, for instance, Black loses his market by
only about 0.15 points per game. A covering sequence that breaks Black’s 8-point is even weaker.
After 4-1 (played 8/4 6/5) followed by dancing, Black loses his market by only about 0.05 points
per game. So while Black has a few market losers, hardly any are really crushing. That’s
discouraging, because when we double we’d like to see a few sequences where our equity shoots
way up into the “pass” category.

In fact, rollouts indicate that a double here is a completely marginal decision – doesn’t gain
anything, doesn’t lose anything. That result in itself, however, makes this a very valuable
benchmark position. Since it’s not an uncommon sort of structure, committing it to memory is very
useful; anything better than this for Black is a clear double, anything worse is a clear no double.
Most serious players are familiar with a collection of take/pass benchmarks, but double/no double
benchmarks are just as valuable.

Knowing that it’s a marginal decision, I would as a practical matter double over the board. There’s
always some chance my opponent will pass which is an enormous gain for me, and if he takes I’ve
lost nothing.

Feb-01-2019 || Taking Risks in a Holding

Game
(A) Black to play 5-1.

White – Pips 148 (-5)

 Black – Pips 153 (+5)
Black to Play 5-1
Problem A shows a routine position in an early holding game. Both sides have an anchor, and the
race is very close. Black’s position is slightly preferable since more of his checkers are arrayed in
front of White’s anchor, and he therefore has better chances of establishing a blockade.

Black’s roll of 5-1 is a pretty routine shot and he has two obvious choices: 9/3, starting the 3-point,
and 13/8 9/8, playing safe while keeping all checkers is front of White. Of these two plays, 9/3 is
very slightly better; 13/8 9/8 creates a stack which will prove a little awkward in some of the
upcoming variations. In the middle game, we try to avoid creating big stacks unless alternatives are
really weak. There’s nothing structurally wrong with 9/3, so it’s a better play here.

There is, however, yet another alternative: the bold and dashing 13/7, slotting the bar point and
leaving two blots, but forcing White to give up his anchor if he wants to hit. Is 13/7 just a crazy
play, or a stroke of genius?

If you found yourself a spectator at backgammon tournaments in the 1970s and early 1980s, you
would have seen plays like 13/7 with some frequency. Slotting to build primes was the essence of
the “pure style” much in vogue at the time. Advocates of this style would have made several
compelling arguments in favor of 13/7:

> If White doesn’t hit, Black can build a prime quickly.

> If White does hit, he loses his anchor and Black can attack. The attack might still let Black build
a formidable position.

> If Black gets several men sent back, he can construct a back game/blocking game formation.
White’s board isn’t very strong, and Black already owns a high anchor, so White has little or no
chance of forming a prime against whatever formation Black can construct.

> The positions that will result from 13/7 will all be more complex than those that will arise after
the more standard plays. The better player will have an edge in these positions.

> Most of the good players play this way, and they’re winning all the big tournaments, so don’t you
want to play like them?

Actually, these are all pretty good arguments. While they’re not good enough to tell you that the
play is right, they are good enough to tell you that the play might be right.

As the 1980s wore on and turned into the 1990s, experience accumulated and plays like 13/7
became less popular, even among the good aggressive players. A general sense took hold that these
plays were a little too over-the-top, although they remained a useful weapon against weaker players.

The arrival of the bots and their rollout capacity in the mid-1990s gave us a tool that let us put plays
like 13/7 under a microscope. The results were interesting and can be summed up pretty quickly:

In normal positions, where White has reasonable structure, double-slotting plays like 13/7 are
wrong. Just how wrong they are depends on the strength of White’s position. Where White’s home
board is not too imposing, as in (A), the plays are only slightly wrong. Against a sufficiently weak
opponent, the slotting plays might indeed be optimal.
But suppose the position isn’t so normal? Take a look at Position B, with the same 5-1 to play:

White – Pips 149 (-4)

Black – Pips 153 (+4)

Black to Play 5-1

In (B), where White has a blot in his 1-point board, a big stack on the 6-point, and a stripped 8-
point, then Black has the freedom to take more chances, and the aggressive slot is more likely to be
correct. In fact, 13/7 is the best play here, and by a considerable margin.

The lesson here: Before taking a risk to improve your position, don’t just look at good your game
could be if you get away with the play. Remember to look at your opponent’s position and see just
how dangerous his home board is if he hits you. If it’s toothless enough, then the aggressive play
may well be right. If it’s got some bite, then you may have to settle for something more prosaic.

Feb-15-2019 || Creating Checkers to Move

 White – Pips 134 (-1)

Black – Pips 135 (+1)

Black to Play 5-3

This problem isn’t difficult, but it contains some interesting points. The right play is just 21/13.
Remaking the midpoint creates a fluid, well-connected position that’s relatively easy to play
compared to alternatives. Black has chances to make the 3-point, and some other rolls that make the
bar-point. He gets some outfield coverage in case White’s next roll is 6-3 or 6-4. He blocks White’s
best roll, 6-6, turning it from a game-changer into merely a good shot.

The great strength of 21/13, however, lies in what happens when Black’s next roll doesn’t do
anything constructive. Because his back checker on the 24-point is free to move, Black can simply
run from the 24-point with any roll that doesn’t actually make a new point, while preserving his
good structure. With 5-4, for example, he can leave all his good points alone and just play 24/15. In
addition, some of the rolls which leave his back checker partly blocked, like 6-1 and 5-2, make
good blocking points instead. (“Playability” is actually an important concept in middle game
positions, but it’s a hard concept to put into practice because it requires mentally running through
all possible rolls to see if there is any large group that plays awkwardly.)

When we compare 21/13 to the main alternative, 24/21 13/8, we can see the difference pretty
quickly. Black’s point-making rolls like 5-2, 6-2, and 2-1 are still fine. But what does Black do with
something like 5-4? Presumably he’s going to play either 9/4 9/5 or 9/4 5/1*, but neither play
inspires confidence. By making an anchor unnecessarily (White wasn’t threatening to block him in
anytime soon) Black has tied up 42 pips of timing, and now he’ll need to throw some good shots to
keep from tripping over himself.

Players often wonder why backgammon seems to be such a streaky game. “I can’t buy a roll! It’s
been like this for weeks!” (Or months, or years …) I think one reason are positions like this, where
a player in good form looks at the position for a few seconds, sees 24/21 13/8 and 21/13, sees that
the structure after 21/13 looks good, and makes the play. A player in bad form never even sees
21/13 as a play. He rolls his dice, sees he can anchor, says to himself “That can’t be bad”, makes the
play and picks up his dice. When we’re in bad form, we tend to see hits and point-makers, but we
miss even the moderately subtle stuff. The long-run effect on our error rate is substantial.

Mar-1-2019 || An Early Double

White – Pips 173 (+38)

Black – Pips 135 (-38)

Black on roll. Cube action?

Proper doubles in the very early stages of the game are somewhat unusual. It takes some time to
build an advantage strong enough to turn the cube. Most correct early doubles come from blitz
positions, where one side rolls a quick double, makes a couple of inner-board points, and catches
his opponent on the bar. Here the attacker gets enough gammon chances to compensate for the fact
that he still doesn’t have a big positional edge.

Genuine positional doubles in the very early stage of the game are rare, but they can happen. This
position is one good example. Although Black has not yet made a new point in his board, he’s made
his bar-point, gained a big lead in the race, and has an impressive collection of builders. Most of his
rolls will make either his 4-point or his 5-point next turn, after which he’ll be threatening to make a
5-prime and snuff out resistance. Many players have conditioned themselves not to double unless
they’ve made at least one additional home-board point, and mostly that’s a good rule of thumb. Be
aware that there are exceptions, however.

At the same time, White has a take. Black’s far from guaranteed to make a quick 5-prime, White
has an anchor, and Black still has a checker to escape. That’s enough counterplay to keep White in
the game for a while. Doubling when you have just a one-point board is unusual, but passing when
your opponent has only his 6-point is really rare indeed.

A very interesting feature of this position, however, is the status of the blot on White’s 5-point. Is
the blot an asset for White, or a liability? It appears to be yet another weakness, and in fact a lot of
players in Black’s position might be encouraged to double, combining the presence of the blot with
their own priming chances. In fact, the blot is actually a strong asset for White!

We can see this if we look at how Black will play his upcoming fours. With 4-2 and 3-1, he will
clearly make a point in his board. With 4-3 and 6-4, he’s indifferent between hitting on his 20-point
and making a home board point. Only with 4-1 and 4-5 is he clearly right to hit White’s blot. With
so few hitting rolls, the blot is clearly good for White since it allows White to build his board faster.
In fact, if we change the position by moving White’s blot from his 5-point back to his 6-point,
Black’s double is even stronger and White has a marginal take/pass decision. It often happens that
we can only decide if a feature of the position is an asset or a liability by looking at how the
upcoming rolls play.

Apr-01-2019 || 5-Prime versus 5-Prime

White – Pips 105 (-10)

Black – Pips 115 (+10)

Black to Play 2-1
This problem shows us one of the most interesting middle game positions possible: both sides have
a 5-prime, and neither side has an anchor. The play will be razor-sharp, and gammons will be
floating in the air for both Black and White.

What are the goals in these positions? Here’s what the players are trying to do, arranged roughly in
order of importance:

(1) Escape a checker from behind the prime. In general, if you roll a six, you’re going to run a
checker to the outfield. This not only releases a checker, but buys you several additional rolls of
timing before your own prime comes under pressure.

(2) Hit checkers in the outfield. This is the converse of (1): you send a checker back to jail, and
eliminate your opponent’s timing in the process.
(3) Get to the edge of your opponent’s prime. You can’t escape without getting to the edge, so
get there when you can.

(4) Knock your opponent off the edge of your prime. (4) is just the converse of (3): if he wants to
get to the edge, you want to knock him away.

(5) Do what is hard for you first; make your opponent do what is hard for him. Something is
“hard” if you need a single number on the dice to do it, like rolling a six to escape. On any turn, you
only have a 30% chance of doing a “hard” thing, so when you have the chance, take it, even if it
seems to leave a vulnerable position. If you pass on doing something hard, you’ll find it doesn’t get
easier later.

With the 2-1, we can quickly see that we can’t do anything about goals (1), (2), or (3). Only goal (4)
applies here; we do have the ability to knock White off the edge of the prime, so we take it. Our
deuce will be 5/3*. Now White needs a three to get back to the edge, and he may not roll a three for
a while.

What about our ace? If we have blots on our 1-point and our 3-point, White has 20 rolls to hit. We
might as well push on and hit the second blot, because we’re just as likely to be hit back as before.
It’s a free hit, and it has an added bonus: we create a new possible game plan. If White dances, or
rolls 6-3, 5-3, or 4-3, we now have the possibility of a blitz, followed by escaping our back checker
later. It’s not a likely variation, but just the possibility adds a lot of strength to our position.

Apr-15-2019 || How to Play a Proto-Backgame

White – Pips 175 (-42)

Black – Pips 217 (+42)

Black to Play 6-2
This position is an example of what I like to call the proto-backgame. Both sides have been busy
whacking each other for a while, with the result that Black now has seven men back, and White has
three. Neither side has managed to make either a new home-board point or a new blocking point, so
each side is free to maneuver, and the cost of getting another man hit is very small. Now Black has
a 6-2 to play from the bar. Clearly he’ll come in with Bar/23, after which he can choose among five
legal sixes, none of which are absurd. It’s a tough problem, to be sure.

Let’s start by reviewing the key ideas for handling proto-backgame positions. After that, we’ll list
Black’s five legal choices and see how they stack up. Although none of Black’s plays are horrible,
some will drop off our radar screen quickly once we see what we’re really trying to do.

Key Idea #1: Don’t kill checkers. This rule is important in all types of games, but it’s especially
important in proto-backgames. You must keep your checkers active and in front of your opponent.
Burying checkers on your 1-point and 2-point is death; don’t do it.

Key Idea #2: Make your opponent play the backgame. A common mistake in proto-backgames
is assuming that the player who initially has the most men back will inevitably be the one playing
the backgame. These positions, however, usually lack any defined structure because so much of the
early game is spent hitting and being hit. Without structure, it’s relatively easy for the side with
more men back to get a lucky hit or two and reverse the situation. To paraphrase General Patton:
“Don’t play a backgame; make the other poor bastard play a backgame.”

Key Idea #3: Make strong points. All the points that are normally good to make in the opening are
even better to make in a proto-backgame. Your blocking points (the 4, 5, 7, and 9-points) are even
stronger because there are more checkers to block. Your anchors (the 21, 20, and 19-points) are
even better because you have more checkers to recirculate to the outfield.

Key Idea #4: Recirculate. Don’t fall in love with backgame points; keep your checkers moving to
your opponent’s outfield. From his outfield, you’re threatening to make points in your outfield,
which are blocks for whatever men he has back.

Key Idea #5: Watch out for your middling doubles. Check your position to see if particular
numbers are blocked around the board. If that’s the case, your game could blow up with an
awkward double. The problem won’t come from 1-1 or 2-2, which are small enough to be handled
in most positions. It also won’t come from 6-6 or 5-5, since your opponent won’t have had a chance
to form a prime yet. The real danger numbers in proto-backgames are 3-3 and 4-4, which are
susceptible to the kind of small blocks that form in these positions. Usually the culprit is a careless
play earlier, where an accurately-played ace or deuce could create a position where all numbers play
well.

That’s a general summary of the ideas to keep in mind when both sides have a bunch of men back
but no real structure yet. Now let’s look at Black’s actual options and see which play makes the
most sense.

Bar/23 24/18. Moving out to the 18-point is the worst play. It doesn’t hit, doesn’t make a new
point, and leaves two blots on the points White most wants to make, his 7-point and 9-point. White
now has a few point-making numbers and lots of double-hits, which often result in White’s building
a quick little prime. This is exactly what Black wants to avoid.
Bar/23 16/10. This is an improvement on 24/18, since Black doesn’t leave blots where White is
trying to make points. In addition, the blot on the 10-point puts a little pressure on some points
Black would like to make, which is good. Still, the play has two significant downsides:

> White gets to hit with threes, which is currently his least effective number around the board.

> The move leaves Black a little thin in White’s outfield, with no presence there and a stripped
midpoint.

Bar/23 13/7*. This was the play I actually chose when the position came up. (It’s from a match
against Nack Ballard at one of the Reno Invitationals back in the late 1980s). I realized breaking the
midpoint was dangerous, but I saw that the 23-point was an awkward point for White to have a
couple of checkers. I thought if I could make a small block of three points, White might get
squeezed, needing to build some front points quickly while at the same time needing to move his
back men.

That’s exactly how the game played out, so I thought I had made a really good move. Years later,
when the bots got good enough in backgames to trust their rollouts, I realized that the play was just
too loose. The three blots on my bar-point, midpoint, and 16-point give White too much of an
opportunity to stick me in a true backgame. My move does win more games than the second-best
play, but loses too many gammons.

Bar/23 22/16. Not a bad play. It keeps the 20-point and makes the 16-point, giving Black a good
anchor and a clear route to the outfield. The downside of the play is that Black is consolidating into
an inferior position. White has a lot of rolls to make a good point somewhere, and this play leaves
Black more likely to end up in some sort of backgame/holding game. Since White still has no
structure, Black is entitled to play more aggressively.

Bar/23 20/14*. This is the right idea when White has no new structure: hit to keep White off
balance and gain ground in the race. Hitting gains 14 pips, so instead of trailing by 34 pips in the
race, Black will trail by only 20. After another such sequence, Black could actually catch up, and
that’s a great result. You always want to make your opponent play the backgame, not you, and this
is the best play to get out of backgame mode as soon as possible.

Leaving the 20-point carries some risk, but it’s very small; White needs to roll an immediate 1-1 or
3-3 to make the point. Otherwise, Black has a triple shot to remake it. Meanwhile, Black picks up
some builders to make a point in his outfield. This play gives Black the best overall distribution and
board control, and beats out 22/16 by a modest margin.

May-01-2019 || Backgammon Explained: Middle Game Maneuvering

 White – Pips 143 (-53)

Black – Pips 196 (+53)

Black to Play 3-2
This position is taken from a game which began with a lot of hitting, but not much point-making. Both sides
have now secured good anchors; Black also has the 22-point, so he has the making of a strong holding
game. Each side has managed to add one outside point along the way. Black has his bar-point, while White
has his 9-point. For good measure, White has built a 53-pip lead in the race.

What are the game plans going forward? White’s is pretty simple. He probably won’t be able to build an
effective prime, so he needs to capitalize on his racing lead by scrambling his back checkers home, and the
sooner the better. He’ll want to start with the checker on his 24-point, and then follow with the checkers on
his 20-point. He’s not averse to building the low points in his board; the spares on his 6, 8, and 9-points don’t
really have anywhere else to go, and a strong board might help him if he can hit a lucky shot.
Black is losing the race, but he’s the one with the priming chances. His job is to get his back checkers out
and try to extend his little prime. His first goal is to make his 9-point or his 10-point, which starts putting real
pressure on White’s rear checkers. For now, he’s not interested in making home board points. Every checker
that makes a home board point is another checker that can’t help build the prime.

With Black on roll, who’s a favorite? Actually, it’s White, but only by a small amount (about 53-47, cubeless).
Black’s positional advantages almost compensate for White’s huge racing lead, but not quite.

Now we get to the real question: How should Black play a 3-2? One play is very obvious, namely 14/11
13/11. It makes a good point and leaves no blots. But if a play’s that obvious, how can it be a problem? The
answer must be something more subtle, like 20/15.

Over the board, it would be very hard not to go on automatic pilot and make the 11-point. But now we have
plenty of time and we’ve been warned this is a problem, so let’s list the relative merits and demerits of the
two plays.

Play A: 14/11 13/11

The strength of making the 11-point are pretty clear: Black makes a blocking point and cleans up two blots.
The weaknesses of the play are a little more subtle, but become apparent on a second look.

(1) After making the 11-point, Black’s position is a little fragile. He has only two spares, both on the 20-point;
a roll that won’t allow him to move one of these checkers will force him to break a point somewhere else on
the board. That point will almost certainly be the 11-point, since his other points are all more valuable right
now.

(2) The 11-point doesn’t actually do much. It blocks White’s 20-point, but White doesn’t want to move those
checkers right now. He’d like to get the checker on the 24-point moving, and if that’s not possible, he
wouldn’t mind making his 2-point. The checkers on the 20-point are quite happy to stay where they are for
the moment.

(3) Black’s position has become hard to improve in the near term. The points he most wants to make are his
9-point and 10-point, to extend his prime. But unless he rolls 1-1 or 2-2, which allow him to shift his 11-point
forward, those points will be hard to come by for some time.

Play B: 20/15
Play B is the opposite of Play A: the weaknesses are apparent, the strengths more subtle. The weaknesses
are that the play doesn’t make an available point, and it leaves three blots instead! Now let’s look for the
strengths.

(1) Black’s position is less dangerous than might appear. White has only 12 hits: 6-2, 5-3, 4-4, 6-3, 5-4, 6-4,
and 5-5. The hits with 5-5 and 4-4 don’t swing much because those are great shots anyway. The other hits
leave Black with a ton of return shots. After 6-3, for instance, played 20/11*, Black has 22 return shots: all 2s
plus 1-1, 5-1, 3-1, 6-5, 6-3, and 6-1. The hits with eights or tens are a little better for White but still far from
crushing.

(2) Black’s position is much more flexible than after making the 11-point. He’s in no danger of cracking
anything vital, and he’s got a bunch of combinations to make the 9-point or 10-point. If White doesn’t hit,
Black will be able to play pretty easily for the next few rolls.

(3) Hopping out lets Black control the outfield. White has lost his grip on the outfield, and his army’s getting
disconnected. The checkers on his 20-point are 11 pips away from his checkers on the 9-point. With 20/15
Black stakes a claim to the outfield, White’s most vulnerable area. Games with multiple men back on both
sides are frequently decided by outfield control, because both sides need a link between their back checkers
and their front position, and the player who loses that link can become an underdog quickly.

Do the advantages of 20/15 outweigh the value of a solid point? Rollouts show that they do, although it’s a
hard judgment to make over the board. Making the 11-point is so inviting that most players would grab it in a
shot and pick up their dice. (I did – the position is from one of my games.) The value of this problem is to
show that massive outfield control, coupled with playable checkers and an opponent’s toothless inner board,
can outweigh plays that are solid but inflexible.

May-15-2019 || Backgammon Explained – Hit Loose or Make a Point?

 White – Pips 160 (+3)

Black – Pips 157 (-3)

Black to Play 4-2
This is a fairly simple, but extremely important problem. At first glance, Black seems to have a lot of
reasonable choices. Here’s a quick list, with a brief description of why each play might be appealing:
(a) 24/18, making the enemy bar-point and duplicating fours, but not making any progress on the front game.

(b) 8/4 6/4, making the 4-point, but leaving two blots and a lot of shots.

(c) 13/9 18/16, making the 9-point and creating some duplication of fours.

(d) 9/5* 18/16, fighting for the 5-point while taking away White’s good sixes.

(e) 9/5* 13/11, fighting for the 5-point and fearlessly bringing down another builder, but leaving White with 6s,
5s, 4s, 3s, and 1s to hit.

Seeing the right play hinges on understanding two key principles of early game play:

(1) A permanent strong asset trumps a lot of aggression and flexibility.

(2) A defensive anchor on your opponent’s bar point is very powerful.
If it’s not now obvious, the right play is 24/18. Black builds a great asset, the defensive anchor on the 18-
point. He also leaves White with minimal threats, the duplicated fours to either make the 20-point or hit
Black’s blot.

In general, permanent assets are better than loose hits in the early game. Loose hitting often evaporates into
no advantage at all, whereas a permanent asset is a plus for the rest of the game. Beginners and
intermediates tend to have trouble with this play, mostly because they’re ambivalent about the value of the
enemy bar-point. Since it’s not an inner point, it doesn’t seem to offer the long-term security of an anchor on
the 20-point. And everyone can remember games where you held on to the 18-point too long and were
forced off it at an inopportune time.

Put those two factors together, and many players downgrade the bar-point, looking for something else to do
with their checkers. This, however, is a pretty big mistake. Once you split to the opposing bar-point, your
game plan is to make it as soon as possible. Loose hits like 9/5* 13/11 or 9/5* 18/16 are just distractions
from the thematic idea.
The second-best play in the position is to grab the other permanent asset with 8/4 6/4. It’s not a bad play,
since it makes a good point and smooths out Black’s distribution. However, it leaves Black more exposed
with more blots and no anchor, and so is slightly inferior to 24/18.

If you’re playing well, you should find yourself in a lot of games where you make your opponent’s bar-point
early. There are problems that can come from sitting in the bar-point, but they’re problems you want to have.
Learn to play these positions well, and your results will improve dramatically.

June-01-2019 || Doubling Weak Players in Tournaments

White – Pips 4 (-2), Match -7 -3

Black – Pips 6 (+2), Match -3 -7

Black on roll. Cube action?
Black leads 4-0 in a 7-point match and owns a 2-cube.

(a) Assume you are Black, you are a very strong player, and you are playing another very strong player. Should Black
double in this position? If Black doubles, should White take or drop?

(b) Same question, but now you are Black playing a weak player.

We’ll start by figuring out the correct cube action assuming you and your opponent will make correct
decisions in the future. Then we can see if the theoretically correct action requires any adjustment depending
on the strength of your opponent.
To figure out the right cube action, we need to estimate three numbers:

(1) Black’s actual chance of winning the game from this point, disregarding the cube.

(2) The value of a 6-0 lead in a 7-point match (which happens if Black doubles to 4 and White drops, or Black
doesn’t double and simply wins the game with the cube on 2.)

(3) The value of a 4-2 lead in a 7-point match (which happens if Black doesn’t double and White pulls the
game out.)
Part (1) is pretty easy. White only wins if Black first doesn’t bear off his three checkers, which happens 31/36
of the time (note that 1-1 is not a winning double for Black), and White then rolls a double, which happens
1/6 of the time.

31/36 * 1/6 = 31/216 = 14.4%

[You might ask, “How do players actually do these calculations over the board?” I use a lot of numerical
tricks, as do most other players. After you’ve played a lot of tournament backgammon, you realize that some
tricks are particularly useful and some numbers recur constantly. In this calculation, I’d note that 31/36 is only
a little larger than 5/6, so what’s 5/6 times 1/6? Well, 1/6 is about 16.7%, so 5/6 of that will be a little less
than 14%. We want a number a little bigger than that, so our answer is 14%+. That’s plenty good enough for
our purposes. Trying to get exact answers in your head is pretty hard, but close approximations are much
easier and almost always good enough.]

What about part (2), the value of a 6-0 lead in a 7-point match? Since the Crawford Rule is in effect, White
must win the next game, taking him to a 6-1 deficit. (It doesn’t matter if he wins a gammon in the Crawford
Game or not.) He’ll then double to 2 at the start of every game. If he then never wins a gammon, he’ll need to
win three more games to win the match, for a total of four straight wins overall. The probability of four straight
wins between two equal players is

½ * ½ * ½ * ½ = 6.25%

But if White wins a gammon in either the second or third game, he wins 4 points and saves a game, so in
that case he only needs to win three straight. The probability of that is 12.5%.

The probability of winning the match is therefore between 6.25% and 12.5%, and a little closer to the lower
number, since you’re not favored to win a gammon in a two-game sequence. A good approximation is 9% for
White’s chances, and therefore 91% for Black’s chances.

Finally, for Part (3) we need the value of leading 4-2 in a 7-point match. Different match equity tables give
slightly different numbers here, but the range is roughly 64% to 66%. I’ll use 65% as a good average value.

Now we’re ready to figure out the optimal doubling and taking decisions at this score. Let’s start with White’s
take/drop decision if he gets doubled.

> If White takes and redoubles to 8 when he can, he wins the match 14.4% of the time (from Part (1)).
> If White drops, he trails 0-6 to 7 and wins the match 9% of the time (Part (2)).
So if White gets doubled, he should take and reship when he can.
Now let’s look at Black’s doubling decision.

> If Black doubles, he must assume White takes and reships (we’re postulating correct play on both sides)
so he’ll win the match 85.6% of the time.
> If Black doesn’t double, he’ll win this game 85.6%, getting to 6-0, and will lose 14.4%, getting to 4-2. His
total winning chances then look like this:

85.6% of the time he’s leading 6-0, and wins 91% of those.
Wins in this variation = 85.6% * 91% = 77.9%.

14.4% of the time he’s leading 4-2, and wins 65% of those.
Wins in this variation = 14.4% * 65% = 9.4%.

Total wins from not doubling = 77.9% + 9.4% = 87.3%.

So he wins 87.3% if he doesn’t double, 85.6% if he does. So Black shouldn’t double, even in this two-roll
position.
Now we’re ready to tackle the two main questions. What happens when we face real opponents of varying
strengths?
(a) Against a very strong player (and assuming Black is a strong player himself) Black should just make the
theoretically correct play and not double. If Black errs and doubles, White should take and redouble to 8 if
Black misses.

(b) What about if Black is a strong player and is facing a weak opponent? This is a really interesting question
and in fact is the whole point of this problem.

The theory of how to play against weak players originated in the 1970s with the publication of Barclay
Cooke’s The Cruelest Game. Cooke expanded on his notions in two later books, Paradoxes and
Probabilities and Championship Backgammon. Cooke’s idea was that you should be very conservative with the
cube against weak players, doubling only when you were pretty sure you’d get a pass, and aiming to grind
them down in a long series of 1-point and 2-point games, giving your huge skill advantage in checker play
the maximum chance to work. The worst possible disaster was to give your weak opponent the cube in a
volatile position, allowing him to rewhip to 4, win an 8-point gammon, and turn the match around.
Cooke was a well-liked fellow, a real gentleman of the old school. In addition, he was an absolutely superb
writer, who was able to convey better than anyone else the glamour and excitement of high-level
backgammon. The Cruelest Game, published in 1975, was one of the big influences driving the backgammon
explosion of the mid-1970s. To this day, it remains the one book I would recommend if a friend who didn’t
know the game came to me and wanted to understand why backgammon was popular and what the fuss
was all about. Cooke captured the drama of the game better than anyone else, before or since.
Cooke’s ultra-conservative approach to playing weak players soon became accepted wisdom and was
echoed in other books in the 1970s and 1980s. But it is, I think, completely the wrong approach. Let’s see
why.

In Greek mythology, the gryphon was a majestic creature combining some disparate parts: the body of a lion
with the wings of an eagle. Cooke’s “weak player” is a little like that: a hybrid containing components not
likely to be found in nature. He plays the checkers so poorly that you’re a huge favorite to grind him down,
one or two points at a time. But he handles doubling decisions superbly; he scoops up cubes in volatile but
takeable positions that might have a strong player scratching his head, then he whips it back when the game
starts to turn in his favor, applying maximum pressure. What a tiger!

Do real “weak players” actually play like this? In my experience, almost none do. In the real world, bad
players handle the checkers poorly, but they handle the cube even worse. Their cube action is mostly
tentative; they know they don’t play well, so they try to postpone decisions that might make them look foolish.
They double late, or not at all, because they’re waiting for positions that are so strong that doubling can’t be
a mistake. When doubled, they’d rather drop than take, because dropping only loses a point, while taking
might lose four points. Besides, they know you’re a better player, and they’re picking up cues from you. If
you’re doubling, then you must believe you have a big advantage. Who are they to argue? Better to drop.

The best way to play against weak players is to be very aggressive. Double a little early, especially in volatile
positions. They’ll probably drop, but if they take, you’re better off in a number of ways:

> Their checker errors will now be occurring with the cube on 2 rather than 1.

> They may redouble prematurely, giving you an extra edge.

> They may redouble late or not at all, giving you a huge edge.

All of these edges add up to huge vigorish over time.

Interestingly, poker players tend to handle weak opponents better than backgammon players do. Poker
players understand the value of relentless aggression, and they apply it ruthlessly, raising their limps, 3-
betting their raises, and pushing the action after the flop. In part, I think, this is because poker players don’t
really attach much importance to individual hands; there are many more hands in a poker session than
games in a backgammon session, so poker players find it easier to just make what their experience tells
them is the best move against this particular opponent, and let the chips fall where they may (pun intended).
Now, after this long intermezzo, back to Part (b). What do we do if we’re a strong player and our opponent is
a weak player?

We double, and we do so quickly, without giving any hint that there might be something to think about. Our
opponent will drop, because it’s a two-roll position, and everybody knows that’s a pass. And we pocket our
two points and our 91-9 edge without risking losing the game.

une-15-2019 || Bearing Off Against the Ace-Point

White – Pips 87 (+45)

Black – Pips 42 (-45)

Black to Play 1-3

In this position White got stuck playing an ace-point game which didn’t go well for him. Now he’s
lost his 6-point, and next turn he’ll either have to break his board or run off his anchor.

Meanwhile, Black is doing reasonably well. He’s cleared his 6-point and managed to bear off two
checkers. The weakness in his position is the stripped 3-point, which might cause problems once the
5-point is cleared.

I call these positions “Bearoffs against Contact”, and they can be very tricky little problems.
Black’s top goal is usually safety: he wants to bear off while leaving the minimum chance of getting
hit. His second goal is winning a gammon. His gammon chances are generally small, but not
insignificant.

Usually one play will be significantly safer than any other, in which case that play will dominate. If
two plays will offer roughly the same winning chances, but one gives better prospects for a
gammon, that play will make it to the top of the list.

Here Black has three plays worthy of consideration: (a) 5/2 5/4, (b) 4/off, and (c) 3/off 3/2. Let’s
see how the plays compare for safety and gammon-winning chances, and see if a clear favorite
stands out.
(a) 5/2 5/4. Clearing the rear point is usually the safest play, but not always. Here the stripped 3-
point comes into play. After 5/2 5/4, Black is odd-ended and his threes will often leave a shot,
making this play much less safe than usual. Here he leaves a blot next turn with 66, 55, 44, 63, 53,
43, and 32, a total of 11 numbers. In addition, playing 5/2 5/4 leaves Black with some horrendous
positions on the following turn. After rolling 65, 64, or 54 he’s left with three checkers on the 4-
point and two in the 3-point, a formation which yields 23 blot numbers.

(b) 4/off. Keeping the 5-point and bearing off a checker instead helps win more gammons in two
ways: Black gets an extra checker off, which always increases his gammon chances by a few
percent, and Black maintains his prime another turn, which may prevent White from releasing a
back checker. Here the play has a third effect: if White rolls 44, 43, 42, or 41, he not only can’t
release a checker but has to break his board instead, giving Black some extra winning chances as
well as extra gammon chances.

If we count Black’s shot-leaving numbers after 4/off, we get only 10: 66, 55, 64, 54, 43, and 41.
Surprisingly, 4/off is actually a little safer than clearing the back point, at least on the first turn.

(c) 3/off 3/2. On rare occasions, breaking an inner point can be the best option. Most of these
situations occur when Black has a full inner board (2-point through 6-point) and has a chance to
clear the 5-point before clearing the 6-point, with a resulting better distribution. When there are two
points to be cleared above the gap, as here, the play is extremely rare and hinges on an otherwise
weird and awkward distribution. That’s not the case in this position and clearing the 3-point is the
worst of the three choices.

Just listing the virtues and defects of plays (a) and (b) makes it pretty clear that 4/off must be best.
Taking a checker off is both better for the gammon, safer on the next roll, and more likely to keep
White trapped and make him break his board some more. A rollout confirms that 4/off is the best of
all possible worlds: it both wins more games than clearing the 5-point (94.2% to 93.1%) and wins a
lot more gammons (16.7% to 10.7%).

July-1-2019 || Hit Twice or Not?

White – Pips 145 (-15)

Black – Pips 160 (+15)

(a) Black to Play 6-3

White – Pips 145 (-21)

Black – Pips 166 (+21)

(b) Black to Play 6-3
 White – Pips 145 (-10)

Black – Pips 155 (+10)

(c) Black to Play 6-3

Here we see three closely related positions. In each case, Black will enter with his three, hitting,
after which he has to decide on the best play for his six. He can run out of White’s board (with
either 22/16 or 21/15) or he can hit in his inner board with 9/3*, breaking his 9-point in the process.
What we want to know is how, if at all, Black’s structure affects his choice of plays.

When studying backgammon, many players make the mistake of examining only isolated positions.
They play a practice match against the bot of their choice, then ask the bot to analyze the match,
looking for errors. A certain play gets flagged as a serious error. It’s a position where they had a
choice between two plays; the choice seemed hard, but eventually they picked one. The bot says
they should have picked the other one. They look at the position for a few moments, trying to
remember it for future reference, and then move on.

The problem with this method is that it doesn’t teach as much as you think it does. It’s all well and
good to know that in such-and-such a position, play so-and-so was right, but even if you could
remember that factoid, the position and roll may never recur in your games. What you really want is
some insight that goes beyond the specifics of position such-and-such.

A better approach is to use the puzzling position as a starting point, then generate some variations
by moving the pieces around a bit. Give one side an extra home board point and see what happens.
If one side has a stack, unstack the checkers and create a new point somewhere. Sometimes small
changes will have no effect on the outcome, while for other positions, small changes will have a big
effect. Either way, you’ll start to get a feel for the factors that really determine the correct plays.

Now let’s take a closer look at these three positions. Before we discuss the hit/no hit question, let’s
settle the issue of which six Black should play if he elects not to hit. Pretty clearly, it’s going to be
22/16, because the 16-point is within direct range of the 21-point. A checker on the 16-point can be
directly covered next turn with a five or a two, while a checker on the 15-point can only be directly
covered with a three. So 22/16 is going to dominate 21/15.

Now let’s move to the hit/no hit question. Clearly, the most favorable position for hitting twice is
(a). Black’s strong inner board makes a potential attack more powerful, while winning the battle for
the 3-point would reduce White to just an ace-point game. The cube also plays a role here. If Black
hits twice and White fans, it’s a double and a huge pass. If Black hits twice and White enters one
checker on the ace-point or deuce-point, it’s a good double and a take. To hold off the cube, White
has to enter with a three, hitting, or enter both men with a 2-1. Black’s strong potential cube action
next turn makes the double-hit with Bar/22* 9/3* clearly right.

The least-favorable position for hitting twice is (b). Here Black lacks a strong home board, and his
little structure with the 8-point and 9-point made is really all he has. Breaking the 9-point to hit now
risks a lot to gain a little. In the very best case, where White fans, Black has a marginal double/no
double decision and White has a huge take, even with two men on the bar. Entering even a single
checker somewhere is enough for White to hold off the double. Now the double-hit is a clear error
and the simple 22/16 is correct.

Problem (c) is trickier. We’ve moved just one Black checker from White’s bar-point to Black’s bar-
point. Normally reassigning a single checker would make only a small difference in the evaluation.
But here the new checker actually plays a dual role. It helps Black’s attack by being a new builder.
But it also hurts Black’s defense by being a new blot. Now if Black plays 22/16, White has a ton of
hits from the bar. (Note that White has perfect diversification: his hitting numbers, fours and sixes,
are the numbers he can’t use to enter.) So hitting with 9/3* functions for both attack and defense,
and becomes the best play by a clear margin. In fact, the runner-up is now the other double-hit
number, 7/1*.

Keep in mind that in most early and middle game positions, double-hitting will be the default play.
The positions here are a little unusual in that Black has four or five checkers in White’s board,
which make Black’s attacking chances less effective. Position (b) is an especially good one to
remember, in that it shows when switching to a plan of preserving structure starts to dominate the
obvious attacking idea.

uly-15-2019 || Saving a Weak Back Game

 White – Pips 75 (-71)

Black – Pips 146 (+71)

Black to Play 4-4

Black has been playing a 1-5 back game (probably the weakest of all back game formations) and
now faces a roll that messes up his plans even further. With a 4-4 to play, he has to sacrifice
something. He can move off the 24-point, move off the 20-point with one or both men, or try to
keep both back game points and play entirely on his side of the board. Nothing is really appetizing,
but he needs to make the best of a bad situation.

In all variations, his chances of winning are small. His chances of being gammoned are also small.
He needs to balance these two chances, keeping in mind that every extra win balances two extra
gammon losses. (In other words, keeping winning chances alive is twice as important as saving
gammons.) In many such positions, the best play is not the play that wins the most games, or the
play that loses the fewest gammons, but some sort of middling play that achieves the best result
between the two.

Having said all that, let’s look at the reasonable choices.

Play (A): 6/2(2) 8/4 7/3 (or any other play which doesn’t move any back checkers). This is hopeless
and can be dismissed quickly. Keeping both back game points is useless if the home board is gone.
This play reduces winning chances while increasing gammon chances, the very opposite of what
we’re trying to do.

Play (B): 20/4. Running only one checker from the 20-point is the best play to win the game, and it
would be correct in a tournament match at double match point. The checker that stays behind on the
20-point will garner Black a few extra hits, which is good. The play, however, has some liabilities.
The obvious downside is that White has some pick-and-pass numbers which will cost Black a few
extra gammons. A less obvious downside is that the extra shots that Black gets from 20/4 come
quickly, while Black’s home board may still be weak. Rollouts show this play winning 20.5%,
while losing 19.5% gammons. Let’s keep those numbers in mind as we look at the alternatives.
Play (C): 24/16(2). Running off the 24-point is the play to minimize gammon losses, but it
sacrifices a huge portion of winning chances in the process. Without the ace-point to generate long-
term shots, Black is pretty much staking his winning chances on getting a shot immediately. He gets
8 shot numbers on the first turn (1-1, 3-3, 2-1, 3-1, and 4-3) and hits those between 30% and 50% of
the time, depending on just where White leaves the shot. (White’s worst rolls are then 3-3, 1-1, or 2-
1, which give Black 18 shots when White stays on his 12-point.) Black also gets some shots when
White gets safe this turn but still has to clear the 6-point or 7-point. Note also that with Black’s
home board, immediate shots are not necessarily winners.

Rollouts show Black winning a bit less than 10% of the time after 24/16(2), with gammon losses
dropping to about 10% as well. (Many of his gammon losses now come when he hits an immediate
shot but gets hit back.) Compared to Play (B), Black is trading wins for lost gammons at a 1:1 rate,
an unfavorable trade when wins are worth twice as much.

Play (D): 20/12(2). With this play Black simply abandons the 20-point, electing to play an
adequately timed ace-point game instead of a poorly timed 1-5 back game. At first glance this play
looks like a surrender, but it’s not. The ace-five is the weakest of all back games. It gives you some
extra shots as White tries to clear his 7-point and 6-point, but that’s it. As soon as White clears
those points, the position reverts to a straight ace-point game anyway.

Clearing the point now has a couple of additional bonuses: Black now has plenty of time to build a
winning board, and his ace-point game is a little stronger than usual because of the open 5-point he
leaves behind. White will have only a couple of rolls each turn to fill the point, and in all likelihood
it will remain open until he finally clears his 6-point.

Compared to 20/4, rollouts show Black gives up a few winning chances but saves a lot of gammons.
His wins drop by a couple of percent, from 20.5% to 19.0%, but his gammon losses drop more than
6%, from 19.5% to 13.4%. That’s a huge saving in gammons lost, and moves this play to the top of
the list.

Note that running from the 20-point isn’t the best play to win the game (that’s 20/4), or the best play
to save the gammon (that’s 24/16(2)). Instead it’s a well-balanced play, preserving plenty of
winning chances while saving lots of gammons.

Note also that this play will be correct in many other back game situations. That is, if you’re in a
marginally-timed back game and you roll a big double, running off the front back game point will
most often be the right play. It will leave you with a good anchor game (with a gap in your
opponent’s board), preserve what timing you now have left, and save a lot of gammons in the
process.
Aug-01-2019 || Playing a Deuce-Point Game
White – Pips 136 (+23)

Black – Pips 113 (-23)

Black on roll. Cube action?

In this position, White has been reduced to a deuce-point game, and Black is in the process of
bringing his men home and trapping White behind a prime. Black’s made a lot of progress, but
there are still a few hurdles to overcome:

> Black’s open 3-point needs to be filled in before he starts his bearoff.

> The open 7-point is a small nuisance.

> Black still has to clear the 16-point.

Are all these problems serious enough to stop Black from doubling? Or is the 2-point game so weak
that White already has a pass? Before we answer these questions, let’s take a little look at the
structure of the 2-point game itself.
 White – Pips 124 (+53)

Black – Pips 71 (-53)

Black on roll. Cube action?

Position A: Black on roll.

Consider the typical 2-point game in Position A. Here things have gone pretty well for Black. He
brought all his men home, formed a prime, didn’t leave any gaps, and now has about as good a
position as he could want. (True, he’d be happier if the two checkers on his one-point were spares
on his 4-point and 5-point, but let’s not quibble.)

If the cube were still accessible to Black here (an unlikely scenario) the cube action would be
double/pass, and both actions would be clear. However, what’s important to note is that this
position is much better for White than a similar ace-point game would be. In Position A White’s
winning chances are around 20%, while Black’s gammon chances are about 10%. If we put White
into an ace-point game while keeping his position on the other side of the board the same, and give
Black spares on his low points, White’s winning chances remain about 20%, but Black’s gammon
chances jump to about 20%, almost twice the gammon chances in the similarly structured deuce-
point game!

Why is a 2-point game so much stronger than an ace-point game? Basically, it’s much easier for
White to get off the gammon, while still retaining significant winning chances. The obvious reason
for this is that the slightly higher inner-board point gives White more chances to release back
checkers before Black gets all his men home. The more subtle reason is that Black’s ace-point acts
as a kind of suction pump, pulling checkers to it as Black tries to clear higher points. Even when
Black finally clears all the points in front of the 2-point, he’ll find himself with a bunch of checkers
still on the ace-point, requiring a few more rolls to bear off.

Low gammon chances for Black means that White is much closer to a take with the deuce-point
game than in other low anchor situations. Take a look at the next position:
 White – Pips 124 (+50)

Black – Pips 74 (-50)

Black on roll. Cube action?

Position B: Black on roll.

Here we’ve given Black’s game one flaw: the open 5-point. Now a take for White is trivially easy,
and in fact Black’s doubling decision is the question. If White were playing an ace-point game
instead, the open 5-point wouldn’t have much effect and the position would still be a big pass.

Now back to our actual position. Here the big problem is not Black’s open 3-point, but instead
Black’s 16-point. If Black clears this point without being hit, the position will be a pass for White.

Black’s 3-point may look like a potentially big problem, but it’s not. Every turn for the next several
rolls, Black will have a minimum of three useful builders bearing on the point, and if he can bring
builders to the 8-point or 4-point he’ll have even more. The awkwardness of a gap is proportional to
the length of time you have to make it. In Position B, Black has hardly any time to make the 5-
point, so it’s a problem. But in the original position, Black has plenty of time to make the 3-point,
so it’s a very minor problem.

Now our doubling problem becomes pretty straightforward. Black needs to double, because he’ll
lose his market if he clears the 16-point. White’s going to take, because he gets solid chances from
both the possibility of hitting Black in the outfield, and the long-run chances of winning a 2-point
game. Neither possibility by itself is enough, but the combination of the two is plenty.

After doubling, Black needs to clear his 16-point as quickly as possible, so he can go to work on the
3-point with plenty of builders. He should run with any reasonable non-double, such as 65, 64, 61,
53, 52, or 43. He’ll stay with numbers that still play constructively on his side of the board, like 63,
62, 54, 51, and the various small numbers.

g-15-2019 || Playing a Middle Game Blitz

In backgammon, the term ‘blitz’ refers to a position where one side is caught on the bar without an anchor,
and the other side is trying to close him out before he can get in and organize his defenses. If the attacking
side is successful, the result is often a gammon. If the defender can get in, he’ll usually save the gammon
and may quickly take the advantage, especially if his opponent has become overextended. Blitzes are an
important class of positions, and the aspiring player needs to understand them well.

Blitz positions fall into three main categories. The first is the familiar early game blitz, where one side (say,
White) runs out or splits his back men and Black then throws a double, making a couple of inner points while
sending White to the bar. When White dances, we’re in an early blitz situation. Most of these positions are
doubles and takes, although there are exceptions, depending on how many builders are available to continue
the blitz and how many vulnerable checkers the defender has.

Early blitzes can be mastered if you take the time to understand a relatively small number of reference
positions. The best collection of examples is in Chapter 1 of Kit Woolsey’s Backgammon Encyclopedia Volume
1. Learn these and you’ll have the tools to reason out the many early blitz positions that you’ll actually see in
your games.
The second class of blitz positions is what I call the middle game blitzes. As in the early blitzes, one side gets
caught on the bar in an awkward moment while the opponent tries to close his board. Unlike the early blitzes,
however, where the defender hasn’t had time to put together any kind of board, here the defender usually
has some sort of position — perhaps three or four home board points, or even a prime of some sort. Now the
position has to be evaluated not only in terms of the attacker’s assets, but also the defender’s assets, which
may be substantial.

The final category is the late game blitz, where the defender has five or six home board points. These are
also difficult and require careful study.

Middle game blitzes arise relatively frequently, are difficult to categorize or analyze, and the cube swings can
be ferocious because at each roll there will be a few variations that will swing the advantage decisively to the
opponent. Contrast this with holding games, back games, and priming games, which are relatively easy to
categorize, and where decisive moments are often separated by long periods of straightforward plays.

White – Pips 113 (-6)

Black – Pips 119 (+6)

A. Black on roll. Cube action?
Position A is a typical example. We’re late in the game, White is on the bar, and Black has a blitz going.
Black has a three-point board with a fourth point slotted, and a lot of numbers to cover his blot. In fact, of
Black’s 36 numbers, 26 cover his blot (all 4s and 5s, plus 31, 32, 22, and 11), four make a different point in
his board (61, 66, and 33), and one number hits White’s other blot (63). Only 21 and 62 play badly. If Black
does cover his blot, he has plenty of attackers on the 7-point and 8-point to put pressure on the 2-point and
4-point.
Unlike the case in early game blitzes, however, White isn’t toothless. He’s got a three-point board of his own,
Black still has to escape two checkers, and White’s extra blot isn’t immediately vulnerable. So how do we
assess the actual strength of Black’s game?

Unfortunately, there is no easy answer. As advertised, these positions really are difficult, and simply counting
points made or builders available just won’t do the job. The bots handle these positions well, but we humans
make lots of mistakes (and big ones at that). Let’s look at this position and a couple of closely related ones,
see what a bot can tell us, and then try to work our way backward to a more general understanding.

We’ll start with Position A, which is a big double and just a marginal take. Here are the results from
an Extreme Gammon rollout:
Black’s equity if he doesn’t double: +0.66
Black’s equity after doubling: +0.99

Given the fact that White’s board is almost as strong as Black’s, that result might seem a little surprising. It
looks like Black’s large number of builders, coupled with the fact that so many of his numbers actually make
a fourth point, are decisive considerations. But before we jump to conclusions, let’s make a couple of
modifications to White’s position and see what happens.

White – Pips 109 (-10)

Black – Pips 119 (+10)

B. Black on roll. Cube action?
First, let’s take a look at White’s big stack on his 8-point in Position A. That’s a weakness, for sure, but just
how big a weakness? In Position B, we’ve moved two checkers from White’s 8-point to his 6-point, creating a
more normal, balanced position. Here are the new rollout results:
Black’s equity if he doesn’t double: +0.47
Black’s equity after doubling: +0.60

Doubling is still correct by a lot, but now the position is a monster take! That stacked 8-point cost White more
than a third of a point in equity after taking a double.

Another slight weakness in White’s position is the open 5-point. What happens if we fix that?
 White – Pips 119 (=)

Black – Pips 119 (=)

C. Black on roll. Cube action?
For Position C, we did a little shift: we moved White’s 3-point back to his 5-point, improving his home board,
but we restored the big stack on the 8-point. Now let’s look at the rollout results:
Black’s equity if he doesn’t double: +0.42
Black’s equity after doubling: +0.40

Wow. Compared to the original position, exchanging the 3-point for the 5-point improves White’s game by a
whopping 2/3 of a point. Now doubling is a tiny mistake, but the position is actually closer to a beaver than a
pass!

Our takeaway from these rollouts is a little unsatisfying but nonetheless important: in these supersharp
positions, every feature of the position matters a lot. A stack here, a blot there, the exact configuration of
points — everything plays a role in the decision making. For a few well-defined types of positions —
particularly those where the defender has a real prime– we can produce some good rules. For most late
game blitzes however, improvement is more a matter of looking at lots of different positions and gradually
honing your instincts.

Sep-01-2019 || Hit loose or make an anchor?

 White – Pips 168 (=)

Black – Pips 168 (=)

A. Black to Play 3-2
In Position A, Black has two choices: he can enter and hit on the 5-point, or he can enter and make the
anchor on the 22-point. To hit or not to hit: what’s right?
The 5-point is a strong point. In the abstract, it’s the best point there is, so hitting to make the 5-point later is
often a good idea. But making an anchor is a good idea too, and very often correct. If we could only do one
of these good things, we’d do it. But here we can do either but not both, so we have to pick and choose.

These choices in the opening are rarely easy. Some writers try to make them seems easy, with comments
like “Making the 5-point can’t be wrong” or “When in doubt, hit”. When you see remarks that those,
remember that writers have deadlines, and a broad (and wrong) generalization is quicker than a carefully
reasoned analysis complete with counter-examples. (And yes, I’ve done this myself. Mea culpa.)
In reality, these decisions can’t be made in the abstract. They hinge on multiple features of the position, all of
which must be carefully weighed together to make a good judgment. Let’s list the features that come into
play in this position.

Features that favor hitting.

(1) The strength of the point. The more important the point, the more you want to fight for it. In the opening, the
two 5-points are the most important points on the board. That’s a strong argument for hitting with 8/5*.
(2) The strength of your opponent’s inner board. The weaker your opponent’s inner board, the more inclined you
are to hit. Here White has no inner board. Good argument for hitting.
(3) Your opponent’s threats. The more your opponent is threatening to do next turn, the more you want to hit
and take away half his roll. Here White has many rolls that make one 5-point or the other. Strong argument
for hitting.
(4) Your opponent’s structure. By “structure” here I mean features like blots, stacked points, and stripped
points. Weak structures take time to repair, and hitting removes some of that time by taking away half a roll.
White’s blots on the 10-point and 11-point coupled with his stack on the 6-point provide a strong argument
for hitting.
Features that favor making the anchor.
(1) The strength of your inner board. The stronger your board, the more you want to hit, as your opponent may
dance. Here you have no inner board. Good argument for making the anchor.
(2) The likelihood of getting hit back if you hit. After playing Bar/23 8/5*, White has 25 numbers that hit back:
everything except 6-1, 6-2, 6-3, 6-4, 6-6, and 2-1. That’s a good argument for not hitting.
The preponderance of positional factors favors the natural play of hitting. The 5-point is very important,
White’s board is weak, and White’s rolls all play very well if Black doesn’t hit. Not surprisingly, rollouts back
up the hitting play by a solid margin.

To see the position more clearly, however, let’s make a couple of small changes and see what happens.

White – Pips 166 (-2)

Black – Pips 168 (+2)

B. Black to Play 3-2

In Position B, we’ve given White his 5-point and eliminated the stack on his 6-point. Not only is White’s board
stronger, but White’s blots are somewhat less vulnerable, and his structure is vastly improved. In addition,
White has fewer actual threats (since he’s already made his 5-point) and thus your need to hit is less. Apart
from the importance of Black’s 5-point itself, all the factors in favor of hitting are reduced, and now making
the 22-point anchor is the only reasonable play, while hitting is just a blunder.
 White – Pips 167 (-1)

Black – Pips 168 (+1)

C. Black to Play 3-2

In Position C, we made only one small change: we left the inner boards alone and instead connected White’s
two outfield blots on the 10-point. This modification changes only two of the features that affect our desire to
hit: White has fewer threats, so we have less need to hit, and White’s overall structure is better, making him
less exposed by a hit, which in turn also reduces our desire to hit. The effect is less dramatic than in B, but
it’s enough; making the anchor with Bar/22 24/22 still becomes correct by a small amount.

These three positions illustrate a key point about opening play: you must consider the position as a whole.
Black’s 5-point is important (very important in fact), but its importance isn’t the only factor driving a hit-or-no-
hit decision. You have to look at all the checkers, and see just what they’re trying to do and how they
interrelate to each other. Ostensibly similar positions can have very different answers.

Sep-15-2019 || An Early Blitz

Sep 15, 2019 | Backgammon Problems: Blitzes
 White – Pips 179 (+44)

Black – Pips 135 (-44)

Black to Play 6-4

In this game Black launched a blitz after a few moves were made on both sides, and now White is
in serious trouble with two men up in the air facing a four-point board with more blots floating
around. Black’s 6-4 gives him several excellent options; his job now is not to get too excited, but to
just find the most efficient way to bring the game home.

In this position Black has three goals. Without trying to assess their relative importance, here they
are:

(1) Close the 5-point. Closing the ace-point would also be nice, but Black won’t have the
ammunition in place to do that for some time. With a small double, he’ll cheerfully switch points,
but otherwise the ace-point will have to wait. (The most likely outcome of this position is in fact a
well-timed ace-point game.)

(2) Pick up blots. Hitting more blots helps in several ways. The extra blots hit obviously lead to
both more gammons and more backgammons. Hitting more blots also buys time to escape the back
checkers before White can get everybody in from the bar. Finally, hitting blots eliminates potential
builders and slows down White’s ability to put his position back together once he enters.

(3) Escape the back checkers. The sooner Black can extricate his back checkers, the sooner he
avoids a potential disaster scenario: White enters both checkers from the bar, and Black is caught
with blots in the outfield to pick up as well as refugees in White’s inner board that need to get out
quickly.

Now let’s look at Black’s possible plays. He has a bunch, some of which emphasize one goal only,
while others are more balanced.

Play A: 21/17* 24/18: The “Get-out-of-Dodge” play, this strongly favors escaping and hitting.
Black picks up one blot now while generating a double shot at the last outfield blot.
Play B: 13/7 13/9: This “Close-him-out-quick” play ignores the blots while creating three builders
for the 5-point, as well as some numbers which might be used to hit on the ace-point if White fans.

Play C: 24/14*: This play hits the blot that’s hardest to hit, while escaping the checker that’s
hardest to escape.

Play D: 21/17*/11: Hit-and-Build #1 puts a third checker up while creating another builder for the
5-point.

Play E: 21/17* 13/7: Hit-and-Build #2 creates a different builder for the 5-point which also shoots
at the ace-point. In addition, Black still has a direct shot at the blot on the 14-point.

Before we discuss the merits of the three approaches, we can prune our list a bit. It’s pretty clear
that Play E, with a builder on the 7-point, dominates Play D, which puts a builder on the 11-point.
The builder on the 7-point not only aims at the 5-point but also aims at the ace-point, while serving
as a slot for the bar if White starts to enter and Black decides he needs a prime. So we can eliminate
play D.

Now let’s compare Play A and Play C. Both involve 24/18. Do we then prefer 18/14* or 21/17*?
Since neither play puts a builder in position for the 5-point, 21/17* looks better, escaping a checker
and getting some additional shots. So we’ll drop play C from our list of candidates.

With those two eliminations, we’ve reduced our list of possibilities to three: Play A, the best for
escaping the back men; Play B, the best for closing the 5-point; and Play E, the best for making
progress on both fronts. Now what?

In the pre-bot era, the standard play here was Play B, 13/7 13/9. The idea was that closing the 5-
point was crucial, after which Black could pick up the blots at his leisure. While playing two
checkers down didn’t actually give that many new numbers for closing the 5-point, it did make
Black a big favorite to hit loose if White entered, after which White would be an underdog to hit
back, while Black would then have multiple cover numbers if White missed. In a high-stakes
chouette in the 1980s or 1990s, this play wouldn’t even have generated much discussion — with
two on the bar, building the board quickly was thought to be paramount.

One of the first lessons we learned from the early bots was that hitting was a big deal no matter how
many men were on the bar. Every blot hit represented more gammons won, and if the gammon was
in the bag then each blot hit started increasing the backgammon count. The problem with building
plays is that blots are never as easy to hit as they appear to be. If you have a hit now but you pass on
the hit to make a structural play, you may never get another chance to hit. In this problem, for
instance, bringing down more builders is always trivially easy, but hitting never will be.

If we eliminate the building play and focus on the two hits, then 21/17* 13/7 dominates 21/17*
24/18. While we don’t want to sacrifice hitting for building, we also can’t ignore building, because
our life will get a lot easier if we prevent White from making our 5-point. In addition, a blot on the
7-point is a fabulous multi-purpose blot: it’s simultaneously a builder for the 5-point, an attacker for
the ace-point, and a slot in case White makes our ace-point and we need the bar-point for control.

To see the power of hitting, take a look at the wins/gammons distribution after an Extreme
Gammon rollout:
– Overall G/BG
– Win % Win %

21/17* 13/7 79.5 63.6

21/17* 24/18 79.1 62.2

21/17*/11 79.2 60.6

24/14* 78.8 61.0

13/7 13/9 78.2 60.7

Although the numbers are relatively close, notice that the non-hitting play scores lowest in overall
winning percentage and almost tied for last in gammon/backgammon percentage. Hitting is the road
to winning more gammons, which is fairly obvious; but it’s also the road to winning more games,
by keeping White on the bar longer allowing Black to get his army home.

How do things change if Black is closer to getting home? Take a look at these three related
positions.

White – Pips 179 (+58)

Black – Pips 121 (-58)

Black to Play 6-4
Problem B: Black to play 6-4

In (B), we’ve moved Black’s rear checker from his 24-point around to his 10-point. Black’s game is
now much stronger, both because he’s closer to closing his 5-point, and he doesn’t need to worry
about escaping the back checker. How does this change the relationship between 13/7 13/9 and
21/17* 13/7?
Actually, it makes the hitting play stronger! With only one checker back, hitting anybody has
become relatively more difficult, so the value of hitting has risen. And as the number of checkers
aimed at the 5-point rises, the relative value of adding yet another builder shrinks. So 21/17* 13/7
now dominates 13/7 13/9 by an even wider margin.

White – Pips 179 (+65)

Black – Pips 114 (-65)

Black to Play 6-4
Problem C: Black to play 6-4

The trend continues in (C), where we’ve moved a checker from Black’s midpoint to his 6-point.
Now 13/7 will put a fourth builder in place, so the gain from a fifth builder (with 13/9) is tiny. Once
again 21/17* 13/7 is right, and both 21/17*/11 and 13/7 13/9 are big blunders.
 White – Pips 179 (+67)

Black – Pips 112 (-67)

Black to Play 6-4
Problem D: Black to play 6-4

If we move enough checkers around, eventually new ideas start to appear. Here we’ve put another
checker in place, on Black’s 11-point. Once again, 21/17* 13/7 dominates two down, as we expect.
But now a new contender rises from the ashes. Hitting on the ace-point with 11/1* now beats out
21/17* 13/7 for top place. The value of preventing White from establishing any anchor is huge as
long as there are cover numbers in place.

Oct-01-2019 || Pay Now or Pay Later

Oct 1, 2019 | Backgammon Problems: Holding Game
 White – Pips 138 (+59)

Black – Pips 79 (-59)

Black to Play 5-1
This position shows White playing a well-timed holding game while Black is struggling to clear his
points and get his men home. Black leads in the race by just over 60 pips, so it’s always been highly
likely that he’s would have to leave a shot or two unless he rolled a useful set of doubles. Now
Black has reached his first key decision point. Out of spares, he can still play safe, but he may not
want to.

With the 5-1, Black has just three reasonable plays. Let’s take a look at them.

Play #1 is simple and safe: 6/1 6/5. Black avoids leaving a shot, but his board gets weaker and he
still has two outside points to clear. Unless he rolls a double next turn, he’ll leave a shot somewhere
with all his big numbers except 6-3 and 5-3.

Play #2 is 13/8 and 3/2. Black volunteers a double shot, but keeps his board and clears the most
difficult point. White has a lot of shots: all fours, all ones, plus 2-2, 3-3, and 6-3, a total of 24. If
Black doesn’t get hit, he’s got a reasonable chance of getting his blot on the 13-point home, after
which he’s a solid favorite to clear his remaining points. If he does get hit, he’s got some chance of
getting in and getting out, since White isn’t positioned to make his 3-point quickly. Clearing the
midpoint now is the high-risk, high reward play.

Play #3 is the in-between play: 8/3 8/7. Black leaves only 11 shots, but loses his landing spot and
leaves the midpoint checkers a bit stranded. Black takes a small risk to keep his inner board, and
gives himself another turn or two of timing (if he’s missed) before he has to make the tough
decision regarding his midpoint.

What we have is what’s generally called a “pay now versus pay later” problem. Black can take a
chance now to reach a playable position, or wait, see if he rolls a double, and pay later if he has to.
Before we try to balance Black’s plays against one another, let’s step back, think about the different
features of the position, and see how they affect the play we want to make.
Guidelines for Pay Now/Pay Later Problems

Pay now/pay later problems are rarely easy. A lot of different features of the position affect the
decision-making, and balancing them against one another can be very hard. Let’s start by making a
list of the features we really care about, and see if they favor one play or the other.

(1) How many shots? A play that pays now and volunteers a shot is better if it doesn’t leave much
more than a single direct shot. Here 13/8 3/2 leaves 24 shots. While 8/3 8/7 leaves only 11 now, the
ultimate cost of that play is some much higher number, since the midpoint remains to be cleared.
Leaving 24 shots is a lot, so this feature favors playing safe.

(2) What about White’s board? The weaker White’s board, the more inclined you are to pay now.
This is the feature that beginners tend to overlook. They see getting hit as a disaster in itself,
whereas it’s only really bad if White can easily contain the checker. If White’s board has a blot, or a
high open point, Black should often volunteer the shot. Here White’s board is pretty good – not
perfect, but he has no blots and he’s made the 4, 5, and 6-points. This feature also favors playing
safe.

(3) Is White’s position improving or deteriorating? If White’s game is improving, you’d rather pay
now, before his structure gets even more dangerous. If his game is likely to deteriorate, you’d rather
wait and play safe. Here White has a fine position, but if he has to move, he’ll give up something.
Rolls containing an ace are especially hard for him to play. This feature favors playing safe.

(4) Is playing safe constructive or destructive? A safe play which actually improves your position
will almost always dominate any play that leaves a blot. Here playing safe is destructive, but that’s
the usual case in interesting problems.

(5) Do you have real gammon chances? In any normal pay now/pay later problem, Black will be
well ahead in the race. If Black is so far ahead that winning a gammon is a real possibility, then
playing safe and destroying the home board will decrease gammon chances simply by wasting pips
and allowing White to pick up crossovers. This is a minor point which might serve as a tiebreaker in
some unusual positions. It’s not relevant in this position where Black’s gammon chances are in the
12% to 15% range, which is a sort of normal background reading.

The most important features to weigh are (1), (2), and (3), and here they all point toward playing
safe. The right play, by a solid margin, is 6/1 6/5.

Having solved the main problem, let’s get a little more experience in pay now/pay later situations
by taking a look at a few riffs on the main theme.
 White – Pips 137 (+58)

Black – Pips 79 (-58)

Black to Play 5-1

Problem A: Black to play 5-1.

We’ve made one tiny change here, changing White’s spare checker from a builder on the 4-point to
a blot on the 3-point with no cover numbers nearby. That change, however, is enough to swing the
position completely, and paying now with 13/8 3/2 is massively correct. If Black gets hit he now
has a 13-number shot at the blot on the 3-point. Combine the inner-board blot with Black’s 5-point
board and White’s resulting outfield blots, and suddenly getting hit doesn’t look quite so costly for
Black.
 White – Pips 151 (+72)

Black – Pips 79 (-72)

Black to Play 5-1

Problem B: Black to play 5-1.

Here we’ve taken away the blot but moved White’s open point to the 5-point. Paying now with 13/8
3/2 is now about equivalent to playing safe. Black will have a lot of chances to come in on the 5-
point if he’s hit, but White will be careful about leaving blots, so Black won’t pick up quite so many
loose gammons.

White – Pips 129 (+50)

 Black – Pips 79 (-50)
Black to Play 5-1

Problem C: Black to play 5-1.

Here we’ve broken White’s midpoint and given him a couple of builders for the 3-point. This is a
more common sort of structure in actual play, and the changes all favor paying now. Playing 13/8
13/12 leaves only 16 shots, compared to 24 in the original problem, and White’s position is now
improving, as he’s getting ready to make his 3-point. Breaking the midpoint now dominates playing
safe by a wide margin.

White – Pips 124 (+39)

Black – Pips 85 (-39)

Black to Play 5-1

Problem D: Black to play 5-1.

Here we’ve made several changes to the original position, many of which favor paying now.

> White has a blot on the 3-point (strongly favors paying now.)

> White gets only 16 shots after 13/8 13/12 (slightly favors paying now.)

> White has a dead checker on the 2-point (slightly favors paying now.)

That’s a lot of reasons to pay now, but there’s one item on the other side of the ledger: Black has a
constructive use of his 5-1. (He can make his ace-point.) Being able to make a useful play is so
important that 6/1 2/1 is about equivalent to 13/8 13/12.

One last comment before we call it a wrap. Notice that in none of these examples was breaking the
8-point the best play. (It was sometimes the second-best play.) That’s because breaking the 8-point
is really a pay now and pay later play. Once you lose the 8-point, you’re likely to have to leave
another shot breaking the midpoint, and you’ve only bought yourself perhaps one extra turn to roll a
double.

Oct-21-2019 || Playing a busted back game

Oct 21, 2019 | Backgammon Problems: Back Games

White – Pips 77 (-109)

Black – Pips 186 (+109)

Black to Play 6-2
In this position Black finds himself at the tail end of an ace-deuce back game. Things seemed
promising for a while, then not so good, then downright awful. Now, with seven men trapped
behind a full prime and his board completely shot, Black has a 6-2 to play.

As problems go, this one is pretty easy. The correct answer is just 3/1, building a three-point board,
leaving a fourth point slotted, and remaining with just one completely dead checker. White will
certainly break his prime next turn, and if Black can roll a six before he rolls a three, he’ll release a
checker and have a reasonable chance to play the rest of the game with just one man out of play.
His idea will be to build his board from the back, making his 4-point and bringing builders to his
11-point and 12-point, bearing on the 5-point and 6-point. With some luck, he’ll hit a checker, and
with some more luck, he’ll actually close it out, saving the gammon and perhaps winning the game.

The 4/2 play has a different idea. Black wants to leave his 1-point open but slotted. He plans to fill
in the high points in his board, while leaving the blot on the ace-point permanently uncovered.
Hopefully he’ll hit White and White will roll some aces as he reenters, allowing Black to recirculate
the extra checkers on the 2-point and 3-point. Eventually, Black will build a prime, White will enter
and expose a second checker, and Black will hit it and double White out.

It should be pretty easy to see that Plan 2 is very farfetched compared to Plan 1. We have a name
for this: FPS, or ‘Fancy Play Syndrome’. FPS can get you gammoned a lot, so avoid it when you
can. Black doesn’t need to catch a second checker to win; with some luck, one checker will be
enough. True, it may be an ugly win, but ugly is OK. When you win ugly, they still have to pay you
the prize money.

Although the position may seem trivial, it yields several worthwhile ideas to note.

Idea #1: Although Black’s game looks hopeless, rollouts indicate that his winning chances after 3/1
are about 15%. That’s a non-trivial number, so even if you find yourself in such a position, you
need to keep playing hard and try to extract all the value you can.

Idea #2: In the absence of objective data, groupthink can overwhelm reason, even among a
collection of highly-skilled experts.

If you had presented this position as a problem to a roomful of tournament players back in the early
1980s, you would have gotten an interesting reaction. The beginners and intermediates would all
have played 3/1. Why not? It’s obvious, right? But all the world-class players (myself included)
would have played 4/2. The idea that Plan 2 was both sophisticated and correct was so ingrained at
that point that no one questioned it. The position actually comes from a match of that period, in
which one of the best players in the world played 4/2, his opponent agreed with the play, and the
transcriber, who later wrote a book about the match, thought 4/2 was so clear that in the manuscript
he didn’t even consider it worthy of a comment!

Idea #3: Rollouts can’t solve this problem. I think Plan 1 is the correct plan, and both Snowie and
XG agree. Setting up a rollout won’t help, however, because when you force the bot to play 4/2 on
its first move, it will subsequently cover the 1-point as soon as it can with any ace or deuce. So if
Plan 2 had merit, the rollout wouldn’t find it. For more on this idea of positions requiring long-
range plans that might not be solvable by the bots, see Mike Corbett’s interesting book
Backgammon Problems.

Nov-01-2019 || A Tactic Against a Back Game

Nov 14, 2019 | Backgammon Problems: Back Games, Uncategorized
 White – Pips 190 (+68)

Black – Pips 122 (-68)

Black to Play 5-2

In this position Black has established a solid grip. He’s escaped all his back checkers, built his 4-
point and his 7-point, and leads the race by 68 pips (122-190) before rolling.

If Black has accomplished all that, then White probably hasn’t done nearly as well, and in fact he’s
stuck in a 2-5 game with an as yet undeveloped front game. Some players refer to the 2-5 as a back
game, but I think of it more as a hybrid between a back game and a holding game. The 2-5 game
can’t really be primed, so White never has any trouble recirculating checkers, effectively
eliminating the main strategy for busting a back game. The flip side for Black is that the 2-5 game
won’t generate nearly as many shots as a pure back game, so Black’s in less danger of being hit.

Did Black miss a chance to double before his roll? No, not at all. While he has an edge, he still has
plenty of work to do: he needs to fill in the 3-point and clear his midpoint, for starters. While he’s
doing all that, White will be filling in his home board. Although White’s position looks weak now,
it will be much more formidable when the crisis comes a few moves down the road. But the
simplest way to see this isn’t a double is to note that Black doesn’t have any market losers. No
matter what he throws (5-3 is probably his best shot) White will still have a take next turn. If your
opponent is always taking next turn, there’s no need to double this turn.

So what should Black do with his 5-2 roll? The obvious play is 13/8 6/4. It leaves no blots,
continues the process of clearing the midpoint, and creates a third builder for the 3-point. Black’s
ongoing plan will be to bring down more spares, make the 3-point naturally over the next few rolls,
clear the midpoint, and find a good spot to double. Most players would choose this route, and it’s
perfectly sound.

A better choice, however, is the slotting play: 8/3 6/4! Black needs the 3-point badly, and while he’s
likely to make it naturally over the course of the next few moves, he may not. Slotting gives him by
far the best overall chance to make the point. It’s also much safer than it looks, since White should
only hit if he rolls 1-1. With any other ace (even 3-1) White should just make his 5-point and keep
building.

It’s easy to overlook these plays because it appears that Black will make the point naturally at some
time in the future. That’s never guaranteed, however, and if your opponent’s position is weak
enough then slotting the needed point will often be the right play.

Nov-15-2019 || Playing the Containment Game

Nov 15, 2019 | Backgammon Problems: Endgames

White – Pips 35 (-56)

Black – Pips 91 (+56)

Black to Play 2-1

Let’s suppose you hold an anchor in your opponent’s board. Dutifully you hang on and wait for
your shot. The shot comes and you hit it. Huzzah! Now what?

In 501 Essential Backgammon Problems, I divided the game after hitting a shot into two big
categories: the Containment Game and the Post-Ace-point Game. The goals of the containment
game phase are these:

1) Arrange your men to best contain the opposing checker.

2) Build a full 6-prime.

3) Roll the prime all the way home until your board is filled in.

4) Bring your remaining spares to good points.

After you fill in your board and bring in your spares, you graduate to the final phase, the post-ace-
point game, where you actually bear off your checkers. Most recube decisions will come in this
phase, although you might have recube decisions in containment games, depending on exactly how
many men your opponent managed to bear off.

In this position, we’re in Part 3 of the containment game. Black built his 6-prime and has rolled it
almost all the way home. Now he has a 2-1 to play, which gives him lots of choices. What’s he
trying to do in this position? Let’s look at a few guidelines for Black.

Rule #1: Don’t break the 6-prime! This rule is crucial. The 6-prime has eliminated any danger of
losing a gammon, and once you break it you’ve turned the gammon danger back on. You want to
avoid plays like 7/5 12/11 or the super-fancy 2/1 19/17. To see why these plays are bad, look at
Rules 2 and 3.

Rule #2: Slot and cover. This is the basic game plan once you have six points in a row. Slot the
front of the prime with a spare, then bring up more spares and cover, while keeping the full prime
intact. Repeat the process until you’ve moved the whole prime home. In this position, for instance,
you would have slotted the ace-point if you had rolled a five. If White rolls an ace and hits, you just
bring more checkers around until you can hit again.

This process is so likely to succeed that there’s no need for a play like 7/5 12/11, which creates a
third builder for the 1-point while giving White a possibility of escaping with 1-6; you have plenty
of time and your plan is easy to implement, so why take any unnecessary risk?

Rule #3: Don’t be overly concerned about hitting the second checker. There is a possibility of
Black’s hitting a second checker in this position. White could enter with an ace, and then roll
another ace, and then another ace, and Black could hit on the ace-point, and White could
immediately hit back, and Black could then roll a deuce — you get the idea. Fuggedaboutit! There’s
a much better chance that as you tiptoe around, neglecting to close your board while waiting for
White’s aces, you roll some horror shot that messes up your plan entirely. If you can close your
board, you’ll be about 60% to win. That’s good enough. Keep the main chance in mind and pursue
it.

Rule #4: Watch how 4-4 and 5-5 play. When you can’t slot your 1-point yet, you’ll need to bring
your remaining spares closer. As you do, keep track of how 4-4 and 5-5 play. You don’t need to
worry about 6-6 and 3-3, because those numbers will close the 1-point. But 4-4 and 5-5 could prove
awkward. Try to arrange your spares so that ideally either number will get a checker to the ace-
point.

In this position Black is fortunate that two different plays will work: either 19/17 12/11 or 12/9 will
slot the one-point after 4-4 or 5-5. I prefer 19/17 12/11 for two reasons: after 5-5 the play will
actually make the ace-point, and the play leaves the two spares farther back, which results in a little
more flexibility on subsequent rolls.

Dec-01-2019 || Playing a Random 6 from the

Bar
Dec 3, 2019 | Backgammon Problems: Early Game
 White – Pips 168 (=)

Black – Pips 168 (=)

Black to Play 6-2

This position shows a typically awkward moment in the early game. Black’s game is temporarily a
little loose, and now he throws a 2-6 from the bar.

Sometimes a six from the bar will allow us to do something obvious and good, like hitting a blot or
building a point. When we can’t do anything good, we’re usually faced with a choice among several
unappetizing alternatives. That’s the case here. We have four legal sixes: 8/2, 13/7, 21/15, and
22/16. None look great, but we have to pick one. Let’s set up some guidelines and see if they can
lead us to the least unappealing six.

(a) Minimizing shots and blots. If the race is close, simply cutting down on our blots and our
opponent’s shots will be a worthy goal. This is especially true if the roll has left us with a bunch of
blots and no anchor.

(b) Staying out of the “zone”. The “zone” is the six-point range from your opponent’s 4-point to
his 9-point. Those are the points your opponent is most eager to make, as well as the best place for
him to establish builders. If you’re helpless and your opponent is looking to land a big punch,
staying out of the zone minimizes what he can do.

(c) Staying connected. All else being equal, you’d rather your checkers were connected (within six
pips of each other) than not. That way, you’re threatening to link next turn, as well as getting some
extra return shots if your outside checker gets hit but your inside checker doesn’t.

(d) Seeing how your opponent’s doubles play. When plays are close, take a careful look at how
your opponent’s doubles play. How many are crushing? How many just improve his position
slightly? A big swing in how the doubles play could be a deciding factor. The medium doubles
(twos, threes, and fours) are the ones to watch here. Double aces will usually just make a single
inner point, while double sixes and fives move a lot of freight but generally won’t hit a lot of blots.
Having said all that, let’s look more closely at our four legal plays.

Play 1: 8/2. If you even considered this play, your game needs some work. If you want to create a
fourth blot, then at least start a valuable point (with 13/7) rather than the weak 2-point.

Play 2: 13/7. Better than 8/2, for sure, but still the wrong idea. Backgammon strategy is replete with
useful bromides which aren’t infallible but which will point you in the right direction most of the
time. “Don’t slot while split” is one of the best of these. When you slot a key point, you’re hoping
your opponent misses you, after which you can use your whole roll to cover. If your back checkers
are split or you have blots strewn around, he’ll use his misses to hit other checkers, and your
chances of covering the slot will be greatly reduced. In this position Black is already flailing, with
three blots and no anchor. Another blot won’t help your cause.

Plays 3 and 4: 22/16 and 21/15. These two plays are the real contenders. The good news is that
neither exposes a new blot; the bad news is that both step out into a double shot in the outfield. To
decide between them we have to go beyond general principles and start looking at specific rolls,
counting shots and jokers.

Moving 22/16 has the benefit of connectivity. Because the 21-point and the 16-point are within five
pips of each other, Black will have some return shots when hit, as well as the possibility of making
the 16-point if White whiffs entirely.

When we start counting shots, however, 21/15 starts to look better. Here’s a quick rundown:

Outfield shots: Playing 22/16 leaves 25 outfield shots (all 4s and 5s plus 31, 32, and 22). Playing
21/15 leaves only 22 (all 3s and 4s plus 21).

Double-hits: Ignoring the double-hits which hit on White’s 2-point, we get 9 double-hits after
22/16 (54, 52, 42, 55, 44, and 22). Playing 21/15 gives just 7 double-hits (54, 53, 43, and 33). In
addition, the double-hits are much weaker after 21/15 because White is hitting outside the “zone”,
while the double-hits after 22/16 are occurring inside the zone.

Jokers: By jokers I mean crushing doubles. There are two after 22/16 (44 and 22) but only one after
21/15 (33). In addition, the 33 joker after 21/15 is less effective because the 3-point is deeper in
White’s board.

Looking at the actual rolls shows that 21/15 is somewhat safer for Black than 22/16, because White
has fewer hits and the hits are a little less dangerous. The connectivity after 22/16 matters
somewhat, but it’s really more of a tie-breaker in positions where the danger from the two plays is
about equivalent. With all Black’s exposed blots, immediate safety is the trump card here.

Dec-15-2019 || Running off an Anchor

Dec 16, 2019 | Backgammon Problems: Holding Game
 White – Pips 67 (-22)

Black – Pips 89 (+22)

Black to Play 5-3

One-way holding games are, for the most part, pretty easy to play. You hold onto your anchor,
watch your opponent try to clear points, wait for a shot, and then hopefully hit it. Alternatively, you
roll a 6-6 or 5-5 somewhere in this process and move into a race where you’re close to even or
maybe a little ahead.

The tough decisions come when you hold onto your anchor but start to run out of moves that
improve your home board. You’re still behind in the race, but not so far behind that racing is
completely hopeless. Now you throw a number that give you some options: you can stay for a last-
ditch shot, break contact and run with both men, or run with one man. How do you decide?

There are no hard and fast rules for these positions (that I know of, at least) but there are several
features that you’ll want to consider before making your play. Put them all together and you should
be able to come to a good answer. Let’s take a look at the key features and how they apply to this
position.

(1) The race. Obviously, the further behind you are in the race, the more incentive you have to stay
and get a shot. Evaluating the race, however, can be tricky. In “normal” racing positions, we often
resort to the 8-9-12 rule for a quick approximation: double if you’re up 8%, redouble if you’re up
9%, and pass if you’re behind more than 12%. Here however, the pip counts after Black plays will
be 67 for White and 81 for Black, with White on roll. Can we easily convert that pip count into
winning chances?

Actually, we can. Let’s start with a useful table. It shows the winning chances in a straight race
where the leader has about 70 pips (a so-called “medium-length” race) and the trailer is behind by
15% or more, with the leader on roll. The table assumes that both sides have well-structured home
boards (no gaps or big stacks) and the trailer has a couple of more crossovers than the leader.
Trailer is behind by 15%, leader on roll with about 70 pips:
Trailer’s chances are in the 19% to 20% range.

Trailer is behind by 20%, leader on roll with about 70 pips:

Trailer’s chances are in the 14% to 15% range.

Trailer is behind by 25%, leader on roll with about 70 pips:

Trailer’s chances are in the 10% to 11% range.

Trailer is behind by 30%, leader on roll with about 70 pips:

Trailer’s chances are in the 8% to 9% range.

(This is a good table to commit to memory. While it helps in this position, it’s especially useful in
tournament matches where you’ve entered a race with a lopsided score. When the player winning
the race also has a big lead in the match, he’ll often be able to use his match equity tables to
calculate a doubling point. The table above will then let him see what racing edge corresponds to
the advantage he needs.)

Here White has a pip count of 67, and he’ll lead by 14 pips (21% of 67) if Black runs. Since his pip
count is a little less than 70, and his lead is a little bigger than 20%, we can look at the table and
guesstimate Black’s chances in a pure race at about 12%.

We need to massage that number a bit more however, because the table assumes a race with well-
structured home board and no gaps or big stacks. In this case, White has two gaps, one on the 3-
point and one on the 5-point. The severity of a gap is related to the number of checkers White still
has to bring in and whether he has time to use small numbers to fill them. Here White has only three
outside checkers, so as he brings them in he won’t have a lot of spare time to be gap-filling. A good
general rule is to add a couple of percent to the trailer’s chances for each gap. Here that raises
Black’s chances from 12% to about 16%. That number actually squares well with the rollout results
after 20/17 20/15, which put Black’s chances at 16.5%.

(2) Pointing numbers and pick and pass numbers. If Black decides to run with just one checker,
he has to pay attention to how pointing numbers and pick and pass numbers play. Are there a lot of
these numbers? How would they play if Black ran with both men? How would they play if Black
stayed with both men?

In this case White has four pointing numbers (2-2, 1-1, and 2-1) as well as eight pick and pass
numbers (1-3, 1-4, 2-3, 2-4). Note that with the exception of 2-2, these are all White’s bad racing
numbers. If Black runs with both men, these are the numbers that start to let Black back in the race.
If Black stays with both men, these numbers don’t play badly.

(3) Hitting chances. Suppose Black thinks his racing chances are just too small and stays with both
men. What are his chances of getting a shot, hitting a shot, and then winning?

Next turn White has no chances of leaving a shot. If White moves one checker off his 7-point, but
keeps four checkers on his 6-point, then he’ll leave a shot on his second turn with just two numbers
(6-2, 5.5%). Black then hits about 30% of the time, or 1.5% overall.

If on his second turn White has two checkers on his 7-point and three on his 6-point, he has a total
of five shot numbers (6-6, 5-5, 4-4, and 6-2, 13.8%). Black will again hit about 30% of the time, or
about 4% overall. But White only reaches this situation after rolling 6-5, 6-4, or 5-4 on his first turn.
All told, Black’s chances of hitting a shot after hanging around for two turns are a little over 2%.
Does hitting a shot win? Not really. Consider the following fabulous sequence for Black:

Black 5-3: plays 6/1 5/2

White 5-2: plays 7/2 4/2

Black 4-3: plays 5/1 4/1

White 6-2: Plays 7/1 6/4, leaving a shot

Black 3-2: plays 20/18*/15

If White now flunks, it’s a double and a marginal take/pass for White. But if White enters, Black is
only even money or a little worse.

We can now put the whole picture together pretty clearly. Running one checker is out, both because
the pointing numbers and the pick-and-pass numbers turn White’s worst throws into great throws,
and because Black’s hitting chances are so small anyway. But staying with both checkers is out
because you’ll need to stay for two turns to get a small number of shots, while your racing chances,
which are currently pretty reasonable at 16.5%, go down the drain. So go with both.

Jan-01-2020 || When to Break a 6-Prime

Jan 1, 2020 | Post-Ace-Point Games

White – Pips 32 (-96)

Black – Pips 128 (+96)

Black to Play 4-5

In our blog post of November 15 we discussed the various stages of a containment game, and
outlined some rules for guiding your play. Leading off the rules was an important one: Don’t break
your 6-prime!
But in backgammon, practically every good rule has a few exceptions. Keeping your 6-prime intact
is very important when you have little or no chance of picking up a second checker. In that case,
you use the ‘slot-and-cover’ method to methodically roll your prime around the board. Once your
opponent leaves a new blot exposed, however, you’re going to need to make an effort to pick it up,
and that may involve breaking your prime, sometimes in very odd ways.

In this position White has exposed not one but two checkers in his home board. If Black makes a
straightforward play like Bar/20 19/15, White will get a chance to roll a deuce and consolidate his
position. If Black wants to hit a second checker, he needs to strike now, either with Bar/20 7/3* or
Bar/21 8/3*. Either play may force White to hit back, giving Black a shot at the two loose White
checkers.

How important is hitting a second checker? Very. If Black closes out just one checker, and arranges
his spares on favorable positions, he’ll be a bit over 40% to win. (White already has nine men off,
remember.) But if Black can hit two checkers and close his board, he’ll be about 88% to win with
his spares well-placed. (In fact, after hitting two checkers he won’t even need to close his board to
double. His proper doubling point will come much sooner.) That’s a huge swing, so Black should
be willing to take big chances to get the second checker.

Both hitting plays are good. Hitting with 7/3* leaves more shots (18 to 16), but this isn’t a
disadvantage because Black wants to be hit before White has a chance to consolidate. To see which
hit is better, we need to notice a subtle tactical point. Imagine that White now enters from the bar
and jumps, hitting only Black’s blot in the outer board. (This happens if Black played 7/3* and
White responds with 6-1 or 5-2, or if Black played 8/3* and White responds with 6-2.) If Black
played 8/3*, he now has 20 return shots: all ones and threes. But if he played the correct 7/3*, he
has 27 returns: all ones and threes, plus 6-6, 6-2, 5-2, and 4-2. That’s a big swing on White’s most
dangerous throws, where he actually gets to Black’s outer board. Train yourself to actually count
shots in critical variations, and you’ll pick up some subtle plays that others would miss.

Jan-15-2020 || Playability
Jan 15, 2020 | Backgammon Problems: Middle Game
 White – Pips 123 (+7)

Black – Pips 116 (-7)

Black to Play 3-2

This position comes from the late middle game. White is on the bar without an anchor, falling
behind in the race and in some danger of being closed out. Meanwhile Black has a couple of
checkers stuck behind a 4-prime. Black needs to escape but he needs to close his board as well, so
he’s under constant pressure each turn to get something done.

Black throws 3-2, which isn’t much of a roll – he can’t cover and he can’t escape. He has only two
plausible plays:

Play A: 8/5 8/6, dismantling the 8-point but creating cover numbers for the 2-point.

Play B: 13/10 13/11, keeping the 8-point while also generating some extra cover numbers.

A static analysis clearly points to 8/5 8/6 as being the best play. It yields more cover numbers for
the 2-point (26, as opposed to 22 for 13/10 13/11). It gives White fewer shots from the bar (11, as
opposed to 13 for Play B). It leaves fewer blots (one, instead of three). And it diversifies Black’s
numbers (he needs 3s and 4s to cover the 2-point, 5s and 6s to hop the prime.) Wow! Clearing the
8-point should be a no-brainer, right?

Well, not quite. Clearing the midpoint has a couple of other factors in its favor, factors which are
more subtle and harder to quantify, but equally important.

The first consideration is the strength of owning the 8-point. With a blot on the 2-point, the 8-point
retains considerable blocking value in case White throws a deuce from the bar.

The second and more important consideration is what I like to call playability. A playable position
is simply one which has spares to move when you need them. It’s the opposite of a stripped
position, where you don’t have any extra men, and you’ll need to break a point next turn. When you
have a stripped position without anything concrete to do, a play which breaks a non-vital point and
creates a couple of spares is often good all by itself.

In this position both of Black’s choices create some playability. Breaking the 8-point gives Black
two spares on the 5-point and 6-point. Breaking the midpoint gives him spares on the 10-point and
11-point. The amount of playability differs, however. If we assume Black has no interest in moving
checkers beyond his 2-point, then the spares on the 5-point and 6-point represent only 7 pips of
playability. The spares on the 10-point and 11-point, on the other hand, account for 17 pips of
playability – more than twice as much.

Note also that the spares in the outer board can play any number Black might throw next turn, while
the spares in the inner board can only usefully play fours or less. This becomes a big deal if White
hits from the bar and Black responds with a small number plus a big number: 1-5, 2-5, 1-6, or 2-6.
These numbers play well if Black’s spares are on the 10-point and 11-point, but they’re horrible if
Black has played 8/5 8/6 instead.

So what’s right? Does the extra “playability” of 13/10 13/11 trump the static advantages of 8/5 8/6?
In this case they do, and in fact I don’t think most good players would have a hard time with this
problem. The position after 8/5 8/6 looks a little peculiar. Having no checkers in Black’s outer
board is liable to cause some sort of problem with Black having checkers so far back. By
comparison, the position after 13/10 13/11 looks much more natural and easier to play. The
difference between the two plays isn’t huge; clearing the 8-point is certainly not a major blunder.
But it does make Black’s position more fragile, and disaster can come quickly to fragile positions.

Feb-1-2020 || Playing a Bad Back Game

Feb 1, 2020 | Backgammon Problems: Back Games

White – Pips 136 (-27)

Black – Pips 163 (+27)

Black to Play 5-4
Back games are, in my view, the most interesting category of backgammon positions. Obvious
plays are often wrong and counter-intuitive plays abound. Some real insight and experience are
often needed to find your way to the right play.

This position is not an especially difficult problem, although most players will get it right for the
wrong reason.

The classical approach to this kind of position was to play 13/8 6/2*, with the idea that if you were
hit, you would fall into a strong back game, while if you were missed, you might even be able to
win going forward. Thus hitting represented a “two-way” play: good winning chances no matter
what course the game took.

The play is actually correct, but the reasoning is flawed. In fact, Black has virtually no chance of
actually timing a back game from here, whether he gets more checkers hit or not. After Black plays
his 5-4, he’ll trail by only 18 pips in the race (16 if he elects to hit). In an adequately-timed 1-3 back
game, Black needs to trail by 90 pips or more. Even if Black gets hit a couple of times, he won’t
have nearly enough timing to play the 1-3 game. Before White starts to break his prime, he has to
move his two rear checkers all the way around the board, then bring down the checkers from the
midpoint. That represents a lot of turns, probably 10 at the minimum. There’s almost no way
Black’s position can hold up for that length of time.

In fact, 13/8 6/2* is just a straightforward attempt to win with a front game. Black is rooting for a
fan or an entering roll like 1-4 or 1-5, after which he can make a good board pretty easily, then root
for some aces, deuces, and sixes to jump White’s prime. It’s certainly something of a long shot, but
much more likely than winning a busted back game. When the timing to hold a back game just isn’t
there, sometimes your best chance is to attempt to win going forward. These can be hard plays to
make since any chance of success seems so small. But the chance of success is small for any game
plan, so just go ahead and follow your logic.

Feb-15-2020 || Priming a Back Game

Feb 15, 2020 | Backgammon Problems: Back Games
 White – Pips 175 (+65)

Black – Pips 110 (-65)

Black to Play 3-2

The lesson of this position is simple: don’t make blocking points against a back game unless there’s
some chance of actually blocking your opponent.

The obvious play is 13/8, filling in the last blocking point in Black’s prime. The blot left on the 13-
point is of no consequence in view of White’s weak board. However, Black has no need for the 8-
point. White has plenty of time to maneuver and build his board with the four spare checkers on his
13-point and 8-point, plus the spare on the 20-point which can be released with any 5 or 6. If he
makes the 8-point now, Black will find himself needing to clear it in a few rolls, at a time when
White’s board is much stronger than it is now.

Instead, Black has a chance to address the real problem in his position – the open 3-point. It’s true
that Black has several builders bearing on the 3-point, and each turn he’s a little less than even
money to make the point naturally. But it’s a disaster for him if he never makes the point – then
White is in effect playing a 2-3-5 backgame, and Black will be leaving plenty of shots when
White’s board may be strong enough to win.

The right play is to go ahead and slot now with 8/3! Not only is White unlikely to hit, but most of
his possible hits are too dangerous for him in light of his weak board. If he throws a hitting number,
he’ll mostly be better off passing on the hit and just building his position. In effect, the 3-2 roll
gives Black a free shot to build the most critical point available.

MAR-01-2020 || MOVIE RECOMMENDATION

Mar 1, 2020 | Backgammon Generally
Stuck indoors in these trying times? Cabin fever starting to close in? Getting uncomfortable
watching The Andromeda Strain and too scared to watch the market?
For a change of pace with a backgammon theme, try watch a little-known but unexpectedly
charming film called The World is Big and Salvation Lurks Around the Corner. If you can’t find it
on a streaming service, Amazon usually has it in stock. You won’t regret it.
MAR-15-2020 || HOW TO PLAY THE OPENING IN BACKGAMMON
PART 1 NOW AVAILABLE

Mar 15, 2020 | Backgammon Books

I’m pleased to announce that my new book, How to Play the Opening in Backgammon, Part 1, has
been published and is available for purchase here at the Gammon Press. To order, click here.

The book is built around the kinds of typical choices that

players face in the opening part of the game. For example: you throw a number that can be used to
make the 5-point or the 20-point. Which point do you make? You throw a number that can make the
20-point or hit in the outfield. What’s right? A few opening plays are forced, but the non-forced
plays boil down to choices like this. How do you make these decisions?

Unfortunately for people just learning the game, choices like this can’t be reduced to simple slogans
like “When in doubt, make the 20-point.” When a real choice exists for an opening play, the answer
will hinge on a number of factors which in varying degree will be contributing to the ultimate
decision. Here are some of the ideas that bear on opening decisions:

> What’s the race? A significant racing lead favors plays that don’t leave blots and plays that
contribute to escaping the back checkers. Trailing in the race favors plays that maximize contact.
> Does one play make a point? A point is an asset that may last a long time. During every turn that
you hold a point is a turn where that point is restricting some of your opponent’s rolls. For a point-
making play not to be best, the alternative needs to create some powerful assets or reduce some
major liability.
> Has your opponent made a blocking point? If so, splitting rises in value.
> Do you have a stripped outside point? If so, adding a spare will increase its value.
> Do you have a stacked point? Unstacking it will improve your position.
These and other ideas will factor into the decision-making for any non-forced play.

__________________________________________________________________

I’ve had a number of requests to show the Table of Contents for Part 1, so here it is.

Chapter 1: The Opening Move

Chapter 2: The Reply to the Opening Move
Chapter 3: The 5-Point
3.1 The 5-Point or the 20-Point?
3.2 The 5-Point or the 21-Point?
3.3 The 5-Point or the 4-Point?
3.4 The 5-Point or the 3-Point?
3.5 The 5-Point or an Outside Point?
3.6 The 5-Point or the 7-Point?
3.7 Make the 5-Point, Breaking the 7 or 8-Point?
3.8 The 5-Point or Some Other Improvement?
3.9 Make the 5-Point or Hit Somewhere? – 1
3.10 Make the 5-Point or Hit Somewhere? – 2
3.11 Make the 5-Point or Hit Two Checkers?
Chapter 4: The 20-Point
4.1 The 20-Point or the 4-Point?
4.2 The 20-Point or the 9-Point?
4.3 Make the 20-Point or Hit? – 1
4.4 Make the 20-Point or Hit? – 2
Chapter 5: The 4-Point
5.1 Make the 4-Point or Hit?
5.2 Make the 4-Point or Double-Hit?
5.3 Make the 4-Point or a Good Anchor?
5.4 Make the 4-point, Breaking the 8-Point?
The opening in backgammon is a big subject, and trying to fit it all into a single book would have
been too unwieldy. The book will appear in three parts, spaced about three months apart. Look for
Part 2 sometime in June.

APR-01-2020 || CHECKER PLAYS AND CUBE POSITIONS

Apr 1, 2020 | Backgammon Problems: Endgames
 White – Pips 94 (+14)

Black – Pips 80 (-14)

Black to Play 4-3

Black on roll. Black to play 4-3 in these situations:

(a) Tournament match, double match point.

(b) Money game, center cube.

(c) Money game, Black owns the cube.

In most positions, the correct play with a given roll is the same regardless of the position of the
doubling cube. This isn’t always the case, however, and a good player needs to be alert to the
situations where the position of the cube can determine the right checker play.
These positions tend to have a couple of salient characteristics:

> One of the possible checker plays will have the potential of swinging the position decisively, as
opposed to some alternative play which will maintain the status quo.

> One play will result in a bunch of potential gammons, for one side or the other or even both,
while the other play will resolve the game quietly, without a lot of gammons.

When these conditions occur, you may have a position where the cube location (and possible
upcoming cube actions) needs to be taken into account. Now let’s look at our first position.

Black currently leads in the pip count by 14 (80-94). He’ll be up 21 after he plays his roll. His
choices are between standing pat with 6/2 4/1, and running off the anchor now, while White has a
blot in his board. Of the two running plays, 18/14 18/15, leaving 21 shots, trumps 18/11 with 24
shots.
At double match point, where no cube is in play, staying put with 6/2 4/1 is very slightly better than
running. In general, when the choice is not clear-cut, you should be reluctant to volunteer decisive
shots in a cubeless game. The problem is that when the shots are missed, you don’t have a cube to
double your opponent out. This means that you’ll leave a few more shots on the second turn that
you could have avoided with an accessible cube.

With a live cube, the cube position often helps determine the right play. If the cube is centered in
this position, then running favors Black. Take a look at the resulting position:

White – Pips 94 (+21)

Black – Pips 73 (-21)

Position A: Black has played 18/14 18/15.

If Black runs with both checkers and White misses (say with a roll like 4-1), Black has a very
efficient double, with winning chances in the low 70s. If Black runs, White hits, and Black fans,
White then has a very inefficient cube. (After a typical sequence like White 53: 13/10*/5, Black
fans, White’s winning chances are in the mid-80s and Black has a monster pass.) Efficient cubes are
more profitable cubes, so if the plays were close in a cubeless game, the efficiency of the resulting
cubes argues for the running play with a centered cube, and that is indeed the correct choice.

If Black owns the cube in a money game his gammon losses are activated, which they weren’t when
the cube was centered. (It was almost impossible then for him to be doubled into a position where
he had a significant chance of being gammoned.) Running two men leads to far more gammon
losses than staying put, so as in the cubeless game 6/2 4/1 is right.

APR-15-2020 || ADJUSTING CHECKER PLAY TO MATCH SCORE

Apr 15, 2020 | Backgammon Problems: Tournament Tips, Uncategorized
 White – Pips 162 (+3)

Black – Pips 159 (-3)

Black to Play 3-1
Black to play 3-1 in these situations:
(A) Cash game, center cube.

(B) Tournament match, double match point.

(C) Tournament match, Black trails 3-4 to 5, Crawford Game.

(D) Tournament match, Black leads 4-3 to 5, Crawford Game.

When you have a choice between constructive plays, the cube position and match score may
determine the play you make, even when no cube turn is imminent. Keep these guidelines in mind:
(1) Making a point in your inner board will increase your chance of winning a gammon.

(2) Making a defensive anchor will decrease your chance of losing a gammon.

(3) Making an aggressive inner point instead of a defensive anchor will result in more gammons for
both sides. The volatility of the position will increase.

(4) Escaping back checkers and cleaning up blots will, in general, increase your winning chances
while decreasing gammon chances for both sides. The volatility of the position will decrease.

All these ideas come into play in money games to a small degree as we try to balance winning
chances and gammon chances to determine the best move. In tournament matches, however, they
play a much bigger role. Depending on the score, gammons may be hugely important or completely
irrelevant.

Now let’s look at our actual problem.

In (A), we just need the best play for money. Here it should be pretty clear that 8/5 6/5 will
dominate the other choices. Making the 5-point leaves Black with a good distribution and helps
unstack his 6-point. White has a 6-shot to hit on the 9-point, but 6-1, 6-3, and 6-4 play well already,
so that’s not as costly as it might be. Since White’s men aren’t anchored, the 5-point sets up a
potential attack in the future. Making the 20-point is good for defense, but White has no board and
not a lot of threats, so defense isn’t a high priority here.

In (B), we’re in a tournament game with a double match point situation. We can’t win a gammon,
and we also can’t lose one, so a couple of our choices drop off the radar screen. The double-hit
(6/3*/2*) is weak positionally, and its only merit is as a gammon play. Toss that in the garbage.
Making the 20-point anchor is great for preventing gammons, but we preferred making the 5-point
even when gammons counted, so that goes away as well. We’re left with making the 5-point and the
passive 13/9. Normally making the 5-point would be a clear winner, but the importance of not
losing ground in the race and the unimportance of gammons at DMP brings 13/9 up to a tie for first.
This is a somewhat surprising result for most players, and one well worth noting. Double match
point is much more of a straightforward racing game than other forms of backgammon.

In (C) we need two points to win the match in the Crawford game, while our opponent just needs to
win this game to win the match. This situation is known by the term gammon-go. In money games,
turning a single win into a gammon gains half as much as preventing a win from turning into a loss;
here the ratio is 1-to-1, so Black is much more eager to seek out gammons.
But what’s the right play for winning a gammon? Obviously making the 20-point or playing 13/9
drop out of contention. Interestingly, making the 5-point is much better than the double-hit; it both
wins more games and more gammons. Playing 6/3*/2* with no board is just a weak play, the only
play among the four which isn’t best at any score.

In (D), we’re in the opposite situation, known as gammon-save: we just need to win a single game,
while a gammon for our opponent wins the match. As you’d expect, the simple 23/20 21/20
becomes the winner here. Nailing down the best possible anchor reduces gammons to a minimum
while still making Black an overall favorite to win.
Solutions:
(A) Money: 8/5 6/5
(B) Double match point: (tossup) 13/9 or 8/5 6/5
(C) Gammon-go: 8/5 6/5
(D) Gammon-save: 23/20 21/20

MAY-01-2020 || HOW TO PLAY THE OPENING IN BACKGAMMON

(BOOK EXCERPT)
May 1, 2020 | Learning Backgammon
A number of readers have asked to see an excerpt from How to Play the Opening in Backgammon,
Part 1. I’ve picked the first section of Chapter 3, which discusses positions where you have a choice
between making your 5-point or making your 20-point. Enjoy.
3.1 The 5-Point or the 20-Point?
I’ll start off our chapter on the 5-point with a battle of the heavyweights: You roll a number that can
make your 5-point or your 20-point, the two most important points on the board. Which one should
you choose?
You might think that, with two great points to choose between, you couldn’t go far wrong picking
either one. Actually, that’s not true. Depending on the position, either play could be a significant
error or even a very large blunder! Let’s look at a few of the factors that should influence your
choice.

Am I losing the game? If your opponent has thrown a great shot (like 6-6 or 2-2) and now has a
solid edge in the game, making the 20-point is likely to be right. You’re now playing defense, and
the 20-point is a great defensive point. If the game is more even, the 5-point goes up in relative
value.
How difficult is each point to make? This consideration will normally favor making the 20-point.
Suppose, for instance, you start the game with a 4-1 and play 13/9 and 24/23. On your next turn
you’ll have only two numbers to make the 20-point (4-3) but a whopping nine numbers to make
your 5-point (1-1, 3-3, 4-4, 3-1, 4-1, and 4-3). Given a choice of two good things to do, in
backgammon we normally try to do the hardest thing first.
After I make a point, what does my distribution look like? Suppose as before you start the game
with a 4-1 and play 13/9 and 24/23. If you next roll a 4-3 and elect to make your 5-point, your
resulting distribution isn’t too good. You still have a big stack on your 6-point, your 8-point is
stripped, and you don’t have any other builders aiming at your home board. If you had rolled 3-1 or
4-1 instead, you could have unstacked your 6-point while making the 5-point. Looking at your
distribution will play a role in selecting which point you want to make.
How’s my communication? If your back checkers are far back (say on your 24-point and 23-point),
then they’re far away from the midpoint and the need to make a connecting anchor is greater. If
you’ve already split your back checkers to a good point, then connection isn’t as much of an issue
and the 5-point rises in value.
Has my opponent escaped a checker? It’s a big deal if your opponent escapes a checker, say with an
early 6-5, because it changes the relative value of several important factors. Your opponent now
very much wants to release the other back checker, which will achieve his goal of escaping both
back men. He also doesn’t want to get hit, which will neutralize what he gained by escaping a man.
You want to counter his goals, so here’s what happens:
> Your 20-point now goes down in value. Since you very much want to send a second checker
back, you want to arrange your rear checkers to have the best chance of hitting. This means you
want them split and far back, which will create some pure double shots if your opponent rolls a
really bad number. The best arrangements are the 24 and 23-points, the 24 and 22-points, and the 24
and 21-points. Actually making the 20-point gives you almost no hitting numbers for a long time.
> Your 5-point goes up in value. Since your opponent’s top priority is now to escape his last
checker, the extra blocking action that the 5-point creates is valuable. And of course, having a better
board is great if you can actually hit a shot.
How many checkers do I have back? If you’ve had a third checker sent back, the 20-point goes up
in value. Now you have extra incentive to avoid being blocked in, and an anchor will provide that.
With all these factors in mind, let’s look at a few positions involving a 5-point versus 20-point
choice.
 White – Pips 161 (-1)

Black – Pips 162 (+1)

Black to Play 4-3
Diagram 3.1.1. Black to play 4-3.
Here’s an easy position where every factor points in the same direction.

Losing the game? White has the early edge with his 4-point, so a defensive point is in order.
Degree of difficulty? The 20-point is harder to make.
Distribution? Using the 4-3 to make the 5-point leaves poor distribution.
Communication? Black’s rear checkers are both far back, so making a connecting point is more
important.
Opponent escaped a checker? Not relevant.
Do I have three men back? Also not relevant.
Add it all up, and 24/20 23/20 is absolutely clear and making the 5-point is just a blunder.
 White – Pips 161 (-1)

Black – Pips 162 (+1)

Black to Play 4-3

Diagram 3.1.2. Black to play 4-3.

Black’s position is the same as in the previous example, but White has played a 5-1 instead of a 4-2.
Let’s see how this modest change affects the decision.

Losing the game? White hasn’t done much yet, so Black’s need for an anchor is low. Strongly
favors making the 5-point.
Degree of difficulty? As always, the 20-point is harder to make. But White’s weak position makes
this indicator less important.
Distribution? Using the 4-3 to make the 5-point leaves poor distribution.
Communication? Black’s rear checkers are both far back, so making a connecting point is
important. But White doesn’t have a position yet, so the need isn’t as great as in Diagram 1.
Opponent escaped a checker? Not relevant.
Do I have three men back? Also not relevant.
White hasn’t made progress in improving his front position, so Black’s immediate need for an
anchor is much less. But note that one new feature of the position has appeared: White’s back
checkers are split, so making an inner point has risen in value for Black. (The stronger Black’s
board becomes, the more dangerous it becomes to have split back men vulnerable to attack.) In
addition, White’s split men pose more danger to Black’s builder on his 9-point, so cleaning up the
blot while making the 5-point is a big plus.

Put all those factors together and making the 5-point becomes correct by a modest margin.
 White – Pips 156 (-6)

Black – Pips 162 (+6)

Black to Play 4-3

Diagram 3.1.3. Black to play 4-3.

Again we’ve kept Black’s position the same, but we’ve given White a 6-5, letting him run a checker
to the midpoint. Now what should Black do with his 4-3?

Some of the features we’ve discussed so far would lean toward making the 20-point. It’s the harder
point to make, it helps connect the back checkers to the rest of Black’s army, and it leaves the front
checkers a little better distributed. As in the last diagram, however, the rear checkers aren’t under
any pressure, so making the 20-point isn’t especially vital right now.

But now a new positional factor enters the equation: White has escaped a back checker. White’s
running play hasn’t created any new builders, so as long as Black keeps good coverage of White’s
inner and outer boards, White may find himself reduced to stacking up checkers or leaving some
unwanted shots. But if Black plays 24/20 23/20, the pressure is off and White can dump checkers in
his inner board while waiting to release his lone back checker. That’s a powerful incentive for
Black to leave his rear checkers alone for now, and hence 9/5 8/5 is the best play by a small margin.
 White – Pips 159 (+1)

Black – Pips 158 (-1)

Black to Play 3-1

Diagram 3.1.4. Black to play 3-1.

Here’s a slightly different riff on the 5-point versus 20-point idea. Black split with an opening 5-4,
after which White rolled a 5-3 and made his 3-point. (A small but extremely common error; as we
saw in Chapter 2, 13/5* is better.) Now Black rolls a 3-1 and can make either point. What’s right?

This position fools many players who feel that, having already split, they now have more of an
investment in the 20-point. As a result, they quickly cover their blot with 24/20. But if we run
through our list of key factors, we might see the position a little differently.

Strength of position? White has made his 3-point, strengthening his inner board and making the
value of an anchor go up a bit. But his 8-point is stripped, so some of his hitting numbers involve
breaking that point. The net favors making the 20-point by a bit.
Difficulty of making the point? There’s been a big swing here. With the 20-point slotted it’s now
much easier to make than in our first few examples. The 5-point is now a much harder point to
make, so a strong edge to 8/5 6/5.
Distribution? Not even close. Making the 5-point unstacks two loaded points.
Communication? Splitting to the 20-point has greatly relieved Black’s communication problems.
Now he has lots of rolls that make either the 20-point or the 18-point, or run the front checker to
safety. Since the need for communication has gone down, the value of making the 20-point has
gone down.
Put all the factors together and making the 5-point is clearly right, while making the 20-point is an
outright blunder. It’s a counter-intuitive result – just splitting to the 20-point relieved so many of
Black’s problems that the value of actually making the point has gone down.
 White – Pips 156 (-4)

Black – Pips 160 (+4)

Black to Play 3-1

Diagram 3.1.5. Black to play 3-1.

We’ve changed the previous problem, giving White a running 6-5 instead of a point-making
number. All the reasoning in Diagram 4 still applies, and in addition White’s escaped checker
makes the 5-point more valuable while the 20-point is less so. Again 8/5 6/5 is the best play. What’s
worth noting about the position is that the two plays are now closer in value than in Diagram 4.
Since White has escaped a man, the 5-point is only blocking one checker rather than two, so it does
a bit less work.

White – Pips 143 (-15)

 Black – Pips 158 (+15)
Black to Play 3-1

Diagram 3.1.6. Black to play 3-1.

Here we’ve changed the position again, this time giving White a 6-6 instead of a 6-5. Now Black’s
checker on the 20-point is in much more danger; White has 10 pointing numbers instead of the five
in Diagram 5. At the same time, White’s rear checkers have escaped, so while making the 5-point
gives Black a good distribution, it no longer blocks anything. The result is a huge swing in the
evaluation, with making the 20-point now correct and making the 5-point is a blunder.

White – Pips 157 (-3)

Black – Pips 160 (+3)

Black to Play 4-1

Diagram 3.1.7. Black to play 4-1.

Here the opening sequence was a 4-3 for Black followed by a 6-4 for White. Although Black hasn’t
split to the 20-point, the fact that he has split to a potentially advanced anchor has once again
lessened his need to actually make the anchor. All other factors favor making the 5-point: his
distribution will be better, his communication is already good, his back men aren’t under any
special pressure, and White has (mostly) escaped a checker. The right play is 8/5 6/5.
 White – Pips 161 (-9)

Black – Pips 170 (+9)

Black to Play 4-3

Diagram 3.1.8: Black to play 4-3.

Here’s a final position from a little later in the opening. Now most factors favor making the 20-
point: White’s builder on his 7-point makes the threat of a block more real; Black’s rear checkers
are far back and isolated; finally, Black has three men back rather than two, so he has a greater need
for an anchor. On the other side of the board, making the 5-point leaves Black poorly distributed,
with a stripped 8-point and a stacked 6-point. Making the 20-point is now the better play.

MAY-15-2020 || ADJUSTING CHECKER PLAY TO MATCH SCORE

May 15, 2020 | Backgammon Problems: Tournament Tips
 White – Pips 162 (+4)

Black – Pips 158 (-4)

Black to Play 6-6

Black to play 6-6 in these situations:

(a) Cash game, center cube.
(b) Tournament match, double match point.
(c) Tournament match, Black trails 3-4 to 5, Crawford Game.
(d) Tournament match, Black leads 4-3 to 5, Crawford Game.
We’ll continue the line of inquiry we started in the April 15th blog post with another early game
position that might be played differently at different match scores. Here Black opened with a 6-3,
running 24/15, and White responded with a 4-1, splitting with 13/9 24/23. Now Black has a 6-6 to
play.

Mostly 6-6 is an easy problem in the opening. If the bar points are open, you make them and pick
up your dice. But if one of the bar points has been made, or the back men have split, you may have
to do some original thinking. That’s the case here. Black actually has four viable plays, two blitzing
plays and two positional plays. Let’s look at all four and see which play suits which match score.

The Positional Plays

Play (1): 13/7(3) 15/9, and
Play (2): 13/7(2) 15/9 24/18
The positional plays reject the hit on the 2-point and instead concentrate on priming and escaping.
Both involve 13/7(2) and 15/9. Play (1) plays the fourth 6 to the 7-point, giving Black a lot of
building potential next turn while leaving the remaining blot on the 24-point, out of danger. Play (2)
instead moves the back checker out to the 18-point, into a triple shot, while keeping a spare on the
midpoint.

In the pre-bot days, no one would have considered Play (2) as an option. It gives White 33 hitting
numbers (everything but 5-5 and 5-4 hits somewhere) and if Black gets hit, he can’t be extending
his prime next turn. What’s the point?
But along came the bots, and in many positions they didn’t mind moving the last checker up, even if
it meant leaving the checker on the enemy bar-point. So there must indeed be some point to the
play. In fact, there are two points:

> If White rolls a 7 or an 8, hitting the blot on Black’s 9-point, Black’s rear checker is much better
placed on the 18-point. Black has some rolls that anchor, and many other rolls that hit on Black’s
16-point.

> White’s checkers are now ideally placed to start building home board points. Moving to the 18-
point forces White to hit there and ignore the home board. While not a disaster, the fact that White
had other good things to do with these rolls lowers the cost of being hit.

None of this means that 24/18 is better than 13/7, only that it’s worth consideration.

The Attacking Plays

Play (3): 13/7(2) 8/2*(2), and
Play (4): 8/2*(2) 13/1*
With these plays, Black abandons the priming game plan and launches an attack on White’s back
checkers. Compared to the positional plays, these moves are highly committal, and win more
gammons while winning fewer single games. Play (4) wins more gammons than (3), but wins the
fewest games of all the four choices.

Now let’s look at our four scores and pick a best play for each score.

Money game. In a money game we’re trying to balance wins and gammons. We’re happy to pick up
some extra gammons, as long as we don’t have to pay too much in terms of extra wins. We’re
willing to give up winning an extra game, as long as we get at least two more extra gammons as a
reward.
The best non-hitting play is 13/7(3) 15/9. Rollouts rate this as solidly better than 13/7(2) 15/9 24/18.
The reason is that leaving the spare checker back on the 24-point wins about 2% more gammons,
while leaving net winning chances about the same. Getting hit on the 18-point slows Black down
and prevents him from launching a blitz or building a prime quickly, thus reducing his chance of a
gammon.

So 13/7(3) 15/9 is our baseline positional play. Now let’s compare the attacking plays. For money,
8/2*(2) 13/7(2) clearly dominates the aggressive double-hit 8/2*(2) 13/1*. The double-hit wins 2%
more gammons, but loses 4% more games, exactly the opposite ratio from what you want. (It also
loses more gammons.) We’re striving for balance in money play, and 8/2*(2) 13/7(2) provides that
balance; it gives good attacking chances while still keeping a firm grip on the position.

Comparing the best positional play (13/7(3) 15/9) to the best attacking play (8/2*(2) 13/7(2)) gives
a clear edge to the attacking play, which sacrifices about 0.5% wins to gain about 3.5% more
gammons. This shouldn’t be surprising, since making any home-board point will boost gammon
chances, while Black still keeps a solid grip on the position and retains the option of going either
way in the future – blitzing or priming. So for money, 8/2*(2) 13/7(2) is a clear winner.

Double match point. If we don’t care about gammons, the positional play 13/7(3) 15/9 is now the
winner. A prime and a racing lead is the easiest way to win a game when gammons don’t count.
This play gives Black his solid racing lead, while providing plenty of builders to extend his prime.
Gammon-go. With gammons trading 1:1 with single games, the two attacking plays now move to
the top. Extreme Gammon rollouts put 8/2*(2) 13/7(2) on top, with 8/2*(2) 13/1* close behind.
Give yourself credit for either choice, as both are preferable to the slower positional approach.
Gammon-save. Here we don’t care about winning a gammon but we don’t want to lose one. Clearly
the positional play 13/7(3) 15/9 dominates, winning the most games while tying for fewest
gammons lost.
Solution:
(a) Money: 8/2*(2) 13/7(2)
(b) DMP: 13/7(3) 15/9
(c) Gammon-go: either 8/2*(2) 13/7(2) or 8/2*(2) 13/1*
(d) Gammon-save: 13/7(3) 15/9

JUNE-01-2020 || BLITZ VERSUS BACK GAME

Jun 1, 2020 | Backgammon Problems: Back Games
White – Pips 157 (+25)

Black – Pips 132 (-25)

(a) Black on roll. Cube action?
White – Pips 158 (+26)
 Black – Pips 132 (-26)
(b) Black on roll. Cube action?
Position (A) arose in a recent chouette. Black, in the box, doubled. After a lot of thought, all the
team members took. Black fanned, and White’s next two rolls were 3-2 and 5-5, winning easily.
Was Black’s double correct? How about White’s take?
The argument for doubling is clear enough. White has practically no chance of playing a successful
back game. His front position is on the verge of crashing, and if Black rolls a 3, White is just about
sunk. Even if Black dances, White will collapse quickly unless he rolls a 5 or 6-1 in the next couple
of turns.

The taking question is much more difficult. From White’s point of view, the game can go in one of
four directions:

1) A collapsed back game. White rolls lots of threes and fours, and his board falls apart. Black
sweeps around the board. White hopes to hit a late shot to save the gammon.

2) A successful back game. Black enters quickly, hitting a blot or two. White dances, or else
reenters and escapes. He preserves his timing until Black starts the bearoff.

3) A low anchor game. White releases some, but not all, of his back checkers. The checkers that
remain (probably on the 3-point), form a well-timed low anchor game.

4) A forward game. Black doesn’t enter quickly and White throws some aces, fives, and sixes to
escape some of his back men while preserving a strong board.

Variations (2) and (4) are good for White. The others are very bad. But how often do variations (2)
and (4) arise?

In the actual game, the White players decided to take, an understandable decision. “When in doubt,
take” is an excellent general rule. At first glance, White’s chances of going forward seem
reasonable, especially considering how his numbers play on the next turn. His sixes (except for 6-1
and 6-5) don’t play, fives escape, threes cover, and aces and deuces move in back; only fours are
immediately useless. The fact that Black doesn’t have a real 5-point prime, but instead a prime with
a gap, is also a factor, facilitating White’s escape. (White can leap from either the 22-point or the
23-point.)

These are plausible arguments, but the position still isn’t a take. White has just a little too much
difficulty getting his back men out quickly, and when his board collapses he’s in great danger of
losing a gammon with few winning chances to balance out. Rollouts show that White can win the
game a bit less than 30% of the time, but he loses too many gammons to make a take worthwhile.

Interestingly, only a tiny change in White’s position is sufficient to take. In (B), Black again has a
double, but now White has a clear take. The addition of 6-2 and 6-4 as good numbers and 6-3 as a
great number is enough to tip the balance from a pass to a take.

Jun-15-2020 || Bearing Off Against Contact

Jun 16, 2020 | Backgammon Problems: Endgames

When bearing off against contact, you often have a choice between playing aggressively to win
more gammons, and playing safely to win the most games. Some of these plays are tricky. Here’s a
good example.

Black on roll, money game, White owns the cube.

White – Pips 118 (+58)

Black – Pips 60 (-58)

Black to Play 4-4
In this position, Black has closed out one checker and escaped all his men from behind White’s
prime. The win is nearly certain, and he has some substantial gammon chances. With a 4-4 to play,
Black has three choices:

Play A: 9/5 6/2(2) 4/off. This is clearly the safest play. Black is even on the end, with two spares on
the highest point; White also has the opportunity to enter with a six, eliminating all danger of
losing.

Play B: 9/1 5/1 4/off. Legal, but this seems at first glance the worst of the three. Black is stripped
on the end, and so more likely to leave a shot than with play (A), while the two extra checkers on
the ace-point might later force him to open high points more quickly, reducing his gammon
chances.

Play C: 9/5 4/off (3). This is the gusto play, going full blast for the gammon, at the cost of
obviously leaving more shots over time than (A) or (B).

This is a problem in balancing extra losing chances against extra gammon chances. As we’ve
discussed in previous posts, losses trade against gammons won at a 2:1 ratio. Changing a simple
win to a gammon gains two points (the difference between +2 and +4). But changing a simple win
to a loss costs four points (the difference between +2 and -2). So if you’re contemplating a play that
wins some extra gammons but loses some extra games as well, you have to pick up at least twice as
many extra gammons as you do games lost for the play to be profitable.

In this position, Black’s losing chances are very small after any play. After play A, they’re almost
non-existent. Even after the risky play C, we might easily have six or seven men off when and if we
get hit, so a hit won’t necessarily win for White. On the other hand, White needs 13 crossovers to
get off the gammon. This implies that our gammon chances must already be pretty good, certainly
in the 40% to 50% range, so it seems extra checkers off should add to these chances substantially.

Let’s start by calculating how often we get hit and lose after each play. While we know from a
casual examination of the position that clearing the 6-point is going to be the safest play, and
clearing the 4-point will be the riskiest, what really interests us is the relative riskiness of each play.
How many extra losses does our aggressiveness cost us?

To solve this problem, we’ll use two tools. One is an Extreme Gammon rollout, which will tell us
how often we lose after each play. The other is Hugh Sconyer’s database, which can tell us how
often we are hit after each play. (Sconyer’s database is calculate recursively from the simplest
bearoff positions, so it’s completely accurate, given the assumption that the player trying to hit will
maximize his hitting chances by maintaining contact. In this position, that’s a valid assumption.)
Both these pieces of information are useful, and by comparing them, we get a third piece of
information, namely how often we can save the game even after being hit.

Here’s the information from the rollouts and database:

Probability that Black gets hit after each play.

(From Sconyer’s database)

After play (A), clearing the 6-point: 1.2%

After play (B), stacking on the 1-point: 3.6%
After play (C), taking three off: 7.7%
Probability that Black loses after each play.
(From Extreme Gammon rollout)

After play (A), clearing the 6-point: 1.0%

After play (B), stacking on the 1-point: 2.9%
After play (C), taking three off: 5.2%

These results aren’t particularly surprising. As expected, play A is safest by a wide margin, play C
is the most likely to be hit, and play B sits in the middle. The numbers show yet another expected
result. If we divide the loss numbers by the hit numbers, we find that A and B lose most of the time
after being hit (83% and 81% respectively), while play C loses only 67% after being hit, showing
that bearing lots of men off before being hit indeed has value.

Next we need to consider the probabilities of winning a gammon. We would expect the two safe
plays, A and B, to win the fewest gammons, while play C should win the most. But here we
encounter a surprise.

Probability that Black wins a gammon after each play.

(From Extreme Gammon rollout)

After play (A), clearing the 6-point: 45.3%

After play (B), stacking on the 1-point: 54.4%
After play (C), taking three off: 48.7%

Taking three checkers off did indeed win more gammons than clearing the 6-point. No surprise
there. But the play that won the most gammons by far was play B, taking one checker off while
moving two checkers to the ace-point! How can we account for this?

There are two reasons that play B wins so many gammons. The first reason is that it keeps a closed
board. The longer Black can keep White from moving, the better his chances of eventually winning
a gammon. The second reason is that by putting two more checkers on the ace-point, Black creates
a speed board. Once White does enter, Black won’t lose time if he throws the occasional ace in the
bearoff. Instead, he’ll keep bearing checkers off. Play B gives Black the best chance for never
leaving a gap in his bearoff, as well as the best chance for using a small double late in the game.
Both these factors help generate gammons when the race is close.

In a play-to-play comparison, B easily beats A by generating 9.1% more gammons at a cost of just
1.8% fewer losses, far above the 2:1 ratio needed. But B crushes C by generating both more
gammons and fewer losses! Can’t do better than that. Moving two checkers to the ace-point while
keeping a closed board is the right play.

JULY-01-2020 || HANDLING SIX-PRIMES

Jul 1, 2020 | Backgammon Problems: Priming Games
Six-primes are the ultimate containment formation in backgammon, but even a six-prime is no
guarantee of winning. Here’s a couple of problems illustrating the strengths and weaknesses of six-
point primes.

(a) Black on roll, money game, White owns the cube.

 White – Pips 118 (-19)

Black – Pips 137 (+19)

Black to Play 6-4

Six-point primes are backgammon’s ultimate weapon. Five-primes are strong, but six-primes are
better. No matter how well you roll, you can’t escape from behind a six-prime. It’s maximum
security. There’s no tunneling out; you have to wait for the walls to fall down.
However, as in most backgammon situations, it’s not completely hopeless. Six-primes do have one
weakness: it takes 12 checkers to make a six-prime, leaving only three checkers left for
maneuvering. That opens up a few defensive possibilities for the side trapped behind the full prime.
If he can build some sort of block of his own, he can create cracking numbers for his opponent.
Once the six-prime cracks, it’s a new ball game, and the advantage can swing quickly, because the
player with the (now former) six-prime can find himself with a timing disadvantage.

Position (a) illustrates a key principle in backgammon: don’t be too clever. It’s easy to fall into the
trap of thinking that Black could lose the priming and timing battle here, and opt for the clever-
looking 24/14 (preserving timing) instead of the obvious 9/3, 7/3. But here the obvious play is, in
fact, completely correct.

Making the six-prime is, of course, right on general principles. Might Black have to bust up later
after being outprimed? That’s possible, but very unlikely. Notice this key fact: White has to play all
his numbers this turn, with sixes going to the 2-point and doubles crushing his position. Even if
White can make the 3-point or the 5-point, how long can he hold it? He probably starts to crunch
the second turn. Meanwhile Black has the checker on the 13-point to move, and he can break the
8-point and still keep a 5-prime with White not at the edge.

No need to be timid here. Although a six-prime can be vulnerable, it’s still the formation you’re
striving for. Making the full prime wins both more games and more gammons than 24/14.

(b) Black on roll, money game, center cube.

 White – Pips 144 (-7)

Black – Pips 151 (+7)

Black on roll. Cube action?

Black has completed a full six-point prime in Position (b), and White has some work to do before
he can finish a prime on his side. Black is on the bar, so perhaps dancing will help him maintain his
prime. In addition, Black has very few numbers that force him to enter and immediately break his
prime — only 8, in fact (3-3, 2-2, 5-1, 4-2, 4-1). Surely this all adds up to a strong initial double,
right?

Wrong. The problem is that Black has to get three men out and through White’s entire army, all the
while hoping that his six-prime holds up. And once his prime does break, he’s in serious trouble,
despite the fact that a five-prime still remains. If he opens with, say, a 4-2 (not his worst breaking
number) and plays bar/23, 9/5, White is already about a 60-40 favorite cubeless, and an even
bigger favorite if he owns the cube as well! If White gets just a little lucky and makes one additional
key point (the 3-point or the 7-point), then any poor throw by Black will make him an immediate
serious underdog.

In fact, we’ve all played these sorts of games many times, where you make a quick early prime,
then lose after what appears to be a fluke roll or two. Actually, they’re not such fluky losses at all.
What’s happened is that you’ve built a prime at the cost of leaving your army severely
disconnected, and in fact you were never much of a favorite at all. Be careful when making your
prime leaves you without any checkers in the center of the board, as here. You may not have
made any mistakes as the rolls came, but you’re still in a vulnerable situation.

Although Black is about a 52-48 cubeless favorite in the starting position, he shouldn’t double.
White has a huge beaver if doubled.

JULY-15-2020 || ADJUSTING TO TOURNAMENT PLAY

Jul 15, 2020 | Backgammon Problems: Tournament Tips
Tournament backgammon requires an extra set of skills beyond those required by money players.
Often decisions have to be made which cannot arise in a money game. Here’s a good example.
Black on roll, center cube, score 0-0 in 7-point match.
 White – Pips 181 (+60), Match -7 -7

Black – Pips 121 (-60), Match -7 -7

Black on roll. Cube action?

This position arose in a Monte Carlo match some years ago between two top players. Black had
been playing for a gammon with four of White’s men on the bar. In the nick of time, White entered
all four men with 3-3, in the process sending one of Black’s checkers to the bar. Note that this
position with a centered cube could only arise in a tournament; in a money game, Black would
have doubled at a much earlier stage of the blitz because of the Jacoby Rule.

Black now doubled, and White passed.

The resulting position engendered some speculation among experts. Perhaps, said some, Black
was too conservative in doubling; he should take another roll for the gammon, since White might
have to expose a blot next turn. A few bold souls (myself included) argued that the position might
already be a take. After all, Black has five checkers to bring around and White might be able to
build up his board from the low points while waiting for a possible winning shot. Others argued that
the play has been correct and double-pass was the proper outcome.

The players engaged in a prop for a while which indicated that the position was certainly not too
good, and passing might be right. Later computer rollouts showed it to be, in fact, a close pass.
Any improvement in White’s game over the current position yields a clear take. White can’t afford
to hit loose inside his board until he makes some additional points. By that time, however, Black’s
men have usually escaped to the relative safety of the 10, 11, and midpoints. Even so, White can
win about 1/3 of the time, but the occasional hit costs him just too many gammons to take.

AUG-01-2020 || BLITZ DOUBLES IN TOURNAMENT PLAY

Aug 8, 2020 | Backgammon Problems: Tournament Tips, Uncategorized

In this position we’re still in the early part of the game. Both sides have one checker back. Black
has a somewhat impure structure with the ace-point already made, but he does have an extra
inner point, plus a lot of checkers that can join in an attack. White has only two inner points, but a
very nice structure, with plenty of builders poised to make priming points. The position might
appear at first to be evenly balanced, save for the small matter that Black is on roll.

White on roll, center cube.

(a) Cash game. Should White double? If White doubles, what should Black do?
(b) Match, score tied 1 to 1 to 5 points. Same question.
(c) Match, White leads 2 to 1 to 5 points. Same question.
(d) Match, White leads 3 to 1 to 5 points. Same question.
Let’s start with the money game question, and look at our Sylvester Rule criteria:

(a) Race: White has a solid 28-pip lead, 112 to 140.

(b) Position: Edge to Black, who is well-placed to build a prime, while White is forced to play an
attacking/racing game.

(c) Threats: White is on top here. It’s his roll, and his doubles all put Black in the air. In addition, 5-4
and 6-4 make the 2-point, 6-2 hits in the outfield, and 24/13 escapes to the midpoint. That’s 14
great shots; in addition, no roll is really bad.

It’s an early position, and we’ve got a solid lead in two out of three criteria, so by Sylvester’s Rule
the position should be double and take. Rollouts show that’s correct. In fact, these decisions are so
clear that it’s actually a ‘blunder/blunder’ position: not doubling is a blunder (error of 0.18 by
Snowie, 0.17 by XG) and not taking is also a blunder (error of 0.18 by Snowie, 0.20 by XG).
Blunder/blunder positions are uncommon but worth studying and committing to memory. When you
get one wrong, it’s clearly a position you need to master. In this case, it’s worth remembering that
in a cubeless game, White wins about 30% gammons, 34% single games, and loses about 36%. In
a game with a cube, Black wins a few more games than this, with most of those extra wins coming
from White’s single wins.

What happens, however, when this position occurs in a match?

Let’s start with the easiest case, which is (d): the score is 3-1 to 5 in favor of White, or 2-away 4-
away. At this score, Black would trail 4-1 to 5 (Crawford) if he passes a double, and match equity
tables make him about 17% to win the match in this case. (He needs to win three games in a row if
he wins a single game at Crawford, and two games in a row if he wins a gammon in the Crawford
game.) Clearly Black will take and reship if he’s given the cube in a position he can win more than
17% of the time cubeless. Since his winning chances here are about 36% cubeless, it’s a trivial
take and reship on his part. With White’s high gammon chances, it’s a huge blunder for him to
redouble. He should just play on and see if he can win the match with an undoubled gammon.
At this score, White only wants to double positions with high winning chances (better than about
80%) but very low gammon chances. As a practical matter, this means he leaves the cube alone
when there’s any significant contact, and only doubles in races and certain high anchor positions
where he has a huge racing lead.

The next easiest case is (b): the score is tied at 1-1 to 5, or 4-away 4-away. Many players are
fooled by this score, since it seems that the end of the match is still fairly far away, and therefore
the cube action should be like a normal money game. But that’s a mistake. Winning a gammon
here actually wins the match by an exact count, which is exceptionally valuable. The easiest way to
see just how valuable is to compare what happens when White wins a gammon in a money game
to what happens when White wins a gammon at this match score.

In a money game, winning a gammon instead of a single gammon exactly doubles White’s profit:
he goes from winning two points to winning four points, a 100% increase. At the 1-1 score,
however, it’s a bit different. Winning a single game takes White from 1-1 to 3-1, and increases
White’s match winning chances (MWC) from 50% to about 68%, a gain of 18%. Winning a
gammon, however, wins the match, taking White from 50% to 100%, a gain of 50%. Gaining 50%
instead of 18% is an increase of 32/18 = 178%, instead of just 100%.

That’s such a big difference that White should double and Black should actually drop! This result is
typical of a lot of early blitz positions at the 4-away 4-away score: easy take for money, easy drop
at the match score.

That leaves only case (c), the hardest case: White leads 2-1 to 5, or 3-away 4-away. This case is
actually most similar to case (d). At 3-away 4-away, White’s gammons are largely (but not
completely) crippled. The problem is that winning a single game takes White to 83% match winning
chances, most of the way to his goal. Adding a gammon only gets him a little bit farther. As a
result, White should mostly adopt the cube strategy of case (d): play for the undoubled gammon,
and only cube if he becomes a bigger favorite with fewer gammon chances. It’s an easy take for
Black, of course.

SEP-01-2020 || DOUBLING AT 2-AWAY 4-AWAY IN MATCH PLAY

Sep 1, 2020 | Backgammon Problems: Tournament Tips
You’re playing a 5-point match, and you lead 3-to-1. You need two points to win, your opponent
needs four. The next game starts out favorably for you. What’s your proper cube strategy?

This scenario is among the most common in tournament backgammon, and among the most
frequently mishandled. The leader’s doubling strategy can be succinctly summarized in these two
rules:

Rule 1: If there is any significant contact in the position, don’t double, no matter how big a favorite
you are. Play for the gammon instead.
Rule 2: In a non-contact position, double when you are better than 80% to win a cubeless race. In
races, this usually occurs with about a 13% or better lead in the pip count, or in short bearoffs with
a slightly more favorable than normal 3-roll position.
To understand these rules, we first need to look at the situation from the trailer’s point of view, and
understand his taking point. If the trailer drops a cube, he will need to win four points to the leader’s
one, starting with the Crawford Game. To win the match, the trailer will most likely need to win
three games in a row: the Crawford game itself, the next game after an automatic immediate
double, and the final game at double match point. The trailer’s chances are actually a bit better
than this, since a gammon in the Crawford Game leave him needing only one more game, while a
gammon in the post-Crawford game also wins the match. The effect of all this is that the trailer’s
chances if he drops at 2-away 4-away are in the neighborhood of 17% to 18%, depending on
whose Match Equity Table you use.

If the trailer takes a cube, he will of course automatically redouble the following turn. From the
leader’s point of view then, a double will result in one of two outcomes: the leader will win one
point, or the leader will own a dead 4-cube next turn.

So what should the leader do? If there is contact in the position, he should usually play on for an
undoubled gammon with any kind of advantage. Consider this position:

White on roll, leading 3-to-1 to 5.

Here White would have a nearly optimal double in a money game, with a strong anchor and plenty
of threats to make a prime. (Black would have a small pass.) At this score, however, White can’t
consider doubling. Black’s raw winning chances in a cubeless game are in the 27% range, far
above his dropping point. If Black has such a trivial take, and there are reasonable gammon
chances, White doesn’t have a good double. Instead, White should simply play on to see if his
gammon chances develop.

In a non-contact position, White can use the cube effectively. He simply has to reach a position
where he’s a big enough favorite to double. In practice, this point comes when he’s very close to
Black’s take point, with some market losing sequences. The next diagram shows an example of a
position of this type.

White on roll, leading 3-to-1 to 5.

White leads in the race by 100 to 114, or 14% of the pip count. His cubeless winning chances are a
little over 81%, which gives him almost an optimal double and Black a narrow take (with a forced
redouble next turn, of course). In most medium to long races, this 13% to 14% lead indicates
winning chances in the desired range.

In effect, White’s ability to use the cube is severely crippled when he is two points away from
winning and his opponent needs four or more points. An analysis of empirical tournament results
by Kit Woolsey in Inside Backgammon showed that at these scores the leader is only winning about
42% of the games!

SEP-15-2020 || DOUBLING WITH A BIG LEAD IN MATCH PLAY

Sep 15, 2020 | Backgammon Problems: Tournament Tips

When you play longer matches, the score can become very lopsided in favor of one player. At
lopsided scores, the doubling strategy for both players can change very dramatically. In this post
we’ll take a look at proper doubling strategy in a race when one player has a big lead in the match.

White on roll owning a 2-cube, leading 11-3 in a 15-point match. Pip Counts are 100 for White and
126 for Black.

Should White double? If White doubles, what should Black do?

You’re playing a 15-point match, and you’ve got a very comfortable lead, 11-3. You were doubled
to two early on, and you took. Now you’ve broken contact, and you’ve got a big lead in the race, 26
pips.

You’d like to redouble, but you have no idea exactly when it’s right to do so. Clearly it’s right at
some point, but — are you there yet?

These sorts of problems arise all the time in match play. Most players have a lot of difficulty with
them, primarily because our experience with backgammon doubles and takes comes from money
play, where all doubles and takes cluster around the 75% range. The doubler wants to be close to
a 75% favorite before he doubles, and the taker needs to be about 25% to take. So we know a lot
about what 3-to-1 advantages look like, but not much about what 5-to-1 or 8-to-1 or 20-to-1
advantages look like.

Solving positions like this over the board requires three steps:
Step 1: Figure out what the doubling window at this score looks like.

Step 2: Estimate your cubeless winning chances in the position.

Step 3: Compare Step 1 and Step 2.

If you’re inside the window, you should double and your opponent should take (but you’re happy if
he drops). If you’re outside the window, either you shouldn’t be doubling or he should be passing.
These problems aren’t as difficult to solve as it might seem, once you know the technique plus a
couple of tables and rules.

First, let’s figure out what the doubling window is at this score and cube level. We’ll start by
calculating the top end of the window — the end corresponding to Black’s take point. If Black
drops, he trails 13-3 in a 15-point match. We can consult match equity tables to get the answer
here. Oddly enough, tables from vastly different eras give almost exactly the same answer! Kit
Woolsey’s table from 1992 (calculated by hand and published in How to Play Tournament
Backgammon) gives the leader a 95% chance of winning at this score. Extreme Gammon’s latest
table (based upon bot versus bot results) puts it at 95.25%, a tiny change. Let’s take 95% for
easier calculations, meaning Black has just 5% chances if he drops the double. If Black takes, he
can rewhip to 8 and reach 13-13 when he wins, where he’ll win the match half the time. So taking
with a 10% chance of winning the game (cubeless) will also give him 5% match winning chances,
and therefore the top end of the doubling window is reached when White is a 90-to-10 favorite in
the game.

Our next job is to estimate the other end of the doubling window — the point at which doubling
becomes more profitable for White than waiting. This part is a little tricky. It depends partly on the
volatility of the position, which we can’t really quantify well over the board. If we’re willing to settle
for a good approximation (which we should in practical play) then we’ll estimate the low end by
comparing White’s gain when he doubles and wins to his loss when he doubles and loses. Here’s
how this goes.

White’s gain when he doubles and wins. If White doesn’t double and wins, he takes a 13-3 lead,
with 95% winning chances (see above). If he doubles and wins, he wins the match. So his gain
from doubling and winning is 5%.

White’s loss when he doubles and loses. If White doesn’t double and loses, his lead is cut to 11-5.
Both Woolsey’s table and XG’s match equity table give about 83% for an 11-5 lead to 15. If White
loses after doubling, the cube will be at 8, since Black will automatically rewhip, and the score will
be tied 11-11, so White’s chances will be 50%. The loss from doubling and losing is therefore 83%
– 50%, or 33%.

In order to profitably risk 33% to win 5%, you have to be at least a 33/(33+5) = 33/38 = 87%
favorite in the position.

So now we have our approximation for the doubling window: 87% to 90%. White shouldn’t double if
his cubeless chances are less than 87%, and Black should be passing if White’s chances are
above 90%. Between 87% and 90%, White should double and Black should take.

That’s all well and good, but what’s going on in our actual race position? White’s pip count is 100,
Black’s is 126. White leads by 26%. That’s way more than he needs to cash for money, but how do
we know whether he’s 90% or not?

Take a look at the following table. For tournament players, where these sorts of problems arise
with some frequency, it’s a good little table to commit to memory:
Leader’s Cubeless Chances Based upon His % Lead in Long Race

10% lead = 75% Cubeless Winning Chances

14% lead = 80% CWC
18% lead = 85% CWC
24% lead = 90% CWC
30% lead = 95% CWC

It’s not a hard table to remember. If you want to make it even easier, note that moving from a 10%
race lead to a 30% race lead takes you from 75% winning chances to 95% winning chances. In
other words, each extra % of lead translates almost exactly into an extra 1% cubeless winning
chances. That’s good enough for over the board work.

The table works best for races in the neighborhood of 85 to 115 pips, which covers most
interesting non-contact positions with checkers still in the outer boards. For shorter races, you’ll
need a slightly larger percentage lead to get to 90% or 95% winning chances. For longer races, a
slightly smaller percentage lead will do.

By memorizing this table, problems like this one become easy. White has a 100 to 126 lead, or
26%. In the table, we see that 26% is about 1/3 of the way from 24% to 30%, so White’s chances
are about 1/3 of the way between 90% and 95%, or about 92% cubeless. (We care only about
cubeless winning chances since Black’s redouble is forced, after which the cube is dead.) Rollouts
using Extreme Gammon confirm that number almost exactly. Since White’s doubling window was
87% to 90%, we’re outside the window on the high side, so White should double and Black should
pass.

OCT-01-2020 || MUTUAL HOLDING GAMES

Oct 1, 2020 | Backgammon Problems: Holding Game

This position is a fairly typical mutual holding game, a holding game where both sides have an
anchor in the other player’s territory. Your first job in these games is to count the race and see
where you stand. Here the pip count is 124 for White, 121 for Black. White trails by 3 pips, but after
he plays his 5-2 he’ll actually lead by 4 pips.

Money game, center cube.

Black to play 5-2.

When the race is close, strategy is fairly straightforward. Bide your time, don’t do anything drastic,
build up your board, and wait for something good to happen. With those simple ideas in mind, let’s
look at our choices.

The horrible blunder is 20/13, making White a big underdog for no reason. Black can make his 5-
point with 9 rolls and hit loose with most of the others. Even if Black rolls his worst (4-2) he’s still
doing fine.

The conceptual error is 13/6. True, it’s only six shots, but why give six winning shots in an even
race? The play isn’t terrible, since it has a clear upside: if Black misses, which he mostly does,
White gives himself plenty of time to hold his remaining position without weakening his home
board. This isn’t enough to compensate for the extra shots, but it does keep the move out of the
blunder category.

Once we eliminate 20/13 and 13/6, we have to start looking at the plays that shuffle in the inner
board. Jellyfish taught us how to play these positions back in the 1990s, and Snowie and Extreme
Gammon have since confirmed that Jellyfish had the right concept. There are two basic ideas:

Basic idea #1: Don’t be afraid to leave blots, even multiple blots, behind your opponent’s anchor.

Basic idea #2: Arrange your spare checkers so that they can play big numbers if possible.

Many players find Idea #1 counter-intuitive and scary. “If I leave a couple of blots, aren’t I just
giving my opponent an invitation to run? Shouldn’t I be locking down my board, so he has to stay?”
The reason these fears are unjustified is that, for the blots to actually hurt you, a parlay of events
has to happen:

(1) Black has to run.

(2) You have to hit him, in a way that doesn’t cover your blots.

(3) He has to hit you back.

Let’s say you think Black would run with half his rolls, and the other two events have about 30%
probability each. In that case, the parlay of all three events happening is about 4.5% — not very
likely, in other words, and nothing that should prevent you from arranging your checkers in the way
that’s most likely to give you a strong board in a couple of rolls.

So what’s the best play? The right way to arrange your board is to play 8/1. This slots the ace and
deuce-points, and leaves your spares back on the 6-point and the 8-point. Next turn you can cover
with fours, fives, and most sixes. If the big numbers can play well, then the small numbers will be
OK as well.

Notice that after a play like 8/3 6/4, White’s spares are deeper in his board, and fours and fives
now play awkwardly. That’s the sort of position you want to avoid: one where your spares are
misplaced and as a result you end up with an awkward, stacked position when your opponent does
choose to run. Remember that the action in this position probably won’t come for another couple of
turns, but when it comes, you want a strong board in place. 8/1 is the play that puts you in the best
position to have that board.

OCT-15-2020 || USING DIVERSIFICATION

Oct 15, 2020 | Backgammon Problems: Priming Games
Here are two closely related positions which illustrate an idea called diversification, which is the
opposite of duplication. Duplication enables us to reduce our opponent’s good shots by moving so
that the same number works for him in different parts of the board. Diversification increases our
own good shots by giving us different numbers working in separate parts of the board. It’s a quick
and useful tool that will generally point to good plays.

(a) Money game, Black owns a 2-cube.

White to play 1-1.

(b) Money game, Black owns a 2-cube.

White to play 1-1.

Problem (a) shows the idea in its simplest form. With two of his aces, White will of course play
2/1*(2), knocking out Black’s chance at an ace-point game and buying some more time to release
his back checkers. Now he has to decide how to arrange his remaining spares. On Black’s side of
the board, White needs fours and fives to escape, so on his side of the board, he’ll try to give
himself different numbers to attack the open 2-point.
Notice that if he plays 8/6 with his last two aces, he’ll need fours and fives to hit on the deuce point
(assuming Black enters with a checker). Those are the same numbers he needs on the other side
of the board, so in effect he’s duplicated his own good numbers — not the right idea.

A better play is 7/5 with his two aces. That gives him sixes and threes to hit on the 2-point, different
numbers from those he needs to escape. By making different numbers work on different sides of
the board, you maximize the chance that your next roll will accomplish something.

Position (b) shows a more difficult situation. This time White needs fives and sixes to escape
instead of fours and fives. Now we have to think a little.

After the mandatory 2/1*(2), White can play 7/5, giving himself sixes and threes aiming at the 2-
point, or 8/6, giving himself fives and fours. Since he needs fives and sixes on the other side of the
board, either play duplicates a number: 7/5 duplicates his sixes, and 8/6 duplicates his fives. But
notice that the duplication isn’t equal: White needs two fives to escape his back checkers, but only
one six. Since White will always prefer escaping to hitting (because escaping is harder, and you
always do what’s harder first), he won’t hit with a five until he’s first thrown two fives to escape.
That makes leaving a five to hit less useful than leaving a six to hit, so the right play is once again
7/5.

NOV-01-2020 || PREPARING FOR A SHOT

Nov 1, 2020 | Backgammon Problems: Holding Game

These next two positions show an unusual holding game situation, with Black’s board somewhat
collapsed while he still has outfield points to clear. As compensation for his messy position, Black
is ahead by 35 pips in the race, and as such is a solid favorite no matter how White plays.

(A) Money game, White owns a 2-cube.

White to play 6-4.

(B) Money game, White owns a 2-cube.

White to play 6-4.

The first part of the problem, Diagram A, shows Black with a pile of checkers on his 8-point and
White waiting for a shot, with White having a 6-4 to play. Since White is far behind in the race,
running isn’t an option; we can therefore rule out any play involving 20/14, despite the clever
duplication of threes. Always remember that duplication isn’t an end in itself, just a means to an
end.

With running out of the question, we get to the real point of the problem. White needs to work on
his board, but what’s the best way?

Ideally, you’d like to slot the key points and then cover later, and in most positions that’s what you’ll
do. You need to pay attention, however, to your opponent’s situation. If he’s about to leave a shot,
slotting might not be right. If you’ve got a constructive play that doesn’t leave a blot in your board,
you might prefer that play to avoid the variation where he leaves a shot, you hit, and he hits back. If
you don’t have a good play other than slotting, then you’ll slot anyway, because it may be the only
route to winning.

In (A), Black won’t leave a shot for a couple of turns, because he has a couple of spares on his 8-
point that he can move. Now you’re free to make the best slotting play available, which is 8/4
combined with 7/1. The alternative 8/4 8/2 looks a little prettier, but costs White a cover number for
the 4-point.

In (B), Black is stripped everywhere, which means next turn he’s likely to leave at least an indirect
shot as he tries to clear his 14-point. Now White wants to play safe if he can. Fortunately, he has a
good safe play: 7/1 5/1, which doesn’t help his prime but does give him a better board. Remember
that if White hits a shot, a prime isn’t absolutely necessary to win; it may be sufficient to just keep
Black on the bar for a couple of turns while White catches up in the race.

NOV-15-2020 || OFF TO AN EARLY LEAD

Nov 15, 2020 | Backgammon Problems: Early Game
White is off to a good start in this position. He’s neatly filled in his 3, 4, and 5-points, making a
strong home board. Black has only managed to escape one back checker, getting it as far as his 8-
point.
Money game, center cube, White on roll.

(a) Should White double? If he does, should Black take?

(b) Assume White doubles and Black takes. How should White play the following rolls:
6-6
4-4
2-2
6-4
6-2
4-3

What a pretty position! At first glance, White’s edge seems overwhelming, especially to a beginner
or intermediate. But let’s step back for a minute and apply Joe Sylvester’s trusty ‘Position-Race-
Threats’ criteria, which serves us pretty well in these early positions.
Position: Big edge to White, obviously.

Race: White leads by only two pips, 149 to 151.

Threats: None. (Of course 6-6 is crushing, but in any early position there will always be a couple of
doubles for which that’s true. When we talk about threats we’re really looking for ordinary non-
doubles that play very well. Here White is threatening to threaten, which is not quite enough to give
him a check in the ‘threat’ column.)

With no edge in the race and no particular threats, White’s game doesn’t look quite so
overwhelming. In fact, it would appear that the take is now trivial, and it’s the double that’s in
question. Rollouts back up this conclusion. The double/no double decision for money is very
marginal (making this a good and easy to remember reference position) while the take is simple.

As we look a little closer into the position, we notice another feature that strengthens our opinion of
Black’s game: he has very few bad shots. All his doubles play well, of course. His sixes either
make a point (6-1, 6-4), run to the midpoint (6-5) or run to the outfield (6-2, 6-3). White’s open
deuce-point has the curious effect of making Black’s aces more playable. Now he makes a point
with 3-1, and can hide on the 2-point with 5-1, 4-1, and 2-1, making those good numbers as well.
He makes inner points with 5-3 and 4-2, leaving only 5-4, 5-2, 4-3, and 3-2 as awkward shots, and
of those, all but 5-4 could be played safe if necessary. We’re trained to assume that positions with
no structure will play poorly, but a close examination will often really more resiliency than might be
expected.

Now we come to the checker plays. Before we look at individual moves, let’s note a couple of
features of the position:
(1) Since White’s board is so strong, splitting is better than usual for him. Black is less inclined to
hit loose, because of the obvious danger, but Black also needs to leave blots in the outfield, and
splitting makes that more dangerous.

(2) White’s bar-point has assumed a larger than usual importance, so White is also inclined to
bring down builders to his outfield.

(3) White’s good board makes hitting loose on the ace-point better than usual. For the same
reason, switching points with doubles may be more attractive.

Now on to the checker plays.

(b1) 66: Making both bars is good, but pointing on the ace-point with 13/1*(2) is the clear winner.
Both plays win about 80% of the time, but making the ace, with Black still undeveloped, wins about
55% gammons, compared to about 35% gammons for the positional play.

(b2) 44: Best here is just the normal 24/20(2) 13/9(2). The attacking play 13/1* 13/9 wins about 5%
more gammons than the quiet play, but also sacrifices about 5% winning chances, a poor trade.
Switching with 5/1*(2) 13/9(2) ruins the board and costs even more wins.

(b3) 22: Now switching is strong, because the resulting inner board, while a little weakened, is still
powerful. After 3/1*(2) and 13/11, you can choose between 13/11 and 24/22 with the last deuce.
While 24/22 looks more thematic, 13/11 does almost as well on rollouts.

(b4/b5) 64 and 62: These two should be considered together. White can choose between an out-
and-down play (24/18 and 13/9 or 13/11) or a slotting play (13/7 and 13/9 or 13/11). Slotting works
better with 13/7 13/11 because the checker on the 11-point is better placed if Black rolls a six. After
13/11, White gets a double shot if Black rolls 6-1, 6-2, or 6-3, while after 13/9 he only gets a double
shot after 6-1. The plays are otherwise very close, and that consideration makes the difference.
Slot and down with 6-2, split and down with 6-4.

(b6) 43: On the opening roll, 24/20 13/10 and 24/21 13/9 are about equivalent. Splitting to the 20-
point slots a better point and guards the whole outfield, but 13/9 produces more combinations to
make inner points. The result is a wash. Here there are no inner points to be made, so 13/10 is a
little better than 13/9 (extra shots on White’s 6-2) while 24/20, attacking the 14-point directly, is a
little better than 24/21.

DEC-1-2020 || COMING HOME IN A HOLDING GAME

Dec 1, 2020 | Backgammon Problems: Holding Game
These next two positions show a couple of closely related holding game situations. Black has the
20-point, but now he’s got a man stuck on the bar. White has a nice 5-point board, and a couple of
blots not in direct range of Black’s anchor. He also has the 9-point, which was an asset for a while,
but is now a liability to be cleared. How much risk should he be willing to take while Black is on the
bar?
 Money game, Black owns the cube, White on roll.

(A) White to play 6-5, 6-3, 5-4, 5-3, 5-2, and 3-2.

(B) Slightly different position, White to play all the same numbers as in (A).
In approaching these technical positions in the later part of the game, I like to use a technique I call
“bracketing” (from the old naval gunnery term). Instead of trying to solve one play for one position, I
pick a bunch of non-trivial rolls, then make one or two modifications to the position, then solve all
the rolls for all the positions, then go back and look for patterns. The patterns will tell you much
more about the positions than could any single problem.

So how should White plan to come home? Here we’ve got six rolls for White, and two positions,
one where Black has a closed board, and one where Black has a high point open with the
possibility of covering it later. Let’s look at the cross-section of plays and problems and see what
we can discover about our starting position.

The first big point to notice is the difference between the two Black positions is pretty much an
optical illusion. Rollouts showed that moving from (A) to (B) only changes the right play in the case
of 6-5, and then only by a tiny margin.

Why wouldn’t a closed board make White play safer? Three reasons:
(1) The closed board doesn’t always hold up. Suppose White’s first roll is 5-2, played 13/6. Of
Black’s 11 entering numbers, 5-1 and 5-4 (4 shots) break his board by force. But on 5-2 and 5-3 (4
more shots), Black should break his board voluntarily, rather than moving into the outfield and
giving White a double shot, which will win a few extra gammons when he hits. Only 5-5 and 5-6
actually keep Black’s board intact.

(2) Black doesn’t hit very often, so whatever difference there may be doesn’t come into play much.

(3) When Black does hit, the 5-point board is mostly good enough to win anyway.

The second big idea is that if White can clear his 9-point safely, he should do so. Clearing with 6-3
and 5-3 is much better than bringing in a checker. Clearing with 6-5 is tied with making the 7-point,
but that’s only because the 7-point makes clearing the 9-point much easier later.

Clearing is such a big deal that’s it’s worth doing with the 3-2 roll (9/6 9/7), despite leaving an
indirect shot. (It’s a closer but still correct play if Black has a closed board, because playing 13/10
12/10 makes 5-5 an awful shot for Black.)

If White can’t clear, but he can bring a blot home, then he should bring home the checker on the
13-point; with 5-2 he plays 13/6, and with 5-4 he plays 13/4. He safeties the checker on the 13-
point because the checker on the 12-point can get home with more numbers.

Note that with 3-2 White doesn’t have the option of bringing a blot home, so clearing the 9-point
becomes best despite the risk.

Solutions:

6-5: (a) 9/3 9/4 (b) 13/7 12/7. Both are very close.
6-3: 9/3 9/6 in both.
5-4: 13/4 in both.
5-3: 9/6 9/4 in both.
5-2: 13/6 in both.
3-2: 9/6 9/7 in both. In (a), 13/10 12/10 is very close.

DEC-15-2020 || STUDYING YOUR

OPPONENT’S POSITION
Dec 15, 2020 | Backgammon Problems: Holding Game
This position shows a pretty normal-looking mutual holding game. White was two pips
down in the race (114-112) prior to rolling. But he fired a great shot, double-fives, which
moved him to an 18-pip lead. What should he do?
 Money game, center cube, White on roll.

White to play 5-5.

The normal rule with a solid lead in a holding game is to disengage from the back. That
would suggest 20/10 and 16/11 with the first three fives, and then either 11/6 or 10/5 with
the last five. Of those two choices, 11/6 would dominate because it leaves fewer shots (14
instead of 15) and the blot on the 10-point is a little more useful as a landing spot when
clearing the 13-point.

“Clearing from the back” is a reliable general principle and I think most players would play
16/6 20/10 quickly. Nonetheless, it’s a huge blunder! Let’s see why.

Poker players are accustomed to seeing their hand from different points of view. Their first
point of view is “What do I have?” The next point of view is “Based on what I’ve seen so
far, what do I think my opponent has?” And a further point of view is “Based on what I’ve
done so far, what does my opponent think I have?” As poker players acquire experience,
they move gradually from a view that only looks at their own hand to one that incorporates
all the information they have so far about their hand and their opponent’s. Failing to think
on levels beyond a simple “What do I have?” gets very expensive very quickly.

Backgammon players face a variation on this same problem. Even though your opponent’s
position is in full view, many players don’t really look at the unique features of their
opponent’s structure when considering a checker play. Instead, they imagine they’re facing
a sort of generic structure, one with no unusual weaknesses, and decide on the best play
against that structure. Often however, your opponent’s position has some exploitable
features, like inner-board blots, dead checkers, or stripped points, all of which can
combine to make some choices better than others.

Instead of just deciding to “move from the back, because I’m ahead in the race”, let’s look
at Black’s position a little more closely and see if anything prods us to do something
different. The first feature we notice is that Black’s outside points are all stripped, and his
only inner-board spare is on the 4-point, giving him just a 3 to play. That means that unless
Black can roll a double or hit something next turn, a lot of his rolls containing a 4, 5, or 6
must be pretty bad for him. Since we have to leave a shot anyway, that insight leads us
directly to the best play: 16/1 6/1! Instead of leaving a shot but allowing Black to move
freely when he misses, we stay back and keep up the pressure, giving Black some good
rolls but lots of bad rolls as well.

Jan-01-2021 || Playing a Blitz

Jan 1, 2021 | Backgammon Problems: Blitzes

This position shows an interesting blitz situation. Black’s been caught with a checker on
the bar, another exposed blot in White’s home board, and a third blot in his own outfield.
White has a three point board with a fourth point slotted, plus a few builders on hand.

Money game, Black owns the cube, White on roll.

White to play 6-1.

If Black were helpless, White would have a strong attack. Unlike the case with an opening
blitz, however, Black actually has a position here, with a strong board and a four-point
block. If White’s blitz fails, Black will get the upper hand very quickly.

White has four reasonable and distinct choices with his 6-1:

(a) Closing a fourth point in his board with 9/2.

(b) Hitting the outside blot with 22/15*.

(c) Hitting inside and picking up, with 10/4*/3.

(d) Hitting inside and leaving two blots, with 10/4* 9/8 or 10/4* 3/2.

Blitz positions tend to be tricky. In general, your top priority is to hit blots and make points.
If you can do only one of these things, you’ve got a nice, easy decision. If you can do both,
you’ve probably got a tough decision. If you can’t do either, you’ve got a choice between
bringing down builders and moving your back men, and those can also be tough decisions.
I like to categorize blitz problems based on the strength of my inner board. (Assuming I’m
the one doing the blitzing!) With a 2-point board, hitting blots tends to trump making a third
point, because the third point still doesn’t make the board all that strong. With a 3-point
board, a play that makes the fourth point is relatively very powerful. The same
improvement occurs when going from a 4-point board to a 5-point board. In this area,
making the extra point (all other things being equal) often trumps hitting another blot.

The other question to consider is just how valuable it is to hit the next blot. If you’re only
attacking one checker, hitting a second checker is very important. If you already have two
checkers on the bar, hitting a third is a low priority. Additional checkers have an even lower
priority.

With those ideas in place, let’s look at our actual problem. First let’s note that among the
hitting plays, 22/15* trumps both 10/4*/3 and 10/4* 3/2. Picking and passing leaves White
with a semi-dead checker on the 3-point, while leaving two blots is just too risky in light of
Black’s board. Another point to notice is that unlike the case in a normal blitz, we’re
already a solid underdog in this position: no matter what play we make, our winning
chances are only about 40%.

So our choice is between 9/2 and 22/15*. We have a 3.5-point board, so making the fourth
point would normally be our default play in the absence of other factors. Here most of the
other factors also point to building our board. Black’s position is much stronger than in a
normal blitz, so getting hit back could be immediately fatal. Hitting and escaping is nice,
but we still have two more checkers to extract, and Black has 21 very strong numbers (2s,
4s, and 55) on his very first shot.

For all these reasons, the best play is the simple 9/2, and rollouts confirm this. 22/15* is
very slightly better at double match point, but 9/2 both wins more gammons and loses
fewer gammons than any other play, moving it to the top spot in a cash game. The plays
that hit in the inner board are much worse.

Can we tweak the position a little to make 22/15* the better choice? Let’s do some
experimenting and see what happens.

Let’s start by relieving some of the pressure on White. We’ll move two of his back
checkers out to the midpoint.
 Position A: White to play 6-1.

This change puts White ahead in the race by 20 more pips. The count is now 121-147 in
favor of White. In addition, he now has more builders at his disposal that can reach his
inner board pretty quickly. Is this enough to tip the balance in favor of one of the hitting
plays?

Alas, no. White’s raw winning chances have now risen into the low-50% range, so at least
he’s a favorite in the position. However, 9/2 is still better than 22/15*, although the
difference is closer. Once again, 22/15* is slightly better at double match point, but 9/2
wins more gammons and loser fewer, making it the overall winner.

Let’s give White a little more help. This time we’ll bust up Black’s board a little.

Position B: White to play 6-1.

We’ve taken away Black’s 5-point, moving the checkers back a bit. Now White’s doing
even better in the race, and has less to worry about if he does get hit. Does this change
the evaluation?

Nope. In fact, 9/2’s edge over 22/15* is now even greater! The difference is that when
White covers the 2-point and Black throws his best number – something containing a 4 –
White’s in much less danger of losing than before. Covering the 2-point is now the best
play at double match point, and it still wins more gammons and losers fewer than before.

Let’s make one more try. From Position B, we’ll strengthen White’s board by moving two
checkers from his midpoint to his 5-point. Here’s the new position:
 Position C: White to play 6-1.

Does that change anything? Actually it does, a little. Making the 2-point is right by an even
wider margin than in any of the other positions, but now we have a new runner-up: 22/15*
has slid back into third place, and 10/4*/3 has moved into a solid second place. This
makes perfect sense. The closer White gets to the actual closeout, the more important it
becomes to eliminate Black’s chance for an anchor. Black’s blot on the 15-point is now
increasingly irrelevant to the outcome of the game.

The moral of the problem: In a blitz, hitting isn’t automatic. Don’t underestimate the value
of simply closing points in your board.

JAN-15-2021 PLAYING A BLITZ PART 2

Jan 15, 2021 | Backgammon Problems: Blitzes
Here we’re returning to the theme of the previous post: a late game blitz with a choice of
hitting outside or making a point inside. (In this case, making the inside point also has the
nice advantage of putting a checker in the air at the same time.) These problems are
inherently very difficult, and require looking at all the features of the position before making
a decision.
 Money game, Black owns the cube, White on roll.
Black to play 2-2.
Let’s start by looking at our goals in a late-game blitz position. Basically, we have four
goals. Roughly in order of importance, they are:

(1) Close points in our board.

(2) Hit all the blots we can.
(3) Bring down builders for the remaining open points in our board.
(4) Escape our back checkers.
Note that these are also our goals for an early blitz. The difference between early blitzes
and late blitzes is that our opponent’s structure is much stronger in a late blitz, which
makes not getting hit and escaping the back checkers a higher priority.

The most common mistake players make in any blitz position is hitting blots instead of
closing points in their board. In general, closing home board points is a higher priority than
hitting outside blots. (There are plenty of exceptions, of course.) However, hitting more
blots is very attractive to most players, and becomes their default choice in blitz positions.
Why? Here are the main reasons.

> Hitting blots will win more gammons. True, as long as you eventually close your board.
> Hitting blots will slow our opponent down while he tries to come in from the bar. True. If
he has two men on the bar, very few numbers will enter both checkers.
> Hitting blots will give our rear checkers time to escape. Also true. Many players remember all
the times they lost a blitz because they couldn’t get their back checkers out. If your
opponent is struggling to come in from the bar, he can’t be building a block against you.
These are all true statements, but they don’t tell the whole story, and taken together they
can often lead in the wrong direction. Here’s a better idea to keep in mind:

> When you have a choice of good things to do, do the harder thing first. Closing your
board is harder than picking up stray blots.
In almost every blitz position, you’ll have only a few rolls to close points. Once you close
your board, however, you’ll often get several shots at loose blots while you bring your men
around. While a lot of players see hitting blots as a way to buy time, closing points is a
much better way to buy time. The longer your opponent dances, the more time you have to
escape checkers and pick up the trash.

Now let’s look at our plausible moves:

(1) 3/1* 5/1 11/9. This play makes the ace-point, puts Black on the bar, and brings a third
builder to bear on the 4-point.
(2) 3/1* 5/1 18/16. Also makes the ace-point and puts Black on the bar, but now gets a
double shot at Black’s other blot. Black, however, now has a few rolls that turn the game
around.
(3) 18/14*(2). Picks up the second checker, but doesn’t make another point in the board.
Black can now anchor if he rolls an ace.
(4) 18/14* 3/1* 11/9. Puts two checkers up in the air and goes straight for the gammon. A
return ace on Black’s part could make things exciting.
From our earlier discussion, it should be clear that White’s first three deuces need to be
3/1* and 5/1, putting Black on the bar against a 5-point board. Playing 18/14*(2) instead
gives Black a shot at making an ace-point game, after which White’s winning chances and
gammon chances drop off dramatically. To see just how dramatically, imagine that White
reaches either a closed board or an ace-point game from this position, with Black’s
remaining checkers in their current position. Here are the rollout percentages for the three
possible cases:

White has a closed board, one Black checker on bar: 98% wins, 73% gammons.
White has a closed board, two Black checkers on bar: 98% wins, 90% gammons.
Black gets an ace-point game: 85% wins, 33% gammons.

White’s entitled to take small risks to hit the second checker, but preventing the ace-point
game is absolutely huge.

So — after making the ace-point, should White play 11/9 or 18/16? Here Black’s strong
position provides the clue. In an early blitz, these plays might be close, but with Black’s
strong board, 18/16 is too risky, and 11/9 is a better choice.

In the same way, the loose double-hit (Play 4) is also too big. A single ace on Black’s part
and the game is up for grabs again.

FEB-01-2021 || CREATING BAD NUMBERS

Feb 1, 2021 | Backgammon Problems: Priming Games
This next problem shows a somewhat unusual middle game position. White, with one
checker in the air, has an outside prime with the 5-point slotted. Black has a bizarre
position with four checkers back on his 24-point. His front game is normal enough, with the
start of a little block. Last turn, White doubled from the bar and Black bravely took. (A small
mistake, actually. The position is a pass, although not by much.)

Money game, Black owns the cube, White on roll.

White to play 5-2.
White’s 5-2 from the bar gives him a few choices. Here’s a quick list of the main options:

(1) Bar/23 13/8. The safest play, this keeps the back checker from being attacked on the
20-point, while adding another cover number for the 5-point.
(2) Bar/20 5/3. Another safe option, this time duplicating twos. This also prevents Black
from simultaneously hitting and getting to the edge of White’s prime. The downside of the
play is that it becomes hard for White to build on his early advantage. Covering the 3-point
won’t make his game appreciably stronger.
(3) Bar/20 13/11. This play is a different way of bringing down another cover number to
make a 5-prime.
(4) Bar/20 7/5. This play shifts points, covering the 5-point and leaving the bar-point slotted.
Those are all the reasonable plays; anything else we can eliminate quickly. The next step
is pruning our tree a little bit more. Are there any of these play that don’t stand up to a
closer inspection?

To make progress, let’s focus on our opponent for a second. What is his big weakness,
and what are his awkward numbers?

Black’s main problem, clearly, is that mass of checkers on his 24-point (our ace-point).
Black needs to get those checkers moving quickly, before his front game stalls and
collapses. He can move them with aces through fours, but his fives and sixes are blocked.
That insight lets us toss two of our candidates right away. Move (1), Bar/23 13/8, makes
fives and sixes somewhat useful by letting him hit on our 23-point. Move (4), Bar/20 7/5,
makes sixes not only active but highly useful, letting him step out to our bar-point while
hitting at the same time. Let’s eliminate both those moves and focus on the last two,
Bar/20 5/3 and Bar/20 13/11.

The choice between these two plays hinges on the cube position. We’ve given the cube
away, so we want to finish Black off as quickly as possible. Making a prime is the best way
to do that, and the risk (a single shot) is not that great. Playing 5/3, after all, still gives
Black a shot, and on a point we don’t really care about making. So let’s leave our blot
where it belongs and play Bar/20 13/11. Making the prime wraps up the game – if Black
misses, he’s in a hopeless position with nowhere near the timing to play a back game.

(Incidentally, if we had forgotten to double last turn so the cube was still in the middle, then
5/3 would be right. The idea in that case would be to minimize the chance of a big
downswing so we could keep our advantage and turn the cube on the following turn.)

FEB-15-2021 || PRIMING GAMES: ACTION

VERSUS TIMING
Feb 15, 2021 | Backgammon Problems: Priming Games, Uncategorized

The next position is an interesting problem with a few non-standard elements. On the one
hand, it’s a prime versus prime problem; both sides have 5-point primes, and both sides
have some escaping to do. On the other hand, it’s an action play problem. White is on the
bar shooting at a couple of blots, and a lot hinges on whether he hits or not next turn.

Money game, center cube, White on roll.

 Should White double? What should Black do if White doubles?
So we have a blend of priming elements and action elements. Which elements are more
important? That’s actually an easy question to answer. Take a look at Position A:

Position A: White on roll. Cube action?

Position A is just our original position with one Black checker moved from his 2-point back
to his 14-point. White now has 27 shots from the bar at three blots, so the action aspect of
the position is even stronger. (Look at how 1-1 now plays!) But – the checker on Black’s
14-point now gives Black more timing, so the priming aspect of the position is worse for
White.

Compared to our original position, White has more action but less timing. Which is more
important? If you said “timing”, good for you. Black’s extra timing dominates White’s extra
action, and in fact White’s winning chances drop by almost 7% in going from the original
position to position A. Fundamentally, this is a prime versus prime situation. The action
element is secondary, although if White’s advantage is big enough, the action element will
push White to double now rather than later, as a bigger than usual swing could happen on
the next roll.

Now let’s take a closer look at the original position itself. Clearly White has the edge. His
threat is to enter and hit a checker – then Black enters and breaks his prime – then White
hops out and hits another checker – then Black enters and cracks some more – then the
inevitable gammon. A grim scenario. White should double and Black should pass, right?

Well, let’s hold up a bit on the pass. In evaluating positions, we need to avoid a certain trap
which is easy to walk into, especially (but not exclusively) in priming games. I call it
the Trap of the Main Line, and it’s simply the tendency to find what appears to be the main
line of a position and assume that it happens much more often than it actually does. In
positions where neither side has an especially strong inner board, the game can slide off
into a lot of different variations, most of which offer the defender more resources than the
main line. Players who train themselves to supplement computer rollouts with the
occasional manual rollout are more inoculated against this trap, but we all fall victim to it
from time to time.
(If you’re a hold’em poker player, the ‘Trap of the Main Line’ has an exact analogy in the
fallacy of “putting your opponent on a hand”, where you assume your opponent has a
single hand and you play against that hand, instead of putting him on a range of hands
and making the play that works the best against that whole range.)

While the main line in the original position is a disaster for Black, there are plenty of other
variations where he does all right. In prime against prime games, I think it’s useful to look
at the hard cold facts of the position as it now stands: White has three men behind Black’s
5-point prime. That’s a lot of men behind a big prime. White is only a slight favorite to hit a
shot, and whether he hits it or not, he still has three checkers to extract. When Black’s
prime does break, it breaks from a 5-prime down to a 4-prime, but plenty of games are
won by a 4-point prime.

On the bright side, White has some timing left and Black has almost none, so there will be
plenty of variations where White hits a checker and wiggles free. Those variations won’t
necessarily lead to a gammon, because White only has a 3-point board right now. But
there will be plenty of games where Black falls into a low-anchor game with a busted
board, and those are easy for White to win.

Conclusion: White should double, and Black has an easy take.

How much timing would make this a pass for Black? Take a look at Position B:

Position B: White on roll, cube action?

Compared to our original position, White has seven more pips of timing. Each pip gave
him about an extra half-percent in winning chances, so B is a strong double and just barely
a pass. There’s no formula that I’m aware of that “solves” these priming games, but notice
that in B, White can play at least two full rolls with his outside checkers (barring an
awkward double) before he has to think about breaking his prime. That idea – how many
rolls can I play without rolling a six and without breaking my prime – seems to be a useful
parameter to keep in mind when judging these tricky situations.

MAR-01-2021 || PRIMING GAMES –

ESCAPE OR ATTACK
Mar 1, 2021 | Backgammon Problems: Priming Games
Money game, White owns the cube.

White to play 4-1.

This position is not difficult but it illustrates a key idea in priming games, whether prime
against prime or prime against blitz: Do the hardest thing first, and force your opponent to do a
hard thing in reply.
By “hard thing” I mean anything that you are a 70-30 underdog (or worse) to do. Usually
this implies anything that must be done and which requires a single number on the dice.
When we begin thinking in terms of “doing hard things” and “making our opponent do hard
things”, complicated positions can start to look pretty simple.

Here, for instance, it’s clear that Black’s prime will not break. Black has to come in from the
bar, which might take a while, after which he has the checkers on the 18-point to move, as
well as the checker which just entered and the checker on the midpoint. So to win, White
will have to escape his rear checker, and that will require an ace (a “hard thing”) plus a six
(another “hard thing”). Since he just threw an ace, he wants to play 24/23 if at all possible.
Since he can use the four to make both a 5-point board and a 5-prime, that’s his play. He
should move 24/23 and 6/2.

What would it take for White to pass up 24/23 with the ace? In most variations of this
position, 24/23 will remain correct, but here’s an example where it’s a mistake:
 Position A: White to play 4-1.
Without a 5-point board to give Black something “hard” to do, White doesn’t have the
security of moving to the 23-point. Here he has to play 2/1, to keep Black on the bar for
some time. After that, either 8/4 or 13/9 are about equal.

MAR-15-2021 || BEARING OFF AGAINST

CONTACT
Mar 15, 2021 | Backgammon Problems: Ace and Deuce-Point Games
Cash game, Black owns a 2-cube.

White to play 4-1.

Back at World Cup VI, in 1998, Kent Goulding and I introduced a ‘Quizgammon’ contest,
consisting of a set of 30 problems taken from all phases of the game. Everyone who was
interested paid an entry fee of $20 and sat down for an hour with their problems and
answer sheet. After everyone handed in their solutions, Kent and I went over the answers
and announced the winners.
The event was an instant success. Players really liked the idea of matching wits, with the
luck of the dice finally and thoroughly removed. The late Herb Gurland, a terrific but then
underrated player from Boston, won the initial contest ahead of more famous players like
Paul Magriel, Nack Ballard, and Kit Woolsey.

The idea caught on and Quizgammons and their variants have been seen at a lot of
tournaments since. This position is taken from a Quizgammon contest in Boston in 2003
(won by Falafel, well ahead of the field). It was the hardest problem in that quiz, the only
one that no one was able to solve over the board.

Here White is bearing off against a busted deuce-point game. His bearoff position is all
right but not great. The pile of checkers on the 6-point combined with the stripped 4-point
indicates that White may have trouble with shots and awkwardness somewhere down the
road. Getting hit isn’t likely to cost White the game, but it might spell the difference
between winning a single game and winning a gammon.

At first glance, the position seems to offer a choice between a “safe” play, 6/1, which stays
nicely even-ended, and a “bold(er)” play, 5/off, which gets a checker off but leaves the 4-
point and 5-point stripped. On closer examination, another play pops up: 4/off 4/3, which
gets a checker off and clears the 4-point, leaving spares on all the other points. This starts
to look appealing because all the spares might let White rip off a lot of checkers over the
next few turns.

Most players stop their analysis at this point. Those are the only plays that don’t volunteer
a shot, and volunteering a shot in the bearoff when you have many reasonable alternatives
is – unthinkable?

Well, not quite unthinkable. It’s just very rare. But here’s a good example of when the rare
becomes possible. Here are some of the features that argue for an unusual play:

(1) Black has no board, so getting hit won’t lose the game.

(2) The gammon is a bit of a long shot, so White wants to bear off in a hurry.

(3) White’s position is just awkward enough so that bearing off both quickly and safely will
be hard to do.

Put all these factors together and a fourth play comes to mind: 4/off 1/off! This looks super-
aggressive at first (volunteering a shot just to get another checker off), but if Black hits he’s
in a vulnerable position, with at least three and maybe four blots strung around the board.
On reflection, this must be the best play to win a gammon, and that in turn raises another
question. If White rips two off, will Black even hit with his deuces?

The answer to that question is – sometimes. Black should hit with 2-1 and 2-2, because
those numbers pick up the blot in his board, eliminating the direct shots. He should also hit
with 2-6 and 2-5, because those numbers get the blot on the 23-point into the outfield,
where it’s a little safe. The intermediate deuces, 2-3 and 2-4, neither safety the blot on
Black’s 3-point nor move the blot on his 23-point, and with those numbers he should pass
up the hit and just move the checker on his 12-point.
Note also that when hitting is right, it’s mostly right by a tiny amount. Only with 2-2, which
leaves only one blot around, is the hit massively correct.

Compared to the best double match point play, 5/off, taking two off with 4/off 1/off costs
about 1% winning chances in exchange for 5% more gammons, a very favorable trade. It’s
a cute play, and a strong argument for looking carefully to make sure you’ve seen all the
plausible plays. You can’t make a play that you never see.

APR-01-2021 || THE SQUAT ZONE

Apr 1, 2021 | Backgammon Problems: Middle Game
In the 1970s, the New Yorkers invented a term for the new style of backgammon they
were playing, a style based upon aggressive hitting and slotting. They called it pure play.
The essence of pure play was the willingness to take risks in the race to build a crushing
prime quickly. If the plays worked, you had a winning prime. If your opponent got lucky and
hit you a few times, you just had to outplay him in the resulting back game/holding game.
(Since the top players played these complex positions very well, this was usually no
problem.)
Cash game, center cube.

Black to play 3-2.

While they were naming their own style, the New Yorkers also coined a name for the
opposite style – the beginner style of playing safe and stacking up your checkers. They
called it playing squat.
Playing squat isn’t the same as playing conservatively. A conservative player may be
uncomfortable with aggressive slotting, but he has enough experience to know that stacks
are weak and that sometimes slotting and other risk-taking is necessary to keep your
position from becoming unplayable. A squat player doesn’t know that. He’s a beginner,
and he thinks the goal of the game is not to be hit. When you believe that, you’re going to
create some big stacks before your game falls apart.

Players who study the game even a little learn the basics of taking small risks to improve
their position, and avoiding big stacks. As a result, they create normal, good-looking,
balanced positions, and they gradually learn the rules of handling those positions. They
don’t see many squat positions in their own games, unless they come about by a freakish
set of rolls.

But here’s a little secret about squat positions: like back games, they have their own logic.
As your position becomes more and more squat, you lose the ability to fix it by making
what would be normally aggressive developing moves. In a flexible, well-balanced
position, you’d rather not be hit after a slotting play, but your game is strong enough that
you can survive and play on. In a very stacked position, being hit and falling behind in the
race can be a disaster. Thus we get to the squatting paradox: the more stacked your
position, the more you may have to make ugly stacking moves.

I call the positions that fit these conditions the squat zone. When two decent players play
each other, they may never see one of these positions. Real beginners, however,
practically live in the squat zone.
This position is a classic example. White didn’t necessarily do anything wrong to get here
– he may have just rolled an ugly set of boxes at some point. But however it happened, his
position is a mess, with a big stack on the 6-point and a smaller stack on the midpoint.
He’s clearly going to enter and hit with his three, and then he can choose among three
different deuces.

In a more normal position, the obvious choice would be between 6/4 (unstacking and
slotting a good point) and 13/11 (safer, and forcing Black to break a good point in order to
hit.) In this squat zone position, however, both these alternatives are too loose. White
doesn’t gain enough when the plays work, and he loses too much when his blots get hit.

His best choice is the bizarre-looking 8/6, putting a seventh checker on the 6-point. His
game plan is to try to capitalize on his big racing lead by running his back checker home,
while trying to avoid leaving any extra blots. In the squat zone, 3-2 almost qualifies as a
perfecta! It hits, gains ground in the race, and plays safe. What a shot.

APR-15-2021 || ROOT NUMBERS

Apr 15, 2021 | Backgammon Problems: Priming Games
Cash game, White owns the cube.

White to play 5-1.

Root Numbers
In backgammon, a root number is just a dice throw that damages or destroys your position.
We mostly encounter these by accident, when we throw an awkward shot that can’t be
played except by wrecking our inner board or leaving a bunch of blots somewhere.
Root numbers don’t always happen by accident, however. Sometimes the only way of
saving a hopeless position is to notice that by making a certain play, you can create a few
root numbers for your opponent which wouldn’t exist otherwise.
This position is a good example. White is in a pretty bad way, with three checkers trapped
behind a 5-prime, none at the edge, and a front position which is collapsing. White owns
the cube, and most players would be thinking about simply avoiding the gammon. With
that in mind, White has a few obvious choices:

(1) 6/1 6/5. Since White has to play the five on his side, this is the only play that doesn’t
expose another blot. Should be good for saving the gammon.
(2) 8/3 24/23. This keeps a strong inner board, and White will save more gammons from
having the 23-point anchor than if he’s back on the 24-point.
(3) 8/3 23/22. This tries to get to the edge of the prime, but Black has too much leeway.
Sixes now hit and jump, while twos, threes, and fives attack on Black’s 3-point.
If these were the only plays you considered, you’d probably choose play (2). Making the
23-point saves a few gammons and offers slightly better winning chances than remaining
back on the 24-point. Leaving a shot is too bad, but breaking your board to avoid a shot
will cost you some gammons down the road anyway.

The best play, however, hasn’t appeared on our radar screen yet. Take a look at

(4) 6/1 24/23!

White makes the better anchor on the 23-point, but leaves a shot on his 6-point rather than
his 8-point. At first glance this seems nonsensical. Why break an inner-board point instead
of an outer-board point? But on a second glance the reason becomes clear. By making the
23-point and keeping the 8-point, White blocks sixes from both Black’s 23-point and 8-
point, leaving Black totally free to play sixes only from his 7-point. Although Black can run
with 6-4 and 6-5 and play 8/1* with a 6-1, rolls of 6-2, 6-3, and 6-6 force him to break his 7-
point. White’s play has created five root numbers, and while those numbers don’t lose for
Black, they do give White some real chances in the game. After the sequence White 5-1:
6/1 24/23 and Black 6-2: 7/1* 7/5, White’s winning chances are in the 36% range with a
few gammons, much better than the 14% to 15% chances he has after other plays of the
5-1.

A root number can ruin a good position, but finding plays to create root numbers for your
opponent is difficult. Look for them in positions where both players have strong blocks and
each side has some men back, and then look to see how your opponent’s big numbers
play. Almost any position can handle small numbers; it’s the big numbers that can cause a
problem. Above all, don’t give up on a position just because you’re losing. Stay alert, and
you’ll see that these kind of plays can occur more often than you think.

MAY-01-2021 || SLOTTING IN THE

MIDDLE GAME
May 1, 2021 | Backgammon Problems: Middle Game
Slotting is an easy idea to understand in the opening. When we slot the 5-point with an
opening 2-1, we threaten to make a very strong point while unstacking a big stack. Since
our opponent has no board, getting hit is just a minor inconvenience. Although it’s not a
hugely correct play (splitting our back men is almost as good), it’s not a hard play to make
because the downside seems pretty small.
Slotting in the middle game or the endgame is very different. Now your opponent almost
certainly has a reasonable home board, so the cost from being hit is much greater. It’s also
unlikely that you still have a stacked position at this point, so unstacking probably isn’t a
big goal.

With a hit being more expensive and unstacking not so important, we’ve knocked out two
of the three pillars supporting an early slot, and we’re reduced to just one: the value of the
point itself. When we slot in the middle game, the point needs to be really important, and
the chance of making it cleanly without slotting not so good. There is, however, a new
factor affecting a middle game slot: the cube. A slot followed by a miss from your opponent
may give you a good double, which in some cases is enough to tip the play in favor of
slotting.

With those ideas in mind, let’s look at Position A.

(A) Cash game, center cube.

White to play 6-1.

The six is clear: 13/7. With the ace White has a choice of two safe plays, 8/7 and 13/12,
and the slotting play, 6/5. Of the safe plays, 8/7 dominates since it gives more ways to
make the 5-point cleanly if White steps up with a three, and the checker in the outfield will
have a few more hitting numbers from the 13-point if White escapes with 5-3 or 6-3. So
now our choice is between 13/7 8/7 and 13/7 6/5.

What’s right? With Black having just one checker back, and White not having a lot of
numbers to make the 5-point naturally, the right play is to slot with 6/5. White’s problem
here is that if he doesn’t slot, he runs out of time fairly quickly. He doesn’t want to move his
back checkers yet, and that leaves him only the checker on the 13-point that can move
cleanly. Black, meanwhile, only needs to roll one good number to escape his back checker
and turn the game around, and his spare checkers give him time to wait for that number.

Does the cube affect the decision? Not in this case. It’s true that if White slots and Black
misses with some neutral roll (say 5-2: 11/4) then White has a huge double and Black
barely has a take, while after 13/7 8/7 followed by a neutral roll, it’s no double/take.
However, slotting is also the double match point play, so we can’t really say that the
potential cube turn makes slotting correct. The potential 6-prime is such a big swing
against one checker back that the slot is worth the risk.
Now look at Position B.

(B) Cash game, center cube.

White to play 6-1.

Here Black has two checkers on his 23-point, rather than just one, as well as one fewer
checker in his outfield. These changes make a big difference. White has less need to
make his 5-point, since Black will require many more moves to escape. In addition, coming
up to White’s 5-point is more dangerous for Black than before, since it now leaves two
checkers exposed, subject to a possible blitz. The absence of the spare on Black’s 11-
point also has an effect, since any six by Black except 6-3 will now leave a blot out there.

The effect of all these changes is that White has no need to slot the 5-point, but can just
play the safe 13/7 8/7 and wait. After a neutral roll for Black like 5-2, played 6/1/ 6/4, White
can already double, although Black will have a clear take.

The general lesson to take away from these two positions is that middle game slotting is
more effective and necessary against one checker back. If your opponent has two
checkers back, slotting is probably an overplay, unless it also lets you unstack an awkward
position.

JUNE-01-2021 || HOLDING GAMES WITH STRAGGLERS

Jun 1, 2021 | Backgammon Problems: Holding Game

One of the most common middle game structures in backgammon is the holding game,
where at least one side has made an advanced anchor, and the other side has to get his
checkers home while leaving as few shots as possible. Holding games are even more
common now than previously, because of the tendency to split the back men with most
opening rolls, which tends to result in anchors for both sides.

Here are a couple of examples of interesting holding game problems:

(A) Cash game, center cube.

 White to play 6-2.
(B) Cash game, White owns the cube.

White to play 3-3.

Holding games don’t come in just one flavor. I like to break them into four main groups, as follows:

Group 1: Pure Holding Game. In these games the defender has an anchor on the 18, 20, or 21-points, and no
other men back. The other side has escaped all his back men at least as far as his midpoint.
Group 2: Mutual Holding Game. Here both sides have made an advanced anchor, and usually have their
midpoints as well. This form of the game doesn’t usually last long. Both sides have a lot of pips tied up in key
points, and are quickly faced with issues of which point to break.
Group 3: Holding Game with 3rd Checker Back. Here one player has an advanced anchor, plus a straggler
somewhere behind the anchor. The other side has escaped his checkers to at least his midpoint. These
positions are considerably trickier than the basic holding games. The side with the straggler has to decide
when it ceases to be an asset and becomes a liability. Should he leave it where it is? Should he move it up to
the anchor if he can? Should he run it into the outfield? The side coming home has some decisions of his
own. Should he play safe? Should he attack the straggler? How does the straggler affect the doubling
decisions?
Group 4: Holding Game with 3rd and 4th Checkers Back. Once in a while you’ll see a position with two stragglers
in the board, creating even more possibilities. Now there’s a chance the stragglers can form a second
anchor, which makes them a real asset. On the other hand, they’re targets for an attack, which makes them
a real liability. When do you run them out? When should you leave them alone?
Here are a few guidelines for handling the anchor plus straggler positions.

1) The Race: The farther behind in the race, the more you want to leave the straggler alone. The straggler
guards points and creates some blot numbers for your opponent, so the farther behind you are, the more you
need your straggler.
2) Closeness to the Anchor: The less distance between the straggler and the anchor, the less work the
straggler does. The ideal spot for the straggler is back on your opponent’s ace-point, where he guards the
most open points.
3) Blot Numbers: The more blot numbers your opponent has, the more you want to leave the straggler where
he is.
4) Opponent’s Home Board: The stronger your opponent’s board, the less work your straggler is doing. His
value is guarding open points, so the fewer open points, the less work he does.
5) Opponent’s Attacking Chances: The more numbers that point on your straggler, the more of a liability he
becomes.
Now let’s take a look at our two problems and see if these guidelines point to a clear solution.

In (A), White has an anchor on the 21-point and a straggler on the 22-point. Let’s see how this position
stacks up according to our five guidelines.

1) The Race – Black trails by 23 pips, 128 to 151. That’s a strong argument for staying.
2) Closeness to the Anchor – The straggler is right behind the anchor, guarding only one additional point (the
22-point). He’s not doing much work, which is an argument for running.
3) Blot Numbers – Because he’s so close to the anchor, the straggler only generates one new blot number (6-
3). That’s an argument for running.
4) Opponent’s Home Board – It’s very weak, with no new points made. A strong argument for staying.
5) Opponent’s Attacking Chances – Not much. Black has one non-double to point on the straggler (5-3), and it
doesn’t gain much since White might reenter on the ace-point or deuce-point and cause even more trouble.
Strong argument for staying.
The race deficit plus Black’s weak board clearly indicate that White should stick around. The straggler only
generates an actual shot on one number, but he causes numbers like 6-2 and 2-1 to be played awkwardly.
There’s little downside to staying and a clear upside.

Once White decides to stay, he has a lot of ways to play a 6-2 on his side. The best is the thematic slot-and-
cover: 13/7 5/3.

Problem (B) shows a position with two stragglers. In two-straggler positions, you have an additional reason
for hanging back: you might be able to make a second anchor, improving your chances considerably. Let’s
look again at our five criteria and see if there’s any reason to safety a straggler with 23/20.

1) The Race – White trails here by 46 pips, 122 to 168. A very strong argument for staying.
2) Closeness to the Anchor – From the 23-point, the rear straggler is attacking the 23-points and 22-points, so
he’s doing a little more work than in our last example.
3) Blot Numbers – Black now has three different blot numbers, 6-5, 6-2, and 5-1. Strong argument for staying.
4) Opponent’s Home Board – With the 4-point made, it’s a little stronger than in (A). Neutral.
5) Opponent’s Attacking Chances – Better than before, but still not that great. Black has two non-doubles that
point on White (6-4 and 5-3). These are somewhat neutralized because each gives a chance of White’s
entering and making a second anchor. Neutral.
The bad race, the extra blot numbers, and the chance of making a second anchor all make staying a clear
choice. The best play on the other side of the board is 7/4(2) and 13/7.

Conclusion: In most normal positions, staying with the straggler will be correct. Over the board, my rule of
thumb is that if I’m well behind in the race and my straggler is guarding at least three points (including the
point he’s on) then I’m staying. If my straggler is guarding only the point he’s on, I’m looking to leave. If my
straggler guards just two points (including the point he’s on) I’ve got a tough decision, but I will tend to stay.

JUN-15-2021 || GAME PLANNING IN THE MIDDLE GAME

Jun 15, 2021 | Backgammon Problems: Middle Game
(A) Cash game, center cube.
 Should White double? Should Black take if doubled?
(B) Assume White doubles and Black takes. White to play
(b1) 55
(b2) 33
(b3) 53
(A) Cube action?
This problem is a more or less common middle game position with some interesting move choices coming
up. First, however, White has to decide if he wants to double or not.

Let’s start by looking at the elements in our standard position-race-threat matrix.

Position: White has some clear assets here. He has an anchor, and Black doesn’t. Black is on the bar, which
is a big plus for White. White has a 4-point block, Black has only three points in front of White’s anchor.
On the negative side, Black has a slightly stronger home board, with three points to White’s two. In addition,
Black has spares on his midpoint, while White’s midpoint is stripped. On balance, we have a solid edge for
White.

Race: White leads 140 to 149, with plenty of contact. Small edge fpr White.
Threats: White has a few numbers to make a 5-prime: 31, 41, 43, and some small doubles. If he can fill in
another point in his board and Black doesn’t anchor, White could develop a blitz. Not a lot of threats, but
some are very strong.
The takeaway from all this is that White has an edge in all three areas, so he should certainly have an initial
double. An edge in every area often indicates a pass, but here all the edges are relatively modest, so Black
can squeeze out a take.

Now let’s assume that White doubles and Black takes, and move on to the checker plays.

(b1) White to play 55. This is an interesting roll because White has many choices, leading to lots of different
game plans. Here’s a quick run-down:
Play #1 — 8/3(2) 7/2(2). The all-out blitz play, making two inner points.

Play #2 – 13/3(2). A priming play, but one which could turn into a blitz if things go well.

Play #3 – 21/11(2). The connectivity play, keeping a compact formation and leaving no stragglers behind.

Play #4 – 21/16(2) 8/3(2). A little connectivity, a little building.

Play #5 – 21/6 21/16. Creates a nice collection of builders at the cost of leaving a few shots.
If this were double match point and White’s only goal was to win the game, the clear play would be 21/11(2).
That play disengages the anchor, keeps a nicely connected position, and leaves White sitting on a 29-pip
lead in the race with no problems playing upcoming rolls.

All the other plays trade some wins for an increased chance of winning a gammon. The play that gets the
most gammon chances is 8/3(2) 7/2(2). White gets a quick 4-point board, but leaves his other checkers
scattered around. At the other extreme is 21/6 21/16, which disengages and gets a nice building structure, at
the cost of leaving a few embarrassing shots. The other plays fit in between these two.

Plays that sacrifice some winning chances for extra gammons tend to be harder to evaluate than most.
You’re not comparing two similar plays to see which one makes a slightly better structure. Instead you’re
measuring apples and oranges. Exactly how much am I giving up in winning chances in these two very
dissimilar positions? Exactly what am I getting in extra gammons? Am I getting more than two extra
gammons for any extra loss? These are usually tough questions.

Here’s a few rules of thumb that I’ve found work pretty well in these positions. They’re not infallible, but they
do help:

Rule 1: If the gammon play doesn’t actually make a point on the defender’s head, go with the DMP play.

Rule 2: Look at the position if the attacker makes the gammon play and the defender anchors. If it’s too hard
to bring home, make the DMP play.

Rule 3: The more structure the defender has, the more you want to make the DMP play.

Rule 4: When in doubt, make the DMP play.

A quick scan of this list shows that generally you’ll be playing to win the most games, and that’s right. In the
bulk of these problems, the best play to win turns out to be the right choice.

Now let’s go back to our 5-5 play.

By Rule 1, the gammonish plays don’t actually point on Black’s head. Play 2 makes a good point, and Play 1
makes two good points, but neither puts a second checker in the air. Rule 1 argues for the positional play,
21/11(2).

For Rule 2, let’s suppose White makes Play 1 and Black then rolls an ace and anchors. How do we like
White’s position? He’s got a couple of loose blots, the 4-point is still open, and White will have to be moving
off the 13-point and 21-point pretty quickly, while Black has plenty of spares to move as he improves his
position. This will be hard to bring home. Edge to the positional play.

Rule 3 makes an argument for the positional play since Black already has plenty of structure – a 3-point
board and a nice little block against the 21-point.

With everything arguing for the positional play, Rule 4 doesn’t really apply because there’s not much doubt.
White should play 21/11(2).

(b2) White to play 3-3. This roll poses a whole new set of problems. The best play to win the gammon is
clearly 7/1*(2). But the DMP play isn’t as clear as before. At DMP, two game plans dominate: the running
game, because races don’t win many gammons and are relatively easy to bring home, and the priming
game, because if you can build a full prime and break your opponent’s timing you become a huge favorite.
Here we have one good candidate for each type – 21/15(2) for the running game and 13/4 7/4 for the priming
game. What’s right?
In a matchup between 21/15(2) and 13/4 7/4, making the 4-point dominates. Making the prime is almost as
good for the win as running (74% versus 75.4%, according to rollouts), but since it actually makes an inner-
board point, it’s hugely better for winning gammons (31% gammons versus 16.4%).
What about the choice between 7/1*(2) and 13/4 7/4? Here Rule 1 favors the blitzing play (which now points
on Black’s head), but Rules 2 and 3 still favor the more positional approach. (Black has plenty of structure
and White’s position is widely spread out if Black ever anchors.) And of course, Rule 4 says to break ties in
favor of the DMP play. So 13/4 7/4 is the winner.

Incidentally, there’s an in-between play with 3-3 which isn’t bad: 21/18(2) 13/10(2). It tightens up White’s
position a bit, and creates some more numbers to make a 5-prime. But since it doesn’t make a new inner
point, it’s not very gammonish, and it won’t be that easy to get off the 18-point once Black anchors, so
making the 4-point still comes out on top.

(b3) White to play 5-3. Another roll, another set of problems. This time the gammonish play is 7/2 5/2, making
another inside point. But the play gobbles up a couple of builders and leaves the 3-point and 4-point still
open, so it doesn’t inspire confidence.
The running play for DMP is the simple 21/13, which cleanly preserves the racing lead and leaves Black with
only the problem of escaping the back checker.

The priming play for DMP is 13/8 13/10, which leaves White in pretty good shape, with four builders to make
the 4-point.

If we look back at our four rules, all of them argue against 7/2 5/2 and in favor of a DMP play. In this case the
two DMP plays are a photo finish. Rollouts show that running to the 13-point wins about 2.5% more games,
but bringing two men down wins about 5% more gammons, making the two plays about equivalent. Give
yourself credit for either choice.

Jul-01-2021 || Cracking a 6-Prime

Jul 1, 2021 | Backgammon Problems: Priming Games

Cash game, White owns the cube.

White to play 6-1.

In this position, Black has managed to build a full 6-prime, and White has one checker trapped
behind it. A single checker behind a full prime is normally a pretty bad position. If Black could
escape all his back checkers and arrange them on top of his prime, while White just filled in his
board, Black would be about a 90-10 favorite, with gammon chances in the 5% to 6% range.
Fortunately, Black hasn’t yet escaped all his checkers, which gives White some extra resources. In
fact, if he makes the right play here, his winning chances bounce up into the 25% range! That’s a
hefty increase, so let’s see if we can figure out the best way to proceed.

To win, White is going to have to force Black to crack his prime. For Black to crack, two things
have to happen:

(1) White needs to build some sort of prime, or at the very least a few blocking points, in front of
some number of Black checkers.

(2) White has to remove as much timing as possible from Black’s position. As long as Black has
some spare checkers to move in the outfield, he won’t crack his prime.

White has six candidate moves that do some combination of hitting, blocking, and buttoning up.
Let’s look at them.

Play A: 8/2 13/12*. Cover the 2-point for safety and hit in the outfield.

Play B: 8/2 8/7*. Cover the 2-point and hit on the bar.

Play C: 8/2 6/5*. Cover the 2-point and hit on the 5-point.

Play D: 13/7* 6/5*. Hit on the bar and the 5-point, aiming to build a strong block quickly.

Play E: 13/7* 8/7. Make the bar-point, creating a 4-point prime.

Play F: 13/7* 13/12*. Hit twice in the outfield, forcing all of Black’s spares into White’s home
board.

Of these candidates, we can quickly dispense with the three (plays A-C) that cover the 2-point.
These plays are aiming for safety, but they’re not really all that safe. If we compare them to the
wide-open play 13/7* 13/12*, which leaves 12 shots, Play A leaves 12 shots, Play B leaves 10
shots, and Play C leaves 15 shots. So there’s very little safety to these plays, but by not using the six
to hit on the 7-point, White wastes a chance to start a real block. So we can dismiss those plays
quickly.

The other three plays involve playing 13/7* and then hitting or making a block with the ace. Of
these, the first one to eliminate is 13/7* 6/5*. Although it hits two men, it leaves a whopping 21
shots from the bar (all 2s and 5s, plus 1-1). The play does pretty well when Black misses
everything, but gets gammoned far too much when Black hits. Even if Black enters just one checker
with a number like 3-4, there’s no guarantee that White can pick up all the pieces next turn.

So we’re down to a choice between two plays – 13/7* and either 8/7, making the immediate block,
or 13/12*, sending two checkers back. The clear winner here is 13/7* 13/12*, for two reasons:

(1) If White plays 13/12* and doesn’t get hit, he’s then very likely to make the bar point anyway.

(2) The Black checker on White’s 12-point represents 11 pips of timing for Black, and it’s hard to
hit.
Hitting two checkers strips away all of Black’s outfield timing and leaves Black with three checkers
back behind White’s block. Barring a hit on White’s 2-point next turn, Black is about to be faced
with a situation where most rolls without a five or six will crack his prime. In this position, that’s a
great result for White.

AUG-01-2019 || HOLDING GAME — BUILDING THE BOARD

Aug 1, 2021 | Backgammon Problems: Holding Game
Cash game, center cube.

White to play 1-1.

This position shows a slightly unusual mutual holding game structure. Both sides have
anchors, White on his 21-point and Black on his 18-point. Right now White trails in the
race by 16 pips (123 to 107), but trailing in the race isn’t much of a disadvantage in these
positions because the side that’s ahead in the race usually has to break anchor and
expose himself first.

White has two decisions to make:

(1) Should he move the checkers on the 21-point or the 13-point, or leave them alone?

(2) What’s the best way to improve his inner board?

The first question is the easiest. Since White trails in the race, he wants maximum contact.
The way to get maximum contact is to stay back as much as possible. so White doesn’t
want to move the checkers on the 21 and 13-points unless there’s no recourse. In this
case it’s even more important than usual to keep both points, because Black’s sixes are
horrible if White stays where he is. Notice that in the current position 6-1, 6-3, and 6-4 all
leave shots, while 6-2 and 6-6 continue stacking checkers.

So let’s leave those checkers on the 21 and 13-points alone and concentrate on the inner
board.

If White wants to play only in his inner board, the obvious first choice is 4/1 6/5, building a
4-point board. It’s a perfectly safe play, and if White gets a shot next turn and hits, he won’t
have to worry about an exposed blot. However, although it’s perfectly safe, it’s also poor
technique. When building a board to prepare for future shots, the right idea is to build it as
quickly as possible by slotting, covering, slotting, and covering. Playing 4/1 6/5 creates a
4-point board, but making the important fifth point will take a while.

A better try is 6/4 3/2(2), which creates a 4-point board with the fifth point slotted. Still, that
slot on the ace-point is a little hard to cover. Better still is 6/4 3/1! which moves the slot
backwards, where it’s in direct range of the 8-point. Now White has a 4-point board with
the fifth point slotted and easy to cover. That approach gives him the best chance of
having a 5-point board when he finally hits a shot.

AUG-15-2021 || THREE INTERESTING PROBLEMS

Aug 15, 2021 | Backgammon Problems: Middle Game

Here are three problems the early stages of a long match. Try your hand and see how you
do.

(A) Match, score 0-0 to 17, center cube.

White to play 3-1.

(B) Match, White leads 1-0 to 17, center cube.

White to play 5-4.

(C) Match, White leads 1-0 to 17, center cube.
 Should White double? Should Black take if doubled?
Position (A): This one should have been pretty easy. When you have a 5-prime with a
checker trapped behind it and not at the edge, your game plan is to make a 6-prime, and
the easiest way to do that is usually to slot the prime from the back, with the idea of
covering next turn. White should therefore see this as a pretty good roll and just play 13/9.
The play has the added bonus of duplicating Black’s aces, since he now needs ones to hit
and ones to get to the edge of the prime.
Hitting with 6/2* is a major blunder. White needs the 3-point or the 9-point to complete a 6-
prime, and he only has three checkers that can participate in that fight. Playing 6/2*
effectively burns one of those checkers, since the 2-point has no importance yet and White
has no need for a tempo hit.

Position (B): A 6-6 on the second roll of the game is usually a great shot, giving White a
lead in the race plus a couple of good points. The follow-up, however, can be tricky. With a
5-4 on the next turn, the best play is usually breaking off the anchor with 18/13/18/14.
When White doesn’t get hit, he’s got plenty of builders and spares and a good chance of
capitalizing on his racing lead.
Attacking with 8/3* 7/3 looks appealing at first glance, but it’s not as strong as you might
think. Black has 12 immediate hits (52, 56, 43, 46, 26 and 16) that catch up in the race,
plus 5-4 as a great anchoring number. Even when Black doesn’t immediately hit, the game
frequently evolves into a holding game where White wants to get off his anchor on the 18-
point but can’t.

Position (C): This position is tricky over the board because the solution depends on just
how you ‘see’ the situation. If you see this as just a blitz, then it’s clearly not a double.
White doesn’t even have a checker in the air and Black just has a 2-point board.
But if you see this through the lens of Joe Sylvester’s Position-Race-Threat matrix, then it
looks very different. White leads in the race by 25 pips, 134-159. His position is better, with
an extra inner point on his side and a strong anchor on Black’s side. White has threats,
with a bunch of numbers to make the 4-point and other numbers that put two checkers in
the air. His position is better and it’s threatening to get better still, maybe by a lot. Looked
at this way, it’s an easy double and Black has the tough decision. He can take because so
far he’s only facing a 2-point board and the threats are not crushing.
SEP-01-2021 || PLAYING BLOCKING GAMES
Sep 1, 2021 | Backgammon Problems: Middle Game

Cash game, center cube, White on roll.

Part (a): White to play 4-3.

Part (b): White to play 5-1.

Both sides have anchors on the opposing 3-points, and both sides have established a few
points in front of the enemy anchor. I like to call these ‘Block versus Block’ positions, to
distinguish them from the better-known ‘Prime versus Prime’ positions.

The types of positions share a few common characteristics. Both sides will have to
consider moves that run off the anchor, because staying too long on the anchor can cause
their own blockade to crack for lack of timing. Both sides will look for ways to make new
blocking points, but usually they will have to surrender an old point to make a new one.
Both sides will have an eye on the doubling cube, but since the starting position is so
balanced, a good double will usually require a series of bad rolls by one side and good
rolls by the other side.
The big difference between priming and blocking games can be seen here. Both sides
have dumped a few checkers behind their opponent’s anchor, and hence don’t have
enough checkers left to form a full prime or even a 5-point prime. The dead checkers
require each side to use the remaining checkers with great precision; apparently risky
plays become commonplace because of the need to put the remaining checkers to work.

Let’s start with Part (a), White to play a 4-3. The obvious 6/2 5/2 is exactly the sort of play
we don’t want to make under these conditions. True, it makes a point, but it’s a point
behind our opponent, and to make it we kill two checkers that should be used to either
make the 4-point (in front of our opponent) or attack (if Black later runs out with a checker.)
Now White is left with a stripped position and only one checker (on the 15-point) that can
easily move. Plays like this are what cause winnable games to slip away.

Instead, White should take the opportunity to play 22/15! White runs into the outfield, while
leaving only one checker around the board that can be attacked. Black has some rolls that
hit, and some rolls that cover the 2-point, but very few rolls that do both. The game then
becomes a struggle where Black has to attack, and White just tries to escape. With the
open 5-point and the blot on the 2-point, Black has a lot of work to do, and he must work
quickly.

Notice one key to this position: 22/15 actually anchors in the outfield. If running out left a
couple of blots in the outfield, the play would be much more dangerous. Now Black has no
extra blots to pick up in the future, making his attack much less dangerous. The annoying
blot on the 2-point also plays a big role in making this seemingly loose play correct.

Now on to Play (b): White to play 5-1. Here the back checkers are stuck so we must work
with the front checkers. There are two bad plays available: 15/10 6/5 and 7/2 7/6.
Recognize that these have to be bad and the right play will suggest itself. 7/2 7/6 breaks
White’s block unnecessarily. That’s a no-no. The other play, 15/10 6/5, creates an ugly
stack on the 5-point, making further improvement much more difficult. These are plays you
make when your opponent’s board is very strong and you simply must not get hit. That’s
not the case here. Black has only a 3-point board plus a blot. You’re not eager to get hit,
but it’s certainly not a disaster. Look for better.

And better is pretty easy to find. Just play 15/10 5/4! By slotting the 4-point, you give Black
minimal shots and look to extend your block. Black has only one hit and cover number (6-
1) which happens to be the only number that hits two checkers. Nice duplication.

After this play, Black will mostly just cover the 2-point, after which you will mostly cover
your 4-point, and the game will go on. Instead of a stripped-out position, however, you’ll
have bought yourself some time and spares. That’s how these positions are won.

SEP-15-2021 || PLAYING FOR A DECISIVE ADVANTAGE

Sep 15, 2021 | Backgammon Problems: Middle Game
Cash game, center cube. Black to play 6-1.
This position is somewhat unusual. We have a roughly balanced middle game in which
both sides have moderately strong home boards. Black has only one man back, and as a
result White trails in the pip count by 15 pips (136 to 121).

White’s roll, 6-1, is awkward since he has no great six. Moving off the midpoint leaves a
shot. Moving off the 24-point creates two blots and breaks his defensive anchor. The only
sensible play that involves moving from the 7-point or 8-point is the loose hit, 8/1*, which
doesn’t accomplish much. Nonetheless, White does have to pick one choice from this
unappetizing situation.

The right play is the counter-intuitive 13/7 6/5, slotting the 5-point. While slotting plays
themselves are not uncommon, one of the preconditions of a good slotting play is that no
other blots are left around the board. The reason is simple: if your opponent fails to hit the
slotted checker, you want the maximum opportunity to cover the slot next turn. Other blots
allow your opponent to hit in other places, reducing the count of cover numbers for your
slot. The opening adage “Don’t slot while split” is a simple reminder of this principle.

Despite the extra blot, however, White should still go ahead and slot his 5-point with 13/7
6/5, leaving Black fours and ones to hit. The arguments for the slotting play are threefold.

> The slot gives White a chance to build a full prime, while alternatives don’t ever lead to a
very strong position.

> There is a significant amount of duplication after 13/7 6/5, so White’s actual risk is less
than might first appear.

> White’s alternatives are very weak.

Let’s look at these three arguments one at a time.

Building a full prime. After 13/7 6/5, a Black miss followed by a White cover can give White
a full (6-point) prime. Black has 20 hits (all fours and ones) and 16 misses, so he’s only a
slight favorite to hit. If Black misses, White can cover the 5-point with twos and eights,
building a 6-prime, or threes, which build a 5-prime. At the very least, White can pick up
his blot on the midpoint, leaving Black with only fours to hit on his second turn.
Building the prime is very significant. For instance, after the sequence: White 6-1 (13/7
6/5) and Black 3-2 (13/8), White is almost a 2-1 favorite in the position. He doesn’t quite
have a double, but he’s close.

Duplication. Most middle game slotting plays hinge on at least some partial duplication of
the opponent’s useful numbers. The current position is typical in this respect. After 13/7
6/5 Black needs fours and ones to hit, but these numbers are already useful elsewhere.
Note that 6-4 and 4-2 make Black’s 2-point, while 4-4 and 5-4 hop Black’s last back
checker. In addition, 6-1 and 3-1 make Black’s bar-point and 5-point respectively. Although
Black will in fact hit with all these numbers if White slots, the fact that the numbers play
usefully on the other side of the board makes the cost of each hit considerably less.
Weak alternatives. If White doesn’t slot, his remaining plays are 13/6, 8/1*, and 24/18 24/23.
Let’s look at each one.
13/6 leaves a blot on the midpoint anyway, but contains no threat. Even if Black rolls a
poor number (3-2 or 5-3, for example), White isn’t prepared to capitalize on it.

8/1* is all downside. It leaves 15 shots (all aces plus 6-2 and 5-3) compared to 20 shots for
13/7 6/5, so it is a slightly safer play. But where’s the upside? Slotting the 5-point at least
leaves White threatening to make a 6-prime. Hitting on the one-point leaves White
threatening – to make the one-point! Not an even trade. This is the worst of the reasonable
possibilities.

With 24/18 24/23, White simply spreads his arms and says “Please – kill me now!” Fully
half of Black’s numbers now at least hit two checkers (6-6, 3-3, 2-2, 1-1, 6-5, 6-4, 6-2, 6-1,
5-1, 4-1, and 2-1. Black will at least have some moderately tough decisions. With 6-2, for
instance, should he make the 2-point or hit two men? (The double-hit is slightly stronger.)
But abandoning your defenses like this is suicidal and must be dismissed quickly.

Slotting the 5-point is an unusual play, but if conditions are right, it can be best. Here the
threat, the duplication, and the absence of good alternatives combine to move slotting to
the top of the list.

OCT-01-2021 || DOUBLING AN EARLY POSITION

Oct 1, 2021 | Backgammon Problems: Early Game
Cash game, center cube. White on roll.

(a) Should White double?

 (b) If doubled, should Black take, drop, or beaver?

Early game doubles cover a wide variety of positions, but in general they can be spotted
by analyzing three key aspects of the game: race, position, and threats. Many years ago,
Joe Sylvester (a very great player in the 80s and 90s, now somewhat inactive) coined a
simple rule: if you’re ahead in two out of three of these aspects, you have a double. Your
opponent may or may not have a take. Let’s evaluate these three features of Problem 12
and see what they tell us.

The Race. This is pretty simple. White leads 149 to 173. He’s up by 24 pips, a solid
advantage. There’s plenty of contact left, but 24 pips is a big edge.
The Position. White is ahead on both sides of the board. although not by much in either
case. He’s made his 5-point and he’s made the 22-point. He’s got a new builder on the 10-
point, which gives him a few new rolls to make the 4-point and the 7-point.
Threats. White at first seems a little lacking in this area. His doubles are very strong, of
course, but that’s true of almost all early game positions. What we’re looking for here are
powerful non-doubles, and there really aren’t many of those, beyond the obvious 6-2, 6-3,
4-2, 6-4, and 5-3 rolls. Still, that gives him 16 good rolls to improve his position. In addition,
he’s got 10 checkers in the ‘zone’ (the area from his ace-point to his 11-point), which
means that he’s got the potential for a strong blitz.
Our scoring gives White an edge in all three areas, although position and threats are
maybe not a strong as he would like. So by Sylvester’s criteria White has a double. And in
fact that’s right: White should double. What’s a little more surprising is that the double is
extremely strong and in fact Black has a small pass.

Some players might ask “How can it be a pass, given that we’re very early in the game
and White’s only made his 5-point?” Good question. The answer is simply that the gap
between White’s various strengths and Black’s weaknesses is enough to make it a pass.
None of White’s advantages seem all that great, but he has a lot of advantages, while
Black has essentially nothing. Compared to the starting position, Black has actually gone
into reverse. He’s moved a checker from his 24-point to the bar, and from his 8-point to his
13-point, making his midpoint stack worse and stripping his 8-point.

One last point before we leave the problem. Not doubling here is an easy error to make
over the board. White’s position doesn’t easily fit any of the usual categories. It’s not a
blitz, it’s not a prime, and in fact White doesn’t have a lot of threats beyond making an
additional point with a few numbers. In a game played at normal speed over the board, we
tend to rely on obvious visual cues (“Am I way ahead in the race?” “Do I have lots of
threats?”) to tell us to think carefully about a double. This position lacks most of those
cues. White seems a little lacking in immediate threats, and since both sides have two
men back, he isn’t obviously well up in the race. Presented as a problem, it’s relatively
easy to break the position down and decide logically that White must be a solid favorite.
But over the board, this is an easy double to let slip by, and many players in Black’s
position would scoop up the cube.

OCT-15-2021 || HIT LOOSE OR PLAY QUIETLY?

Oct 15, 2021 | Backgammon Problems: Early Game
Cash game, center cube. White on roll. White to play 5-3.
Many backgammon problems boil down to a simple question: hit, or don’t hit. In essence,
backgammon is a pretty simple game. In general, you want to make points, and in general,
you want to hit.

When you can hit a checker on your opponent’s side of the board, gaining both time and
racing equity, you almost always want to do so. (The only exceptions occur when the
alternative is to make a very strong priming or blocking point on your side.) But when the
only possible hit is to hit a blot in your inner board, the choice is more difficult. Now you’re
risking a significant loss of race equity if you get hit back, so the hit is rarely automatic. For
a hit in your inner board to be correct, one of these two reasons will usually apply:

> You’re hitting on a key blocking or priming point, which you very much need to make.

> Your opponent has so many threats that a tempo play is necessary; that is, you’re hitting
to prevent your opponent from attacking with his entire roll.

Keep these ideas in mind as we look at this position.

This problem is best solved by a process of elimination. White will enter with his three,
Bar/22, and choose among four fives, none of which stands out as an excellent play. Try
discarding the obviously worst choices first until you’ve narrowed the field, then see which
looks most appealing between the survivors.

6/1*. Hitting loose on the ace-point in the early game is a tantalizing play. It often looks
necessary, it’s almost always wrong, but on the occasions when it’s correct, it’s usually
correct by a lot. The hit is a tempo play (designed to take away half of the opponent’s roll),
but to be correct, the need for a tempo play must be huge. That means that your opponent
needs plenty of builders ready to pounce, and you absolutely must put him on the bar.
Here the play is wrong because Black doesn’t have enough serious threats. True, Black
has some pointing numbers. But to make his 3-point, he’ll have to break his 7-point or 8-
point. He’ll do that if he can, but it’s not a threat you need to guard against because of the
broken points and the return shots. Meanwhile, 6/1* just dumps a checker out of play and
risks losing plenty of ground in the race.
8/3*. The same idea as 6/1*, but even worse. White strips the important spare off the 8-
point, while leaving almost twice as many shots as 6/1*.
11/6. Better than the first two choices by a lot, but look at that hideous stack on the 6-point.
In the absence of crushing threats, the idea in the early game is to unwind stacks, not
make them worse.
13/8. Doesn’t do anything great, but doesn’t damage the position either. Here it’s the
winner by default, as the other choices are all ruinous.
In this position, Black’s threats weren’t really all that serious, so a quiet play made sense.
If Black had a more dangerous collection of builders, 6/1* might have become the best
play.

NOV-15-2021 || HIT LOOSE OR SPLIT IN THE OPENING

Nov 16, 2021 | Backgammon Problems: Early Game, Uncategorized
Cash game, center cube. White on roll.

White to play 3-1.

Here’s the same position from the last blog post, but this time White has a different roll to
play: 3-1.

Here the choice is a little different from before. The only available hit, Bar/24 6/3*, is now a
horrible blunder. It has all the disadvantages of the hits in the last post, but in addition it
leaves White stuck on the 24-point, just when White needs to be taking some small risks to
get an advanced anchor in Black’s board.

Instead, White needs to enter with the three, Bar/22, which gives him both an escaping
number (6) and a threat to make an anchor, and then consider whether 24/23 or 22/21 is
his best ace. The former is a little safer since White avoids moving to the point Black most
wants to make next (Black’s 4-point). The latter play moves directly to that point, hoping to
later grab the best anchor available.

Either play might be right depending on circumstances. Here the circumstances favor
moving to the 21-point. To see why, we’ll use a frequently handy trick in these sorts of
positions. Find Black’s best non-double that attacks or advances his prime, and see how
that number plays on the other side of the board. The right play will often duplicate this
number.

After Bar/22/21, Black’s best non-double for advancing his prime is clearly 4-2, which plays
8/4* 6/4. But on the other side of the board, 4-2 is also a great shot, making the 20-point
anchor. Eureka — duplication!
Now consider Bar/22 24/23. Black’s best non-double for moving his prime is 5-3, which he
would play 8/3* 5/3. But on the other side of the board, 5-3 is pretty useless. Hence the
24/23 play creates a new great number for Black, which isn’t the right idea. So White
should just play the simple Bar/22/21.

DEC-01-2021 || SPLIT OR SLOT IN THE OPENING

Dec 1, 2021 | Backgammon Problems: Early Game
Cash game, White owns the cube. White on roll.

White to play 2-1.

Slotting to make a key point and splitting your back checkers are two tactical ideas that
dominate early-game play when more obvious choices like hitting blots and making points
aren’t available. The 1970s and 1980s were the heyday of slotting. The preferred method
of winning a game was to build an imposing prime (often by slotting points, then covering)
and follow it with a crushing double. The older method, taking the points you were given
and looking for a chance to escape your back checkers, was seen as antiquated and
wimpy, a game plan only suited for geezers playing in the park.

This all changed in the 1990s with the arrival of the bots, first Jellyfish and then Snowie.
The bots didn’t slot their 5-point with an opening roll of 2-1, 4-1, or 5-1, as had been
customary; instead, they split their back men with an ace. (Extreme Gammon, the latest and
greatest of the bots, prefers slotting with the 2-1 roll, and rollouts back up that decision.)
These results swept the backgammon world, and soon almost everyone was splitting,
rather than slotting with opening aces.
While there was nothing wrong with copying the bot’s plays with the opening rolls, players
soon began making much more serious mistakes. Since these opening rolls were the most
obvious examples of slotting, they “learned” that slotting was simply an error except in a
few bizarre circumstances. As a result, they started missing strong slotting plays in all
sorts of opening and middle-game situations. They’d discarded a key tactical idea on the
basis of a tiny set of opening positions.

So when is slotting to be preferred to splitting? In general, you’re looking for a combination

of factors, some of which argue against splitting, others of which argue in favor of slotting.
Today’s problem illustrates these ideas pretty clearly.

——————-
Here White finds himself in a weak position, with stacks and stripped points, while facing a
strong Black board. With the 2-1 roll, White can try various things. He can play very safe
with 13/10, split his back men with 24/21, split and build with 13/11 24/23, or purely build
with 13/11 6/5. At first glance, no play leaps out as clearly right. Let’s see if we can whittle
down the possibilities.

The problem with the splits is that Black’s position has become just a little too dangerous
to abandon the anchor. Black doesn’t actually have a lot of rolls to fill in the gaps in his
prime, but he’ll be happy to launch a blitz if he can, and splitting gives him that opportunity.
In fact, either split boosts White’s chances of losing a gammon enormously – from about
20% after the non-split plays to around 28% after the split plays. Such high gammon
chances would require the split plays to win at least 4% more games than the non-splits to
be contenders. There’s nothing in the position to suggest that could happen, so let’s toss
out the splits.

Absent the splits, we’re now down to a choice between the aggressive 13/11 6/5 and the
quieter 13/10. The key here is to remember that White doesn’t want to split anymore. But if
splitting is too dangerous, then White will need to build a front position quickly to stay in
the game. There’s no guarantee that 13/10 will give him a position anytime soon. That
play, after all, leaves 5 shots but still doesn’t give White a lot of good point-making
numbers. 13/11 6/5, on the other hand, leaves 13 shots but gives White a ton of point-
makers if it works. Slotting with 6/5 is right by a wide margin, and it’s right whether the
cube is centered or White already owns it.

One footnote to this position: you might reasonably think that duplication plays a role in
this decision. When White slots his 5-point, Black needs fours to hit, but 4-2 and 6-4
already make good points in his board. But in fact the play is structurally correct and the
duplication is irrelevant. If we move Black’s inner-board points to the 4-point and the 2-
point, so that fours don’t build any new points, then the slot is still correct, and by almost
as wide a margin.

DEC-15-2021 || LATE GAME BLITZES

Dec 15, 2021 | Backgammon Problems: Blitzes
Cash game, White owns the cube. White on roll.

(a) Should White double?

 (b) If doubled, should Black take, drop, or beaver?
Among the many relatively unexplored position types in backgammon is one I call the
“Late Game Blitz”. The general idea is pretty simple. One side has a blitz in progress. The
other side, unlike the case in the basic opening blitz, has some sort of structure in place,
which might range from a few scattered points to an imposing five-prime. The blitzer has
some number of checkers to extricate from behind this structure before he can claim the
game.

These Late Game Blitz positions are relatively common and often incredibly difficult. Many
points are swung with errors in this type of game, and the errors are often very large. If
you’re looking to work hard to improve your play and results, these are good positions to
focus on. The ability to handle these positions well will make a big difference in your play.

This problem illustrates a sub-category of positions in the Late Game Blitz world. White
has three of Black’s checkers trapped on the bar against a 5-point board. (That’s the good
news.) But on the other side, he has to escape three checkers from behind a 5-prime, and
one of those checkers is not at the edge of the prime. What to do? Gammons are certainly
floating in the air, but that 5-prime could be hard to jump.

There’s a crude rule of thumb that applies to positions where your opponent is trying to
enter against a 5-point board, and you have a 5-prime to leap. Count the number of
checkers your opponent has to enter. (Here it’s three.) Now count the numbers you have
to roll exactly to escape his prime. Here White needs an ace plus three sixes – four
numbers in all. If your count is the same as his count, and your spare checkers aren’t all
used up yet (here the two spares on the 16-point and 11-point have several rolls left before
they’re dead – remember, you won’t move them with sixes) then the position is probably
double-take. If your count is higher than his (the case here where you need four and he
needs only three), don’t double. If your count is lower than his, it’s a big pass and perhaps
even too good.

Solution:

(a) White shouldn’t redouble.

(b) Black has a very easy take if doubled.

JAN-01-2022 || TAKING YOUR LAST CHANCE

Jan 1, 2022 | Backgammon Problems: Middle Game
Cash game. Black owns the cube. White on roll.
 White to play 5-1.
One of the most dangerous positions in backgammon is that of the out-timed and rapidly
deteriorating position. This problem is a good example. These overstretched positions
usually arise when one side (here White) has built a great front position quickly, but at the
cost of leaving one or more stragglers disconnected from the main force.

Most players in this situation assume that they must have done something wrong to get
here. Perhaps they built an inner board point when they should have run, or brought down
a builder instead of making an anchor. Sometimes that’s true, but often these positions just
happen. White may have correctly pursued an all-out attack, and Black just happened to
anchor at the last minute. No need for recriminations; however, White does face a serious
problem. What does he do next?

To save these crumbling positions, you have to make the most of your assets. In this
position, you (White) have two assets: you’re ahead in the race by a ton, and right now
your board is stronger than Black’s. To use these assets, you’ve got to force a conclusion
to the game (at least this phase of it) right now. Come up to the edge with Bar/20, and
make the only reasonable ace, 9/8. You can’t punt with Bar/24 and 9/4. That play isn’t
even safe, and you have to roll a four almost immediately just to get to the edge of White’s
developing blockade.

Could Black crush you if he rolls a 43 next, pointing on you? Sure. But guess what? If you
enter on the 24-point and he rolls 43, you’re crushed anyway. Don’t guard against rolls that
beat you no matter how you play.

True, there’s some delicious duplication involved here – Black needs 4s and 3s to hit your
new blots, the same numbers that hit cleanly on the 20-point. But that’s just a bonus.
You’d make this play even if there were no duplication involved, because you’ve got to get
your back checker out immediately. There’s no time left to pray for yet another good roll.
51 actually is a pretty good shot (61 or 62 would be much worse), so make the most of it
and see who survives the next roll.

JAN-15-2022 || WHEN YOU’RE DESPERATE…

Jan 15, 2022 | Backgammon Problems: Middle Game, Uncategorized
Cash game. White owns the cube. White on roll.
 White to play 5-3.
A lot of backgammon positions are pretty simple: the right play is either forced or
completely obvious. Many others involve a clear decision between two very different
alternatives. These problems may be hard to solve, but at least the choices are clear.

Some positions, however, involve a lot of possible plays, all of which are somewhat
reasonable. These positions can be very tricky, and one of the dangers is overlooking the
best play altogether while sorting through the wealth of possibilities. Be alert, and try to
enumerate all the plays before starting to rank them.

Take a look at this position. Here’s a choppy-looking block against block game, in which
neither side is particularly satisfied with their position. Black’s not likely to fill in his 4-point,
while White has big gaps on his 4-point and 5-point. 53 is not an especially good shot for
White, although he can try a few different things. What to do?

Let’s consider some of the plays that come to mind.

> 24/16 is a really bad idea. White’s 34 pips down in the race, so trying to disengage isn’t a
super plan to begin with. And suddenly some really bad shots for Black become great
attacking numbers – 51, 65 and the like. Throw this idea out.
> 24/21 6/1* is also bad. White is now very vulnerable, with a weak board and three
exposed blots. Even if Black dances, White has a ton of work to do.
> 9/6 8/3 is safe, but that’s about all. White’s still way behind in the race, and now his front
game looks like it will never come together.
> 9/4 7/4 is better – White swaps the 7-point for the more valuable 4-point, and his position
becomes a lot less awkward. But filling in the 5-point or the 7-point is now quite unlikely, so
White’s game after this move is probably as good as it gets.
If White stops his analysis here, he’ll likely play 9/4 7/4. Not bad, but he won’t even have
considered the best play!

The right idea is 9/4 8/5, the hyper-aggressive double-slot! White seizes his last chance to
get a really strong position. Suddenly the pressure is on Black to throw a three or a four
immediately. If not, White’s position will suddenly improve to a 5-prime or even a 6-prime,
and Black will be squeezed and crumbling. Even if Black does hit, White now has a pretty
good ace-point game with reasonable timing. The double-slot loses a few extra gammons,
but picks up a new win for every gammon it loses. It’s the clear first choice.
FEB-01-2022 || THE TEMPO HIT
Feb 1, 2022 | Backgammon Problems: Middle Game, Uncategorized
Cash game. Center cube. White on roll.

Position 1: White to play 5-2.

Position 2: White to play 4-2.

In backgammon, most hits are done for one of two reasons: to gain ground in the race, or
to attack a key point. A rarer (but still important) use of the hit is a defensive idea called the
tempo play. Here the plan is to prevent your opponent from using his whole roll to do
something good. By hitting (usually in your home board), you force him to spend half his
roll coming in from the bar, so he’s not in position to do something devastating elsewhere
on the board.

Diagram 1 shows a common situation where beginners make a tempo hit incorrectly. Black
won the opening roll with a 6-3 and ran his back checker to the outfield. White now rolls an
innocuous 5-2. Many beginners will go astray here and play 6/1* 24/22. Since it’s a hit, the
play looks somewhat active and aggressive, but it actually doesn’t accomplish anything.
Black had no powerful threats that White needed to stop, and the checker left on the one-
point is both immediately vulnerable and a long-term liability. A better play is the simple
24/22 13/8. It does a few good things (unstacks the midpoint, adds another builder to the
8-point, and splits the back checkers), but most important, it doesn’t do any bad things.
Position 2, on the hand, shows a very different situation. White is ahead in the race and
hence has less timing than Black. This means that White will actually have to escape
Black’s prime: waiting for it to collapse is not an option. If White is going to escape, he’ll
need to throw a two at some point, and – guess what! – he’s just thrown one. So there’s a
really strong case for playing 23/21 with the deuce.

Once the checker gets to the 21-point, Black, if left alone, will point on it, or at the very
least hit loose. White needs a diversion to keep the dogs at bay, and 5/1* fits the bill
perfectly. It has an added bonus (don’t miss this) of winning more gammons for White than
any other play. It’s true that shoving what was a nice builder down to the ace-point
weakens White’s chances for a full prime, but changing a priming game into a sudden blitz
is often the right strategy, especially when neither side has an anchor.

The difference between these two positions is simply the amount of immediate danger that
White faces. You don’t like to hit loose deep in your home board, both because getting hit
back is usually costly, and because the checker becomes a future liability even when it
isn’t hit. So to make the hit correct, you need to be facing very serious threats. In Part (b),
Black has those threats; in Part (a), he doesn’t.

FEB-15-2022 || AGGRESSIVE EARLY DOUBLES

Feb 15, 2022 | Uncategorized
Cash game. Center cube. White on roll.

Part (a): Should White double? If White doubles, should Black take, drop, or beaver?
 Part (b): Should White double? If White doubles, should Black take, drop, or beaver?

When contemplating a middle game double, don’t make the mistake of looking only at your
position. Remember to look just as carefully at the weaknesses in your opponent’s
position. It may be his weakness, rather than your strength, that gives you a good double.

Part (a) is a perfect case in point. White has escaped his back checkers and built a little
structure, while Black has grabbed your 5-point. In most positions of this general type,
White’s advantages wouldn’t even add up to an initial double. But now look at Black’s
position:

> His back men are split and vulnerable to potential blitzing rolls like 66, 55, and 44, both
now and on subsequent rolls. If his two back checkers were anchored on the 23-point or
the 22-point, the position wouldn’t be a double.

> His front position is still chaotic and will be for a couple of turns. If he had a small 4-
prime or even a good board with, say, the 4-point and 5-point made, he’d have a threat to
contain any checker hit on the next couple of turns, and White wouldn’t have a double.

But with both these weaknesses, Black’s game is toothless enough so that White has a
very solid double. Black still has a clear take of course.

In Part (b), White is off to a decent start. He’s got a good defensive anchor, while on the
offensive side he has – well – something. He’s got some great points slotted, and next turn
he might actually cover one or two of them.

The key to the position is not White’s game but Black’s. While White has something, Black
has a bit less than nothing. No points, just blots. Something versus nothing is a good
prescription for an early double, especially if the defender doesn’t have an anchor. Without
an anchor, there will always be variations where things go terribly wrong and White’s
messy position turns into a powerful blitz. Did you stop to guess what White’s cubeless
gammon chances were in Part (b)? If you did, did you realize they’re over 25%? Numbers
like that almost always guarantee not just an initial double, but a strong and mandatory
initial double. White’s checkers aren’t just passive slots. They’re also potential attackers,
which can be activated by a single good sequence. Couple that with a rock-solid defensive
anchor, and White has a great double.

Clear take, of course. There are plenty of variations where things don’t go so well and
Black recovers quickly.

Mar-01-2022 || Make a Key Point or Hit?

Mar 1, 2022 | Backgammon Problems: Early Game

Cash game. Center cube. White on roll.

Position (a): White to play 5-1.

Position (b): White to play 5-1.

In the opening, plays that hit blots or make key points tend to easily dominate all other maneuvering
plays. Interesting choices, however, arise when both plays are available. Do you hit, or do you make
a point?

Five simple rules guide most of these plays.

(1) The stronger your inner board, the more you want to hit and the less you need to make an
additional point.

(2) The better the point you can make, the more you want to make it.

(3) If you can make a point while unstacking, your desire to hit goes down.

(4) If you have to break a good anchor to hit, your desire to hit goes down.

(5) If you have a vulnerable, exposed blot, your desire to hit goes up.

These two positions illustrate the relative importance of rules (4) and (5). Note that in both parts of
this problem, points (1) through (3) all suggest making the 5-point as the better play. White has a
weak inner board, the 5-point is the best point available, and he can make the 5-point while also
unstacking the 6-point.

In part (a), the decisive criterion is that White now has a great anchor on Black’s 4-point, and to hit,
he’d have to break that anchor. So making the 5-point is clear, and in fact every hitting play is just a
blunder.

In part (b), however, the picture changes. Now White has no anchor, so hitting doesn’t cost him an
asset. In addition, making the 5-point now leaves the checker on the 21-point exposed to nine
pointing numbers (11, 22, 44, 54, 52, and 42) plus some annoying double-hits (23, 43, 53). In
addition, Black gets great diversification because his escaping numbers (all sixes) don’t duplicate
his other good numbers. Hitting becomes essential for White both to gain ground in the race and to
protect his otherwise vulnerable blots. In fact, making the 5-point now becomes a blunder!

After hitting in part (b), how should White play the ace? The right play is 16/15, because it
duplicates Black’s threes: Black now needs threes to hit in the outfield and threes to anchor.

Mar-15-2022 || Backgame Timing

Mar 15, 2022 | Backgammon Problems: Back Games

Cash game. Center cube. White on move.

 Part (a): Should White double? Should Black take if doubled?

Part (b): Should White double? Should Black take if doubled?

Part (c): Should White double? Should Black take if doubled?

One note before we begin. When I said ‘Cash game’, I meant ‘Cash game with the Jacoby Rule in
effect.’ The Jacoby Rule simply states that you can’t win a gammon unless the cube has been
turned. Every cash game I’ve ever played has had this rule in effect, (except for a few weird
chouettes I played long ago in Istanbul), so I didn’t mention it explicitly, but I should have. For
future problems, always assume ‘cash game’ also means ‘Jacoby Rule in effect’.

Backgame Review

A backgame is a position where one side (the side playing a backgame) has established two or more
points in his opponent’s inner board, while his opponent (who is said to be defending against the
backgame) has a prime in front of the points. In our diagrams, Black is playing a backgame, and
White is defending.

Both conditions need to be met for a position to be a backgame. If one side has a bunch of men in
his opponent’s inner board, but his opponent hasn’t built at least a four-point prime, the position
isn’t a backgame, since the player with the checkers back can (and almost certainly should) try to
slither some checkers into the outer board. We call these and many other related positions proto-
backgames. They might turn into backgames, but then again they might not.

Backgames are labeled by the points that the backgame player holds. The three positions given
above are examples of a 1-3 backgame, because Black holds the 1 and 3-points in Black’s board.
The 1-2, 1-3, and 2-3 are sometimes called the deep backgames, because the backgame player has
points deep in his opponent’s board. Backgames like the 3-5 or 2-4 are sometimes called high
backgames, for the obvious reasons.

Backgames depend upon timing. A backgame player is said to have timing when he’s able to move
his remaining checkers and wait for a shot without destroying his home board. A backgame position
that’s likely to be good when a shot comes is said to be well-timed; otherwise it’s poorly timed.
Unlike normal positions, in backgames you want to be well behind in the race, and the further
behind you are, the better.

Ranking Backgames

Not all backgames are created equal. To win a backgame you need to be able to do three things:

(1) Get a shot.

(2) Hit the shot.

(3) Win after hitting the shot.

Condition (2) is obviously a matter of luck. Your backgame might yield a triple shot, but if you
miss it, that’s just bad luck. Conditions (1) and (3), however, are inversely correlated. The more
likely a backgame is to get a shot, the harder it is to time, and therefore the less likely it is to win
after hitting. The best backgame for getting shots is the 1-2 backgame, which can often generate a
whole series of shots as the opponent tries to clear his points. However, the 1-2 requires immense
amounts of timing, which is almost impossible to obtain in practice.

In my experience, the best backgame is the 2-4, which combines ease of timing with the ability to
generate a lot of shots early. Close behind is the 2-3. After those come the group of high
backgames: the 2-5, 3-4, 3-5, and 4-5. These are relatively hard to prime and generate shots early.
They don’t get as many shots as the deep backgames, but they don’t lose as many gammons either.
The true deep backgames, the 1-3 and the 1-2, are very hard to time and lose lots of gammons and
backgammons, but do generate lots of shots. Bringing up the rear are the 1-4 and the 1-5, which are
little more than glorified ace-point games.

Note, by the way, that ranking backgames has only a little practical significance. Unless you roll a
particularly opportune set of double-aces or some other small number, you mostly can’t upgrade
your weak backgame to a stronger one. But knowing the rankings might help us avoid some bad
backgames in the first place.

Doubling in Backgames

Once a backgame has been established and a containing prime has been built, we reach positions
like 25a through 25c. Here and for awhile, the checker play for both sides is fairly simple.
White will bring his spares down on top of his prime, trying not to get hit in the process. If he
throws a good number, he will make his 2-point. If he doesn’t make the 2-point naturally, he will
need to decide if he wants to slot the 2-point, and pick a good time to do it. Eventually he will move
all his spares into the home board and start to dismantle his prime from the back.

Black, meanwhile, will slot the front and back of his prime and try to build a strong position as soon
as possible. If White leaves a shot somehow, Black in general will try to hit it and contain it. Rolls
like 4-4 and 5-5 will crush Black’s timing. If he rolls 6-6, he will often have to abandon the 22-
point anchor and play a well-timed ace-point game rather than a poorly timed backgame.

During this phase of the game, the doubling window is very narrow. “Doubling window” is simply
a term used to describe the set of positions where double and take are the correct options. The
doubling window is said to “open” when White has a marginal double, at which point Black will
have an easy take. The window “closes” when White has an optimal double and Black has a close
take/pass decision. Positions within the window are double and take, while positions outside the
window are either no double and take or double and pass. In blitz positions, or positions with a lot
of blots strewn around the board, the doubling window is very wide. Even a few variations where
you vacuum all the blots and gammon your opponent will justify an otherwise early double. But in
long races or backgames, the window is typically very narrow. The vast majority of rolls result in
little or no fundamental change to the position, so the side with the edge has no need to rush. You
can creep up to a double slowly, and double when your opponent just barely has a take.

These three positions illustrate exactly this idea. In (a), Black trails by just 49 pips in the race.
That’s not enough timing, and the position is double-pass. In (b), Black has 55 pips of timing.
That’s a little better, and Black just barely has a take when White doubles.

Position (c) shows the other end of the scale. Now Black trails by 65 pips, and he has an easy take,
while White just barely has enough of an edge to turn the cube.

These last two numbers, 55 pips and 65 pips, are what I call the characteristic numbers for this
particular backgame structure. By remembering those, you can handle the cube properly in these
and a lot of related 1-3 backgame positions. However, let’s be clear that these numbers apply only
to backgames of a very particular structure. The following conditions have to be satisfied:

(1) Black has a 1-3 backgame with no additional checkers behind White’s prime.

(2) White has a 5-prime from the 4-point to the 9-point.

(3) There is no significant contact in the outer boards.

(4) Black’s home board is structurally sound. (He doesn’t have a gap on his 5-point, he hasn’t made
his ace-point, things like that.)

If we keep a 1-3 backgame but start changing some other features of the position, the characteristic
numbers will change, sometimes dramatically. Here are a few examples.

> If we add a fifth checker back for Black, but on the edge of the prime (the 22-point), Black needs
about 10 more pips of timing to take. So he’d need to trail in the pip count by about 65 pips for the
position to be double and marginal take.
> If we add a fifth checker back, but not at the edge of the prime (say on the 24-point) then Black
needs about 15 more pips of timing for a take.

> Breaking up Black’s home board a little, say by moving his checkers from the 5-point down to the
2-point and 3-point, has the effect of requiring 10-15 more pips of timing than in the basic position.
The more easily he can fill in the 5-point with his remaining checkers, the less extra timing he
needs.

In short, once you remember the 55 pip – 65 pip numbers for the edges of the doubling window in
the basic structure of a 1-3 backgame, you can make some educated guesses for a lot of real
positions and handle the cube much better than most.

Apr-01-2022 || Mobility
Apr 1, 2022 | Backgammon Problems: Middle Game

Cash game. Center cube. Black on move.

Part (A): Black to play 6-2.

Part (B): Black to play 5-4.

In both positions, White’s game suffers from a serious flaw: the big stack of checkers on the 20-
point. Stacks are always bad, but in the late middle game they become even worse because so many
checkers are tied up in one section of the board. As a rule, repairing the problem by moving the
checkers off the stack becomes a very high priority, often outweighing all other considerations.

Problem (A) is very typical. White trails in the race by 35 pips (163 to 127), but he has some
chances to contain Black’s rear checker. White has a decent little board and good control of the
outfield. The only glaring problem in his game are the four checkers massed on the 20-point.

White can play safe this turn with 13/5, but he shouldn’t. While that move leaves no shots, it does
leave the mid-point and 8-point stripped, so next turn White will be virtually required to move from
the 20-point. The trouble is, however, that he may not be able. His next roll might be 5-3, or 6-2, or
3-3, any of which play awkwardly once all the remaining points are stripped. Or Black might move
his back checker somewhere, after which White is obliged to attack it, while simultaneously trying
to release the back checkers.

Instead, White should just play 20/14 13/11! While this play leaves a few shots, it takes control of
the outfield and puts the onus on Black to roll a good number. If White gets hit he will probably
have return shots, if not he might roll a 6 to make the 14-point, or simply reposition his checkers to
control the outfield.

Floating into the outfield like this is a completely standard play once you have several checkers
back. The idea is what I like to call mobility. Your goal is to keep your checkers moving and
connected, while making new outfield points if possible. Since you’re typically far behind in the
race when this situation occurs, counting shots is rarely an issue.

Problem (B) is another application of the same idea. The hit with 8/4* is forced, to stop Black from
simply running his last checker home. Now if White didn’t have a stack problem, the logical five
would be 13/8, remaking the 8-point. With the big stack on the 20-point, however, the play 20/15 is
considerably better, unstacking and grabbing more control of the outfield.

Apr-15-2022 || Two Backgame Problems

Apr 15, 2022 | Backgammon Problems: Back Games

Cash game. White owns the cube.

 Part (A): White on move. White to play 2-2.

Part (B): Black on move. Black to play 4-2.

Back games are among the most interesting, and the most difficult, of backgammon game types. In
a true back game, one player makes two or three points in his opponent’s home board, then hopes to
hit a shot and contain a checker as his opponent bears off. If he’s succeeded in maintaining his
timing (that is, he can still build a containing prime on his side of the board), and can hit an enemy
checker soon enough (before his opponent can bear off too many men), then he may have good
winning chances. If not, he may be reduced to a desperate struggle to avoid a gammon.

That’s the theory, anyway. In reality, back games can take a lot of different forms, each with its
own unique set of problems.

Back Game Position Types

I like to classify back game and related positions into five very distinct types. Each type of position
is governed by its own characteristic goals and strategies. Here’s a brief description of each position
type.

Proto-back-game: These are positions in which at least one side (perhaps both sides) has a lot of
men back, but the opponent lacks a strong board or a prime. In this case a back game is just one
possible result of the position. Often what happens is that neither side can establish any real control,
and the advantage shifts back and forth over many moves. These positions are exceptionally
interesting and difficult.

Back Game with Prime: These are the positions most commonly discussed when people talk about
back games. One side has two or more back game points, the other side has a containing prime. The
side in the back game tries to maintain his timing by releasing checkers, the defending side (the side
with the prime is considered the “defender”) attempts to throttle those efforts.

Back Game without Prime: The difference between this and the previous category is that the
defender has never managed to complete a full prime. (Typically the bar-point is missing.)
Consequently, the back game player has an easier job maintaining his timing, although timing
problems can still occur.

Containment Game: After the back game has hit a shot, we switch into the containment game phase.
Now the job is to contain the loose checker, and possibly look for the right moment to double.
These positions can arise out of other game types besides back games. (Low anchor games, for
example.)

Post-Ace-Point-Game: When the back game player succeeds in containing the loose checker and
actually closes his board and reaches a bearoff, we get to the post-ace-point game. The main
problem here is when to double. The answer usually depends on how many men the original side
bore off before getting hit, and to a lesser extent, the quality of the bearoff structure on both sides.
Checker play problems also arise and can be very tricky and difficult. Like the containment game,
these positions can arise from other game types besides back games.

Now let’s look at our two examples.

Position (A) is the type we described above as ‘Back Game without Prime’. White has reached a 1-
3 back game, but Black never managed to secure his bar-point. As a result, White should have an
easier than usual time getting his checkers to the outfield.

The 2-2 roll is a great shot for White, and the first three deuces are obvious and strong. White
should hit with 18/16*, and make his 4-point with 6/4(2). But what should he do with the last
deuce?

White decided that he wanted to reduce his chances of being hit, and played 16/14 with his last
deuce. He correctly didn’t want to play 12/10, because he didn’t want two outfield checkers on the
same point. By playing 16/14, he noticed that he was duplicating Black’s numbers to some extent.
(Black needs ones, twos, and threes to enter from the bar, and after 16/14 he also needs ones and
threes to hit.)

Although it was a clever play, White missed the main thread. In all back games, the key idea is to
make sure your checkers can keep moving into the outfield. Accordingly, White should move
24/22(!) with the last deuce. By moving his other back spare to the highest possible point, White
prepares to jump that checker into the outfield and gives himself the best possible chance of
preserving his timing. In back games, timing is everything!

A couple of moves later in the same game, we reach a ‘Containment Game’ problem. Take a look at
Position (B).
Since the last diagram, White has flooded the outfield with his spares, while Black has managed to
safety one of his loose blots. Now Black has a 4-2 to play.

Black elected to try 24/22 8/4. It looks like a good move. White doesn’t have any direct shots at the
rear checker, while 8/4 puts that checker on a good point and prepares to clear the 8-point. It’s the
play most players would make.

But there’s a better play: 24/18! It looks risky, because Black is apparently walking into a hail of
direct shots. But in fact the play gives him the best overall chance of getting home. If White misses
the shot, (6-6, 6-4, and 4-2 miss) Black is poised to run for home. If White hits loose on the bar-
point, Black will have six return shots from the bar to hit the blot (6-1, 5-2, and 4-3), and a few
other rolls that also leap into the outfield (6-3, 6-2, and 5-3) plus a bunch of rolls that leave him on
the 2-point or 3-point.

Players tend to reject 24/18 because they think it presents too much risk and jeopardizes their racing
lead. What they overlook is that they’re already an underdog in the position! White’s control of the
outfield has made him the favorite, and Black needs to decide the game quickly, before his front
position starts to crumble. Precipitating an immediate crisis with 24/18 is the best way to proceed.

May-01-2022 || A couple of Proto-Backgame

Positions
May 1, 2022 | Backgammon Problems: Back Games

Cash game. Center cube. White on move.

Position (A): White to play 2-1.

 Position (B): White to play 6-5.

We’ve talked a little in previous posts about proto-backgames, those transitional positions that lie
between ‘normal’ backgammon and true backgames. Here are our first couple of examples of proto-
backgame positions, so let’s pause for a bit and discuss just what each side is trying to do.

Proto-backgames are defined by two key conditions. First, one or both players have several men
back in their opponent’s inner board. In Positions (A) and (B), both sides have extra men back;
Black has five men back and White has three. In addition, both sides will have blocking positions,
but neither side will have a strong prime yet. ‘Strong’ in this context means a five or six-point
prime; four points in a row are good, but not quite enough to really control your opponent’s back
checkers.

In a proto-backgame, both sides have the same overarching goal: build a five-point prime and force
your opponent to play a true backgame. The closer you get to your goal, the bigger your edge. In
Position (A), White has a clear advantage (although nothing close to a doubling advantage) because
he’s well ahead in the race, and the priming positions are about the same on both sides. In Position
(B), the game is about even; White still leads in the race, but Black now has a better prime.

So we know the strategic goal is to build a prime. But what are we looking to do tactically, to get us
closer to our goal? In general, we’re looking to do the following things from turn to turn:

(1) Kill no checkers. This is really the First Commandment of backgame and proto-backgame play.
In this context, a ‘killed’ checker is any checker that moves deeper into your board than your
opponent’s front anchor. In Position (A), for instance, White doesn’t want to move any checker to
his 1-point or 2-point, since those points are behind Black’s anchor on the 3-point. Good players
obey this rule religiously in complex position, while weak players are constantly distracted by the
lure of making a deep inner-board point. In Position (A), White will eagerly make the bar-point and
will fight hard for the 4-point, because those points are in front of Black’s anchor. But he will at all
costs avoid moving down to the 1 and 2-points.

(2) Make new blocking points whenever you can. This is pretty obvious. You’ll never have a lot of
rolls on any turn to make a new blocking point, so when you can it will probably take precedence
over anything else.

(3) Circulate checkers into the outfield. The outfield is the real battleground in proto-backgames.
When you move into your opponent’s outfield, you accomplish several good things. First, you jump
over his blocking position, which reduces the chance that you’ll get stuck in his inner board with
some later awkward shot. Second, you create builders for new priming points of your own, since
checkers in his outfield bear on your outfield. Third, you put pressure on your opponent; by
controlling the outfield first, you may prevent him from moving out.

With these goals in mind, Positions (A) and (B) become fairly easy.

In Position (A), White should play Bar/24 6/4*. The checkers on the 6-point have no function now
other than to make the 4-point. The 4-point is clearly the most important point on the board right
now, since making it will not only give White his best possible home board, but, by pushing Black
back, will make it harder for Black’s checkers to get into the outfield.

The safe play Bar/23 22/21, on the other hand, allows Black to grab White’s 4-point without a fight,
after which White’s two spare checkers on his 6-point have nothing to do for awhile. That’s bad.
White only has 15 checkers, and he’ll need 10 of them to make a five-prime. Everybody has to keep
working! Allowing Black to grab White’s 4-point effectively kills White’s checkers on his 6-point.

The right idea in (B) is 21/15 21/16! White doesn’t want to get stuck behind Black’s little prime,
and the outfield is currently up for grabs, so White moves there first. Note that although Black has a
lot of hits, the hits cost Black the midpoint. That’s a big concession, effectively isolating Black’s
rear checkers from the rest of his army, so White really doesn’t fear being hit. Notice in addition
that the alternatives are very weak. Playing 13/2* kills a checker and strips the midpoint, and 13/7
6/1* does the same thing in a different way. Running with one checker by 21/10 looks safer, but
allows Black to hit with a six without making a positional concession.

Playing 21/15 21/16 is another example of what I called in the post of April 1 a ‘mobility’ play.
White needs checkers to move so he doesn’t have to disturb the points that will eventually make up
his prime. Releasing these two back checkers gives him that mobility. When you look at this
position, don’t look at the two checkers on the 21-point and see some sort of key defensive anchor.
Instead, you should see two checkers that are currently restrained from moving and are yearning to
breathe the free air. Remember that Black has too many checkers in White’s board to succeed in
doing much of anything offensively.

May-15-2022 || Creating Mobility

May 15, 2022 | Backgammon Problems: Middle Game, Uncategorized

Cash game. Center cube. White on move.

 White to play 6-4.

This is a comparatively easy problem if you can properly balance the key features of the position.
Let’s step back for a second and look at just what is happening, before we try to evaluate the
different choices.

The race: White will trail in the race by 16 pips after he plays his 6-4. Considering that he has five
men back to Black’s two, he’s not as far behind as one might think at first glance. Since he’s
trailing in the race, however, he wants to maintain a good anchor (to generate some shots) and a
good blockade (to contain blots he may hit).

Blockades: White has four good points in front of Black’s anchor. That’s a solid plus for him, if he
can maintain it. Black has a motley collection of scattered points, which indicates that he probably
won’t be able to build a good block anytime soon, and that he’ll likely have to start leaving shots in
the near future.

Weaknesses: For White, what might seem a strength is actually a long-term weakness. He has two
great anchors, on the 20-point and the 18-point, but that’s one great anchor too many. The 20-
point/18-point combination doesn’t work well together; they tie up 76 pips at a time when
maneuvering freely is still key.

Black’s weakness is glaringly obvious; it’s the 2-point, too deep in his board to be useful at this
stage. Black might have had good reason to make it in the past, but now he’d be better off if those
checkers were back on the 4-point or the 9-point.

Now let’s put all this together and see just what we can do with the 6-4.

8/2 6/2. A bad choice. White burns two of his remaining builders to make a useless point far behind
Black’s anchor. Now all his remaining points are stripped and his only convenient rolls next turn
are those that can be made entirely with the blot on the 24-point. Take a look at how numbers like
4-1, 3-2, 6-1, 5-2, 4-3, 5-1, and 6-4 play next turn. In complex middle games with action on both
sides of the board you need checkers that can move easily, and sometimes you have to take risks to
preserve those checkers.

24/18 6/2 and 24/20 8/2. Not as committal as making the 2-point, but half-hearted versions of the
same idea. You only have 15 checkers, and you want everyone in play at this stage of the game.
20/10. To those who worship the 5-point, this looks like a shocking idea. White breaks the
defensive 5-point before he must. But it’s really a fine move, which solves all White’s problems at
once. White doesn’t need both anchors, so he gives one up voluntarily.

Take a look at the position after 20/10 and notice how White has solved most of his problems. He
now has five spare checkers, ensuring that he won’t have to concede any valuable points in the near
future. He’s got more combinations to make his 5-point or 7-point, as well as more ways to attack if
Black should split his back checkers for some reason. Finally, he’s resolved the issue of too many
anchors in a neat and efficient fashion.

If you missed this problem, it’s probably because you’re too focused on static features of the
position, and not enough on the flow of the game. Try to anticipate how the game is likely to
develop over the next couple of rolls, and avoid positions where you have a real shortage of
checkers that can move.

JUNE-01-2022 || IMPROVING YOUR TECHNIQUE

Jun 1, 2022 | Backgammon Problems: Middle Game, Uncategorized
Cash game. Center cube. White on move.

White to play 2-2.

The advent of the bots in the late 1990s enabled players to solve a myriad of small technical plays that
recurred frequently but couldn’t really be tackled with hand rollouts or pure reasoning. Hand rollouts were so
slow that they really had to be reserved for positions where the solution was unknown but the difference
between plays was likely to be large and important. Players ignored what appeared to be small technical
stuff, on the theory that solving these problems, even if possible, was most likely a huge waste of energy.

This position and roll is a perfect example. If you’ve practiced against bots a lot, you’ve seen this idea a few
times and the answer probably seems trivially obvious. If you haven’t, it most likely seems non-obvious but
also not terribly important.

First, let’s reject the clearly erroneous lines. White is holding the best possible defensive anchor, one that will
cause Black a lot of problems. So we’ll reject any play that includes 20/18(2) or 20/16(2).

Let’s also reject the hit 11/3*. The 3-point has some value but it’s not nearly as important for White as the 5-
point or the 7-point. In addition, the hit leaves the midpoint stacked and undeveloped, a situation which we’d
like to fix.

Eliminating those ideas makes most of our play fairly clear. We’re going to use three deuces to play 13/9
11/9, making an excellent point which bears upon all the points we’d like to make next, and takes a further
step toward building a good blockade. The problem then becomes the play of the last deuce. Do we play 6/4
or 13/11?

Both plays seem to have some obvious merits. Splitting off the 6-point looks like it unstacks a bit and creates
a new builder for the 3-point. In addition, the play doesn’t create a new blot. But 13/11 creates another
builder for the 5-point at a very small risk. What’s better?

The right idea, in almost all positions of this type, is 13/11. The real point of the play is that the two checkers
on the 6-point belong where they are, taking aim at the 5-point. The structure consisting of the 4-point, 5-
point, and 6-point (known as “the rack”) is much stronger then the 3-point/4-point/6-point structure, so White
should keep as many checkers as possible aimed at the 5-point. Playing 6/4 removes a builder for the 5-
point and aims it instead at the less-important 3-point. Even though the cost is small, that’s a mistake.

A large part of playing good backgammon consists in having hundreds of these little tactical ideas at your
fingertips, which is why practicing against bots and reviewing each session afterwards is such a vital part of
your development as a player.

JUN-15-2022 || SPLIT OR RUN?

Jun 15, 2022 | Backgammon Problems: Early Game
Cash game. Center cube. White on move.

White to play 5-2

The early part of a backgammon game is dominated by two key goals: hit blots and make points. The easy
moves are the ones where you can only do one good thing. The hard moves are those where you can do two
good things, and you have to make a tough choice, or no really good things, and you have to decide how
best to arrange your checkers for future action.

This position is an example of the latter situation. White can’t make any points with a 5-2 roll, and his only hit,
6/1*, doesn’t accomplish anything good. So he has to shuffle his checkers around somehow and get ready
for action next turn.

My cardinal rule in these positions comes from the medical profession: “First, do no harm.” In backgammon
terms, that means don’t try plays that make your distribution worse rather than better. Here, I’ll reject 13/8 for
just that reason. After 13/8, White has gone from a nice position with a spare on both the 13-point and 8-
point to a position with a small stack on the 8-point and no spares on the midpoint. That’s not an
improvement, so let’s reject all the plays involving 13/8.
Since we’ve already rejected the awful 6/1*, we’re now left with just two candidates: 23/18 13/11 and 23/16.
Running all the way out and trying to escape with 23/16 is the safer play: fewer ways to get hit and fewer
blots. Since Black has a better board right now, extra safety is not a bad idea.

The alternative, 23/18 13/11, tries for a bit more. White creates a new blot and exposes himself to more hits
in return for a chance to make a great anchor on Black’s bar-point. The problem with the move is a bit subtle.
The purpose of the new blot on the 11-point is to give White some extra chances to make his 5-point with
rolls like 6-3 and 6-1. However, White won’t have a chance to execute those threats because he’ll most likely
be on the bar next turn. Black is going to hit on his bar-point with all his ones and sixes, and he will probably
hit on his ace-point with fives as well. In fact, Black’s only non-hitting numbers are 4-3 and 4-4, and 4-3
actually makes White’s 5-point, rendering the blot on the 11-point somewhat useless!

Here’s a quick rule of thumb: a move like 13/11 is excellent when you have an anchor somewhere, so the
blot on the 11-point is a useful builder immediately. It’s not so useful when a hitting contest is about to ensue
on the other side of the board. As long as the battle for Black’s bar-point is unresolved, a blot on the 11-point
is really just an extra target. Play the simple 23/16 instead and try to escape a checker.

JULY-01-2022 || BEARING IN AGAINST THE ACE-POINT

Jul 1, 2022 | Backgammon Problems: Ace and Deuce-Point Games
Cash game. Black owns the cube. White on move.

White to play 5-1.

When bearing in against an ace-point or other low anchor game, you generally have two goals in mind. The
first is safety; you want to create formations that are less likely to leave blots as you bear off. The second is
winning a gammon; you’d like to maximize your chances of winning a gammon if you can.

It’s usually good practice to look at the gammon chances first. If your gammon chances are either very large
or very small, then it’s not likely that any play you make will affect them enough to matter. In those cases,
you just make the long-run safe play whatever that might be. But if the gammon is up for grabs (which in
practice means gammon chances in the 15% to 40% range) then you may need to look for riskier plays
which win more gammons at the cost of some extra losing chances. (Typically these plays involve piling
checkers on the 6-point and 5-point, hoping to hold the prime as long as possible.)

So what’s happening in this position? Here it’s pretty obvious that White is going to win a gammon unless he
gets hit. Black has one checker to enter off the bar, then four checkers to extract from the ace-point, and
several checkers in the outfield as well. All told, he needs 20 crossovers to get his checkers home, even after
he manages to enter. Any reasonable play leaves White with gammon chances in the 58% to 60% range,
which is so large that White can forget about the gammon as an issue and just concentrate on safety. So
now we can ask the interesting question: What’s the long-run safest play?

When playing strictly for safety, White has four goals. Here they are, arranged in order of obviousness:
(1) Don’t volunteer shots. Here this simply means that White won’t slot the 7-point with his ace. Giving Black
even a single indirect shot from the bar means giving him an extra 5.5% to hit, which could easily be a game-
winner.
(2) Try to ensure that 6-6 and 5-5 don’t leave shots. This won’t always be possible, and even when it is possible
you may decide to leave one of these numbers in order to secure better distribution.
(3) Strip the 6-point for quick clearance later. In general, you want to place your spare checkers on the 3, 4, and
5-points, preparing to clear the 6-point when you get all your men in.
(4) Avoid phantom interior gaps. A real interior gap occurs when an interior point like the 3-point or 4-point is
actually open when the bearoff starts. Interior gaps are very weak and those formations will leave many more
shots than a completely made board. Less weak (but still a serious flaw) are what I call “phantom gaps”,
where you have all the points made but some points lack spares. For example, if you have spares on the 6,
5, and 3-points, but no spare on the 4-point, you have a phantom gap on the 4-point. Most players ignore this
situation, but it’s actually more serious than it appears, leading to awkward formations later and more shots.
Note that some phantom gaps are worse then others. The 2-point and the 5-point are the least serious. The
2-point is so deep that it generally gets filled later, and the 5-point isn’t too important because it’s sometimes
an advantage to clear the 5-point before clearing the 6-point. The serious phantom gaps occur on the 3-point
and the 4-point.

If we now put all these ideas to work, we can find a clear winner with the 5-1, namely 8/3 6/5! All criteria are
met: no shot volunteered, 6-6 and 5-5 are both safe, the 6-point is stripped, and no phantom gaps.

Other plays don’t work as well. 10/5 4/3 blots on both 6-6 and 5-5 and leaves a phantom gap on the 4-point.
10/5 6/5 doesn’t blot but also doesn’t put a spare on the 3-point, which may prove useful.

JULY-15-2022 || WHERE TO LEAVE BLOTS

Jul 14, 2022 | Backgammon Problems: Middle Game
Both positions: Cash game. Center cube. White on move.

(a) White to play 5-4.

 (b) White to play 6-2.
In Problem 140A, White has no way to safety the blot on his 16-point. In fact, he can’t avoid creating a
second blot as well. He has a few reasonable plays: 13/4, 16/11 13/9, 16/11 6/2, 13/8 13/9, and 6/1* 13/9.
None of these plays look terribly strong. How should he decide among them?

Most players ask two questions when they’re trying to evaluate plays that leave blots:

(1) How many shots does each play leave?

(2) How important are the points that I am starting by leaving a blot there?

If we start counting shots, we find that the safest play is 6/1* 13/9, which leaves only 19 shots. Then comes
16/11 6/2, which leaves 21, and 16/11 13/9 which leaves 22. Last place goes to 13/4, which leaves 25 shots.
The safest play is the least constructive: 6/1* 13/9 actually leaves three blots rather than two, and starts the
ace-point, which doesn’t look very good in this position. Arguably the most constructive play is 13/4, which
unstacks the midpoint and begins to build the 4-point, but that leaves by far the most shots. At least in this
position, the shots versus construction criteria take us in opposite directions.

There’s another criterion, however, which is much more likely to lead us in the right direction. Let’s ask
ourselves this question: What checkers will our opponent use to hit, and how much does he want to hit with
those checkers?

For instance, suppose we leave the blot on the 16-point. If Black hits, he’ll hit from his midpoint. That
surrenders a point, but the hit slots the back of his prime and brings down a couple of builders for his inner
board. All in all, that’s pretty constructive.

Or suppose we make a play that includes playing 6/2. To hit that blot, Black has to use the checker on his
24-point. No harm done there.

But suppose we play 16/11 13/9. Now in order to hit, Black has to break his anchor on the 18-point. Oops!
The 18-point is Black’s strong defensive anchor. That hit could be very costly down the road. As a result,
16/11 13/9 is White’s best move.

——-

The right way to attack these problems is to think about the checkers your opponent has to use to hit. In
most cases he’ll have some big preferences. Here’s a partial list that illustrates how hits look from your
opponent’s point of view.

Your opponent most wants to:

Hit from a stacked point, diversifying.
Hit and create new builders for the inner board.

Hit and threaten to build a prime.

Hit and escape a back checker.

Hit with a spare checker from a point.

Your opponent least wants to:

Hit deep in the home board.

Hit and break a point.

Hit and break a crucial defensive anchor.

As a rule, directly counting shots is an overrated idea in many positions. It’s very useful at the end of the
game, when the boards are strong and getting hit may lead directly to a loss. In the early game and middle
game, it’s much less useful. Instead, look at how your opponent will hit you and see if a hit will be
constructive or destructive for his position.

Position 140B is the same idea in a different form. The play leaving fewest blots and shots is 16/8. However,
that play allows Black to hit and release the spare on the 22-point. That’s very useful for Black, giving him a
new checker to move while keeping the 22-point anchor. A much better play is 13/7 9/7. Even though it
leaves two blots instead of one, it requires Black to break a point somewhere to hit. (And not to be
overlooked is the fact that it also builds the very strong 7-point.)

AUG-01-2022 || BLITZ OR CONSOLIDATE?

Aug 1, 2022 | Backgammon Problems: Blitzes, Uncategorized
Cash game. Black owns the cube. White on move.

White to play 3-3.

White’s off to a good start in this position. He’s already made a three-point board, whereas Black hasn’t yet
made a new point, and White has hit a blot, leaving him 17 pips ahead in the race. Black, meanwhile, is still
scrambling to make an anchor. Last turn White offered an aggressive double, and Black quite reasonably
took.

Now White throws one of his best shots, 3-3, and has three game plans:

(a) The consolidation play with 14/8 13/10(2), leaving him firmly in control with a nice edge, or

(b) Consolidation plus a little attack with 24/21 14/8 6/3*, or

(c) All-out blitz with either 13/4*/1* or 13/4* 6/3*.

What’s the right idea?

Here’s the general approach for handling these sorts of positions. If your opponent has no structure, and the
cube has already been turned (activating gammons), then the blitz dominates any safe game plan. If the blitz
fails, White can just drop back into some sort of holding game where he holds a slight edge. If White makes
one of the solid plays, he’ll reach those holding games anyway since almost all of Black’s rolls will anchor
somewhere. White will be slightly better off if he goes for the holding game right away, because of his racing
lead, but the difference is small. But if the blitz succeeds White wins a gammon, and with the cube already
turned that’s a quick four points and a huge swing.

As Black acquires more structure, the blitz drops in value. If we alter Black’s position and give him his 5-point
(as though he had rolled a 3-1 at some time), then the blitz plays are only slightly superior to the
consolidating plays. If we give Black two extra points, say the 5-point and the 3-point, then the blitz plays
become pretty big errors and the consolidating plays becomes correct. (There’s very little difference between
Play (a) and Play (b) no matter what structure Black has.)

So we’re blitzing. Next question: what’s the right way to blitz?

What makes this problem especially interesting is that White has two distinct ways to blitz: the obvious
13/4*/1* and the obviously riskier 13/4* 6/3*. Problems with two plausible blitzing moves are rare, but we can
choose between them by noticing that the double-hit with 13/4*/1* exposes only one blot in the board, and a
hit may only allow Black to get an ace-point game later. If White hits on the 3-point and 4-point with two
checkers and Black then throws a three or four, he may get a good anchor quickly. The two blitzing plays are
close (and far superior to the non-blitzing plays) but the play that exposes only one inside blot is slightly
better.

AUG-15-2022 || PLAYING AGAINST A BUSTED BACK GAME

Aug 15, 2022 | Backgammon Problems: Back Games
Cash game. Black owns the cube. White on move.

White to play 4-3.

Something a little different this time. Identify the worst of these three plays:

(a) 11/7 5/2

(b) 11/4

(c) 7/4 6/2.

This one is actually pretty easy. The worst play is the only completely safe play for this turn, 11/7 5/2. White
doesn’t need to be safe in this position. Black is helpless, with a busted board and some loose blots. Black
doesn’t want to hit right now; he wants a couple of turns to consolidate his position and hopefully hit later and
get off the gammon.
White’s idea should be to put his checkers in a good position for the bearoff. For that, he wants to clear his 7-
point and 8-point, and make sure he has plenty of spares on the 4, 5, and 6-points. Playing 11/7 5/2 does all
the wrong things: it (1) puts a checker on the 2-point, where it doesn’t belong, and (2) doesn’t put anyone on
the 4-point, where White wants spares, and (3) makes a point that White will immediately want to clear.
Conceptually, that’s about as bad as you can do.

What about the other two plays? They’re actually very close in equity, if you’re playing a strong player. But if
you’re playing a weak player, they’re not close at all: 11/4 is now much better than 7/4 6/2. The reason is that
after 11/4, leaving a blot on the bar-point, Black shouldn’t hit unless he rolls 6-6 or 4-4. For any other roll
containing a 6 or a 4, the hit is a big mistake, exposing Black to lots of extra gammon losses for relatively few
winning chances. Weak players won’t necessarily see this, so leaving the blot on the 7-point can induce a
blunder. After 7/4 6/2, however, even weak players will mostly handle the next roll correctly, moving their
outfield blot.

SEP-01-2022 || WHEN YOUR OPPONENT IS ABOUT TO CRUNCH

Sep 1, 2022 | Backgammon Problems: Priming Games
Cash game. White owns the cube. White on roll.

Should White double? If White doubles, should Black take or drop?

In this position, White took an early cube based on his ownership of Black’s 2-point and the fact that Black
still had a checker left to escape. After that, the game developed almost perfectly for him. His deuce-point
game caused Black to bear in awkwardly, while White’s front position came together and prevented Black’s
back checker from escaping. After Black’s last roll (an awkward 4-4), White finally has a clear advantage,
although he still trails by 47 pips in the race. Is this the right time to double?

The answer is yes, and in fact Black should give this game up. His pip count lead is largely an illusion, since
White is so close to completing a full prime and Black isn’t even at the edge of the 5-prime yet. In addition,
Black’s game is on the verge of collapsing completely. Plenty of numbers leave additional shots next turn for
Black (6-5, 5-4, 6-2, 5-1, and 4-2 are the obvious ones), while doubles crunch his position further.
When your opponent’s position is overstretched and crumbling, you have to double before the blots appear;
doubling later will just give him an easy pass.

Part of doubling, however, is knowing how to play the positions that arise. Suppose you do double and Black
takes. How would you play these numbers for White? (Scroll down a bit to see the answers.)

6-5?

6-4?

3-1?

4-3?

5-1?

6-5: Run with 23/12. Don’t break your prime by hitting on the 2-point. The prime is very powerful with Black
not yet at the edge, and hitting may prevent Black from moving.
6-4: Run with 23/13. Similar to the 6-5 roll, although it’s a closer call because making the 2-point is
constructive.
3-1: Slot with 6/3 8/7. (6/5 instead of 8/7 is also good). This makes you a favorite to complete your 6-prime
eventually, while allowing Black to roll his disaster numbers like 6-5 and 5-4.
4-3: 8/4 6/3, for the same reason.
5-1: 8/3 6/5, for the same reason. Slotting is a key idea in this sort of position. Killing checkers by playing 6/1
8/7 makes the 6-prime too hard to complete later. You always want your checkers active rather than dead.

SEP-15-2022 || HANDLING A PROTO-BACK GAME

Sep 15, 2022 | Backgammon Problems: Back Games
Cash game. White owns the cube. White on move.

White to play 2-2.

First, let’s try to orient ourselves. White looked like he might get stuck in some sort of miserable ace-point
game, but has just thrown a fantastic shot, 2-2, which is so good it actually lets him pursue a few different
options. In backgammon, it’s good technique to try to list all the reasonable plays before you start analyzing
the merits of any one play. With that goal in mind, let’s see what we can find for candidate plays.
* Bar/23 11/9*/7*/5. White turns the tables on his opponent with this play, which ignores defense and goes
straight for the attack. By closing his 5-point while putting two Black checkers on the bar, White gives himself
the chance to win by going forward. If he can hit one or two more blots and escape a checker or two from
behind Black’s prime, his plan might succeed. On the negative side, he hasn’t done anything yet about his
rear checkers.
* Bar/23 24/22*(2) 11/9*. This play combines a little offense with a lot of defense. White makes the 22-point,
shoring up his defenses and giving himself a good chance to make a second back point. Meanwhile, he’s still
put two Black checkers in the air, so he could develop some offensive chances if Black doesn’t roll a five.
* Bar/23 24/22*(2) 23/21. Maximum defense, no offense. White hits only one checker, but gives himself the
best chance to establish two good back game points, in this case the 21-point and 22-point.
* Bar/23 24/22* 11/9*/7*. White hits three checkers while spreading out his back men. Plenty of offense, but
the lack of the 5-point could be dangerous. If Black rolls a five, a lot of men could be headed to the rear.
* Bar/23 24/22* 11/9*(2). Hits a couple of checkers while leaving no extraneous blots. Aggression plus safety,
although the lack of the 5-point is once again a factor.
That’s quite a lot of choices. How can we narrow the field a bit?

One way of narrowing the field is to remember a very reliable principle. In general, you want to go forward.
Plays that contain a significant chance of going forward tend to dominate more defensive plays unless the
position is truly critical and the offensive chances are unrealistic.
That argument favors the initial play, Bar/23 combined with 11/9*/7*/5. Are the offensive chances after this
play realistic? Certainly. Black has two men in the air, so he’s not even a favorite to enter both men from the
bar. In addition, he has two more blots vulnerable to aces and deuces. It’s not at all a stretch to imagine that
Black could shortly have four men behind three or four White points. For this plan to work, White will need to
escape a checker or two in the near future, but Black only has a four-prime, so that’s not an impossibility.

The other plays aren’t bad, but in all of them White has only a one-point board, so Black is under much less
pressure. In proto-backgame positions, always keep your eyes open for a breakout play, something that has
the potential to alter the direction of the game completely. It’s often the best choice.

OCT-01-2022 || PRIME VERSUS PRIME TACTICS

Oct 1, 2022 | Backgammon Problems: Priming Games, Uncategorized
Cash game. White owns the cube. White on move.

White to play 2-2.

This problem is an example of a somewhat rare breed, a true prime against prime game. Although we talk
about priming games a lot, real priming battle don’t arise all that often. Much more common are positions
where one side has a prime and the other just a loose connection of points, or games where one side has a
prime but the other is conducting a strong attack.
In genuine priming games, you have two ways to win: either escape the other guy’s prime before he escapes
yours, or force him to crack. Once your opponent makes a full 6-prime, as here, you’re down to just one plan:
make him crack.

In order to make Black crack, White is going to have to build a 5-prime and then arrange to spend some R&R
time on the bar while Black tries to escape. In light of this plan, we can assess the choices as follows:

9/7*/3* 5/3. Making the 3-point is the beginner’s play. White doesn’t build a prime and puts Black on the bar,
thus ensuring that Black keeps his prime for some time.
9/7*(3) 5/3* and 9/7*(3) 4/2. White is on the right track with these plays, both of which are pretty reasonable.
White makes a prime and dumps a checker in his board, hoping to get hit. If he gets hit, he’s in reasonable
shape, and he might be able to stay on the bar long enough for Black to break.
9/7*(2) 5/3* 4/2! White makes his prime and goes for the double-dump, leaving two checkers to be hit.
Compared to the single-dump plays, White increases his winning chances by 4%-5%, but also increases his
chances of being gammoned by about the same amount. Since new wins are worth twice the value of new
gammons lost, it’s the right play, but by a narrow margin.
The double-dump play looks ingenious, but it won’t always be the right play. You need to check and make
sure your opponent is indeed on the verge of cracking. That’s the case here as Black’s outside checker gives
him only about one extra roll of timing. If Black had more time, the double-dump wouldn’t gain enough wins
to make up for extra gammons lost.

OCT-15-2022 || A POST-ACE-POINT GAME PROBLEM

Oct 15, 2022 | Post-Ace-Point Games
Cash game. White owns the cube. White on move.

(a) White to play 5-1.

 (b) White to play 5-1.
These two positions take us into the fun world of post-ace-point games.

“Post-ace-point” is a little bit of a misnomer. These positions can be reached from ace-point games, but also
from deuce-point games, or back games, or even games where someone was on the bar and closed out.
The main idea is that you held on and finally hit a shot, then contained the hit checker or two, then completed
a closeout, and finally started to bear off. Mostly your problem is figuring out exactly when to redouble, but
sometime the problem lies in how safely you should play your checkers.

These positions show two examples of the most common checker play quandary. In each case, White has a
choice between bearing off one checker and playing completely safe (5/off 5/4), or bearing off two checkers
while leaving a shot (5/off 1/off). What’s right, and how do we make the decision?

The first metric we want to calculate is the crossover count. A crossover is simply a move of a checker from
one quadrant to another, or from the bar to the opponent’s inner board, or from the inner board to the
bearoff. Let’s start with Position A. White has 15 checkers in his inner board to be borne off, so his crossover
count is easy: it’s just 15. Black’s is a little more difficult. His six checkers in his inner board represent six
crossovers obviously. His checker on the bar represents another five crossovers: one to enter, three more to
get from White’s inner board to Black’s inner board, and one more to bear off. Black’s total crossover count is
11.

So in Position A, White trails in the crossover count by four, 15 to 11. In Position B, he also trails by the same
four crossovers, 14 to 10.

Next we employ the following rule of thumb:

If you trail by two or less in the crossover count, play safe. You’re doing well enough in the race that there’s
no need to take additional risks.

If you trail by five or more in the crossover count, take two checkers off and leave a blot. You’re a big
underdog in the race, and you need the extra checker speed.

If you trail by three or four, you’re in a grey area.

Well, that’s nice. We’re in the grey area in both positions. What next?

In the grey area, decisions depend very much on the exact arrangement and count of checkers in the inner
board. You next want to look at all of the following considerations and see if they point toward one play or
another.
(1) If you trail by three crossovers, tend to play safe. If you trail by four, tend to bear off.

(2) If Black has a blot in his board, tend to bear off. If no blot, tend to play safe.

(3) If taking two checkers off brings you to an even number of checkers, tend to bear off, otherwise tend to
play safe.

(4) If you have a speed board, tend to play safe, otherwise tend to bear off. A speed board is one where
White’s home board spares are heavily concentrated on the one and two points, which implies that small
doubles are more likely to bear off four checkers through the bearoff. With a slower board, where the
checkers are spread evenly across points, small doubles often won’t save a roll.

Now let’s see how Positions A and B compare across these four criteria.

(1) Crossover count? White trails by four in each position.

Problem A – favors bearing off.
Problem B – favors bearing off.

(2) Black blot? Black doesn’t have a blot.

Problem A – favors playing safe.
Problem B – favors playing safe.

(3) Getting to even? Taking two off in A brings White to 13 checkers, an odd number. But in B, taking two off
brings him to 12, potentially saving a roll.
Problem A – favors playing safe.
Problem B – favors bearing off.

(4) Speed board? White has a slow board in both positions.

Problem A – favors bearing off.
Problem B – favors bearing off.

For Position A, our four criteria split two and two. Rollouts show the position is actually a tossup, with a
minute edge for playing safe.

In Position B, three of our four criteria favor bearing two off, and rollouts show that’s the correct play by a
wide margin.

NOV-01-2022 || TWO MIDDLE GAME DOUBLES

Nov 1, 2022 | Backgammon Problems: Middle Game
Cash game. Center cube. White on move.
 (a) Should White double? If he doubles, should Black take or drop?

(b) Should White double? If he doubles, should Black take or drop?

These two positions show a couple of very typical middle game doubles. In each case we’re six to eight
moves into the game, one side has finally grabbed a noticeable advantage, and now they’re thinking about
turning the cube. Double? Take? What’s right?

Let’s start with the doubling question. The best general guide to early/middle game doubles of this sort came
years ago from Joe Sylvester. (Joe was one of the titans of backgammon in the 1980s and 1990s, and he
won the first World Cup in 1988. Today he’s somewhat inactive.) Joe recommended looking at three features
of the position: the race, the structure, and threats. His rule was the following: if you have an edge in at least
two of these three, then you have a double.

With this idea in mind, how’s White doing in Position (a)?

> White leads in the race, 133 to 149, a 16-pip lead.

> White has a better structure, with a 4-point block, his 4, 5, and 6-points already made, and good
distribution. Black lacks his 4-point and 5-point and has a big stack on his 6-point.

> White has plenty of immediate threats. Twos hit the blot in Black’s board, 6-1, 6-3, and 3-1 make a 5-point
prime, and 6-4 points on the 2-point. White’s edge is threatening to get much bigger next turn.
With an edge in every department, Sylvester’s rule suggests White should have a strong double in Position
(a), and in fact he does.

Now let’s look at Position (b).

> White leads in the race, 134 to 162, a 28-pip lead.

> White has a better structure, with four points made in front of Black’s anchor. In addition, Black has three
men back on his 23-point, which is weak. Black also has no inner board yet, which is also weak. Here the
issue is not so much that White is strong, but that Black’s pretty weak.

> White has no particular threats. True, 6-1 makes his 5-point, and a few numbers will run his back checker
into the outfield. But that’s more the sort of background threat noise that’s present in every position.

Here, we can say that White has an edge in two out of the three criteria. Again, he has a solid double.

Now, what about the take/drop question? Here I’ve got my own rule. I ask myself three quick questions. If the
answer to the first and third questions is ‘yes’, and the answer to the second question is ‘no’ I’m pretty sure
I’ve got a take. If not, then I’ll look at the position more closely. My questions are:

> Do I have an anchor?

> Does my opponent have a 5-prime?

> Is there still contact on both sides of the board?

Take a look at Problem 1 and Problem 2. In both cases Black has an anchor, in both cases White hasn’t yet
built a 5-prime, and in both cases we still have contact on the other side. With all these conditions in place,
it’s hard (although not impossible) for Black to be a 3-to-1 underdog in the game. In both positions, Black’s
best guess should be that he probably has a take. And in fact, rollouts show that’s the correct action.

NOV-15-2022 || HOLDING GAME DOUBLES

Nov 15, 2022 | Backgammon Problems: Holding Game
Cash game. Center cube. White on move.

Should White double? If he doubles, should Black take or drop?

Here’s an interesting cube position. Black has an anchor on White’s 5-point. White’s ahead in the race by 21
pips, 117-138. White also has a pretty good 4-point board. Black’s remaining checkers are in play and his
board is in the process of forming.
Those features are routine and we see them in most holding games. But this position has a few unique
features as well.

> Black’s on the bar.

> White doesn’t have a point in his outfield to serve as a landing spot.

> Black’s home board still needs some work before he’s ready to hit a shot.

In the absence of these features, we’d have no trouble with this position. Take a look at Position 148A, for
instance:

Position 148A: Center cube, White on roll.

Position 148A is a well-known position type. White leads by 20 pips in the race, Black’s not on the bar, and
Black’s home board is in good shape. White has a good landing spot for his outside checkers on the 8-point.
It’s a trivially easy take. The double/no double decision is the hard one, because White has very few market-
losers. The four big doubles (66, 55, 44, and 33) which clear the midpoint are market-losing threats, but
that’s about it. White actually has a very small double now, but he can’t make a big mistake either way.

Now let’s look back at our original position. White is worse off because he lacks that landing spot in his outer
board, although he has some threats to make it. Black is worse off because he’s on the bar, and his home
board hasn’t come together yet. How do these factors affect the outcome?

The situation in Black’s home board is a plus for White. Until Black enters and covers his 5-point, White
doesn’t have much to worry about and can take some small chances to improve his position.

Being on the bar is a negative for Black. Although Black’s a favorite to come in each turn, White will probably
get a couple of turns where he can take some small chances to consolidate.

Not having a landing spot is a big deal for White. He badly needs a point like the 7-point or 8-point so he has
some chance to move off the midpoint without constantly having to break his board when he rolls small
numbers. However, he already has a landing spot slotted, and about half his rolls will let him make the 8-
point right away.

The upshot is that these factors roughly balance out, and your judgment on Problem 148 should be very
similar to 148A: easy take and a small but correct double. The doubling decision is easier in Problem 148
because White actually has a fair number of market-losing sequences: any roll that makes the 8-point,
followed by a dance for White, will either lose White’s market or bring the position very close to a pass.
DEC-01-2022 || PRIMING GAMES: ESCAPE OR BUILD
STRUCTURE?
Dec 1, 2022 | Backgammon Problems: Priming Games
Cash game. Center cube. White on move.

(A) White to play 6-1.

(B) White to play 6-1.

One of the most difficult choices in the early and middle stages of a backgammon game is the choice
between creating structure (a blocking prime) and attending to issues on the other side of the board. Those
issues vary: you might be able to hit a checker, or make a defensive anchor, or escape one of your back
men. In some cases, making structure is correct. In other cases, playing on the other side of the board is
correct. Let’s take a look at a couple of examples, to see the ideas that have to guide us in these decisions.

Let’s start with Position (A). It’s not a tough problem. White can hit a blot with 24/17* or build some structure
with 13/7 8/7. The structural play has two problems: the structure isn’t that impressive, and it gives Black a
direct shot at White’s blot on the 14-point. For structure to trump hitting, you want structure which is solid and
imposing.

24/17* might look loose, but it accomplishes two great things: hitting an important blot, and escaping a rear
checker. True, Black may hit back. He has a total of 16 return hits (all twos except 2-6, and all fives except 5-
6). But that leaves 20 rolls that don’t hit, and those are great rolls for White – he’s ahead in the race and his
rear checkers are out. Potentially getting all your back checkers out is a great result, and 24/17* puts White
within striking distance of that goal.

Problem (B) occurs much later in the game. White has two choices: he can block in Black’s two rear
checkers with 13/7 8/7, or he can escape his own last checker with 24/17. Running out is more volatile – if
White gets away with it, he’s close to a double, but if Black hits, White is an immediate underdog. Making the
7-point, on the other hand, leaves White a solid but unspectacular favorite in most variations.

What’s right? White should go ahead and make his 7-point. There are two reasons:

(1) With an advantage and a centered cube, you’re not looking to make big swing plays. You’re more
interested in plays that preserve your advantage and creep closer to an eventual good double. When in
doubt between the merits of two plays, lean to the more conservative choice.

(2) Trapping two men will increase your gammon chances dramatically. There’s actually not much difference
in raw winning chances between the two plays, but locking in Black’s two back checkers will win many more
gammons.

The basic idea in these positions is a simple one: the quality of the structure you build is crucial. Turning a
very weak structure into a slightly better structure, as in Position (A), isn’t worth that much. Turning a broken
structure into a 5-point prime, as in Position (B), is huge, even when the alternative is escaping the last
checker from behind a 5-prime! The lesson to be learned is that creating a 5-prime or even a 4-prime may
outweigh making progress on the other side of the board, but just building a blocking point or a 3-prime is
probably not enough.

DEC-15-2022 || A BACK GAME WITH QUESTIONABLE TIMING

Dec 15, 2022 | Backgammon Problems: Back Games
Cash game. White owns the cube. White on move.

White to play 4-3.

This isn’t a particularly hard position when presented as a problem. The right play is 8/5 13/9, keeping both
back points, slotting the 5-point, and playing 13/9 so as to create two cover numbers for the 5-point.

Over the board, with no one hinting that this is actually an interesting position, it’s fairly easy to make a small
mistake. I’d expect to see a lot of players move either 13/9 13/10, a slight error because it doesn’t start the 5-
point, or 8/4 8/5, another slight error because the builder on the 4-point is somewhat misplaced and White
has fewer cover numbers for the 5-point than he should.

Leaving a blot on the midpoint after 13/9 8/5 is not especially costly because for the most part Black doesn’t
want to hit it. Let’s take a quick look at how Black should play his aces after White plays 13/9 8/5.
Black needs to notice these features of the position:

> If he can play safe and not hit, he should do so. Not hitting leaves White’s timing in jeopardy, while hitting
improves White’s timing somewhat and may give White a shot at Black’s blot on his ace-point. Right now
White trails by 65 pips in the race, which is enough to give him some reasonable winning chances, but not
enough to say that he has a well-timed back game. One extra checker back, especially if White could dance
for a turn, would make a big difference.

> Playing safe is essential for Black, so if he can only play safe by hitting, he will do so. Black very much
doesn’t want to get hit right now, because White’s board is already strong enough to cause real trouble.

> If Black can’t play safe, hitting wins more gammons, and may decrease the count of hit and cover
numbers.

So with 6-1, 5-1, and 4-1, the best plays are 13/6, 13/7, and 13/8, all without hitting.

With 3-1, Black can only play safe by hitting, so the right play is 13/12* 4/1.

With 2-1, Black can’t be safe no matter how he plays, so he should hit. Hitting substantially increases his
gammon chances compared to the non-hit play (13/11/10), while his losing chances are close after both
plays.

As a last point, note that White shouldn’t consider playing 23/16 with his 4-3. While it’s true that his back
game/holding game isn’t ideal, it’s the only game he has. Playing 23/16 breaks much of the contact and
leaves him 58 pips behind in a game that will mostly become a 5-point holding game, an essentially hopeless
situation. If White really wanted to break one of his anchors, the better choice is to keep the back anchor and
play 20/13.

JAN-01-2023 || ASSET OR LIABILITY?

Jan 1, 2023 | Backgammon Problems: Holding Game
Cash game. Black owns the cube. White on move.

White to play 6-2.

Extreme Gammon (XG) is the most useful tool ever invented for improving at backgammon. It’s both the
strongest commercially available backgammon software, and, when used properly, the best teacher.
Getting the most out of XG’s teaching ability, however, requires a little thought and planning. In this post I’ll
give an example of how using XG’s power, combined with a little critical thinking, can help you patch weak
spots in your game.

Take a look at today’s position. White has escaped both his back checkers and made a couple of good
points in the process. Black is holding onto White’s 5-point, playing what we call a basic 5-point holding
game. White is trying to come home without leaving any shots. Last turn White doubled and Black correctly
took.

Now White rolls 6-2. He can’t play safely off the midpoint, so he’s got a few choices. He can make the 2-
point, breaking the 4-point but keeping plenty of spares available. He can start the 2-point with 8/2 6/4,
keeping a better point but leaving himself with one less spare to move. And finally he can break the 10-point
with 10/4 10/8.

Your play here depends on whether you think the 10-point is an asset or a liability. In general, when you’re
trying to bring a position like this home your watchword is “Clear from the back”. Your back point here is the
midpoint, so you’d like to clear that first. The 6, 8, and 10-points are all landing spots for the checkers on the
midpoint, so they’re all assets right now.

When this position came up in a game of mine, that was my train of thought. “The 10-point is an asset
because it helps me clear the midpoint, so I’ll use one of my spares and make the 2-point. I don’t care about
the blot on the 4, because I’ll remake that later.” Very reasonable thinking.

But quite wrong.

The 10-point isn’t just an asset – it’s both an asset and a liability, all rolled into one. (A little like Kris
Kristofferson’s Pilgrim – “a walking contradiction, partly truth and partly fiction.”) It’s an asset because it
provides a landing spot for the midpoint checkers as they try to come home. But it’s a liability at the same
time because it will have to be cleared later, and only 11 numbers clear the point – combinations of 2, 4, and
6, plus doubles except 5-5.

Now we’ve thrown a number that allows us to clear the point, so now we have to decide – is it more of an
asset (in which case we want to keep it) or more of a liability (in which case we want to clear it)?

In this position, the answer is that it’s more of a liability. It only helps us when we throw precisely a 5-3 and
clear the midpoint. But it hurts us when we need to clear it but can’t, and on any given turn 70% of our
numbers won’t clear it without leaving a shot. So now our play is clear – get off the point with 10/8 10/4, and
hope to play with our spares while we wait for a double to clear the midpoint.

Suppose instead of the 10-point we owned the 11-point or the 9-point. What would we do with a potential
clearing number in those cases? The 11-point is even harder to clear than the 10-point, so if we threw a 5-3
we’d be delighted to clear it. But the 9-point is much easier to clear, so if we had the 9-point instead of the
10-point and threw something like a 6-3 or 6-5 we’d keep the point and dump checkers in our home board.

JAN-15-2023 || BACK GAMES: WHEN TO REDOUBLE

Jan 15, 2023 | Backgammon Problems: Back Games, Uncategorized
Cash game. White owns the cube. White on move.
 Should White double? If he does, should Black take, drop, or beaver?

Positions like this are fairly commonplace when playing back games, and they’re tricky enough to lead many
players astray.

White has played a 5-2 back game and has just gotten a double shot. Besides fives and twos, he can also hit
with 4-1, so he has a total of 22 hits and 14 misses this turn. In the future of course, White may get even
more shots.

Some players, encountering this position for the first time, might reason as follows:

> Wow, I have 22 hits! I’m already the favorite!

> And if I hit, I can easily lose my market!

> And I might get even more shots in the future!

> And I could win a gammon!!

> I double!!!

Anything wrong with this reasoning? Well, just a little bit. Let’s look more closely.

Let’s start by examining what happens when White doubles. True, he then hits 22 times out of 36, a bit more
than 60%. But how many of those can he win, once Black owns the cube? Let’s give White a pretty average
hitting roll, like 4-2, and see how we think he’s doing.
 Position after White hits with 4-2 and plays 20/18*/14.
Although he just got hit, Black still leads by 50 pips in the race, which has to be worth something. In addition,
he has some pretty good shots in this position: 6-2, 5-2, 6-1, and 1-1, all of which leave Black in a lot of
trouble. Let’s be conservative and say that Black can pull the game out a little less than a quarter of the time
from this position. In that case, out of White’s 22 hits, we’ll say he can win about 17 of them, losing the other
five.

What about White’s 14 misses? Now he’s in real trouble, trailing by 60-70 pips in the race, with his opponent
owning the cube. Black won’t redouble immediately, but he’ll be able to use the cube very effectively in the
near future when his position improves a little more. At worst, he’ll at least be able to play the game out to
the end. I’ll give White four of these games, but no more.

Overall, White’s chances after doubling look like this:

If he hits, he wins 17 and loses 5.

If he misses, he wins 4 and loses 10.

With the cube on 4, White wins about 21 and loses about 15, for a net of 6 games, worth 4 points each.
Total, +24 points.

Now suppose White keeps the cube and rolls. Again he hits 22 and misses 14. But now his 22 hits are very
strong. Black needs a great shot immediately or he’ll pass a double, and even if he gets his shot, White can
hang around until the end. Let’s make White about a 20 to 2 favorite in these games.

If White misses, he still has plenty of chances in the game. Let’s give him 6 games of these 14, losing the
other 8. Now, his chances after not doubling look like this:

If he hits, he wins 20 and loses 2.

If he misses, he wins 6 and loses 8.

With the cube on 2, White wins about 26 and loses about 10, for a net of 16 games, worth 2 points each. His
total here is +32 points. So he does substantially better by not doubling.

This is a pretty typical result when you get a double shot in a back game. You’re a big favorite if you hold
onto the cube, but just a small favorite if you double. Barring some unusual features, these positions are
mostly all no double and take.
FEB-01-2023 || BACK GAMES: REDOUBLING AND TAKING
Feb 1, 2023 | Backgammon Problems: Back Games
Cash game. White owns the cube. White on move.

Should White double? If he does, should Black take, drop, or beaver?

In our last problem we looked at a back game where the back game player got a double shot, but
still couldn’t double until he actually hit the shot.

While that’s a generally good rule for many normal back game positions, it’s not always the case.
When playing a massive back game, stay alert for positions where your opponent’s game has
deteriorated so much that you can double much earlier.

In this position, White has patiently held on to his 1-3-4 back game while Black has dumped a total
of eight checkers on his 2-point. Given his structure and his open 5-point (which makes White’s
back game even stronger) Black is likely to leave double and triple shots as he tries to clear each
of the three remaining points. Although White is likely to run one checker off the 21-point this turn,
that won’t help Black much. He still faces leaving a series of shots, and when he gets hit, most of
his entering numbers will shake more blots loose.

Most surprising of all might be the fact that White is the side with the gammon chances here! He
wins over 75% of the games from this position, with about a third of those being gammons.

White should double and in fact Black already has a pass. It’s a somewhat surprising result, but
back games with three good anchors and a sloppy structure for the side coming home can be
enormously strong.

MAR-15-2023 || HOW MATCH SCORE AFFECTS EARLY GAME

PLAY
Mar 13, 2023 | Backgammon Problems: Tournament Tips, Uncategorized
Center cube. Black on move.
 Black to play 3-3
(a) in a cash game.
(b) at double match point.
(c) trailing 1-2 in a 5-point match.
(a) Cash game.
As a cash game play, this position has an interesting history. When I started playing serious
backgammon in the late 1970s, the game was dominated by a group of aggressive young New
Yorkers centered at the legendary Mayfair Club, who emphasized making big plays early on, to set
up quick cube turns and gammons. They were bold, ingenious, highly aggressive, and very
successful, and most aspiring players followed their lead.

At the time, the old-fashioned play with 3-3 after an opening split to the bar was the obvious
13/7*(2). Why not? It hits a blot, makes a good point, leaves no blots, and unstacks the midpoint.
That’s a lot of good things at zero risk. The New Yorkers rejected this play and instead played
13/7* 8/5(2), in accordance with the new (at the time) emphasis on making the 5-point early on no
matter what the cost.

When I saw the new play I enthusiastically switched, following my general rule of thumb for
beginners: “Ape your betters”. (At least until you know enough to question their judgment.) After a
few years, though, I started to have second thoughts. How bad could 13/7*(2) really be? It had a lot
to recommend it: good point, no blots, takes a solid initiative. I did some analysis and just couldn’t
convince myself there was anything wrong with the play, so I switched and started to play it. I got
some hoots of derision, but pretty soon more and more players were switching over, and by the
1990s this simple play was the standard, and the ‘old-fashioned’ 13/7* 8/5(2) looked ‘too loose, too
fancy’.

Extreme Gammon rollouts long ago confirmed that 13/7*(2) is in fact best, while 13/7* 8/5(2) is a
fairly close runner-up. Also in the mix is 13/7* 6/3(2), also making an inner point, unstacking, and
leaving fewer shots and blots. Prior to the bot era, no one would even have considered making the
3-point, although I think most modern players would immediately spot it as a strong alternative.
(b) Double match point.
Double match point is simply any match score where gammons don’t count for either side and the
result of this game decides the match. The simplest example occurs when each side is one point
from victory. Other match scores can convert into double match point (DMP) pretty easily. For
instance, if both players are two away from victory, and someone doubles quickly and the other
side takes, then we have a double match point situation by default.
With gammons not counting, strategy in this situation undergoes a few changes. Here’s a quick
summary of the major alterations.

1. The best game plans at double match point are (a) escaping your back checkers and winning
the race, and (b) building a prime and winning the race. Racing advantages create a lot of wins but
not a lot of gammons, which is perfect.

2. Blitzes are a poor choice of game plan unless the dice allow no reasonable alternative; too many
gammons, not enough wins.

3. Anchors are less valuable because one of their functions is to prevent being gammoned, which
is no longer necessary. The strength of an anchor lies in its ability to transition to a favorable race.

4. Inner board points are still good, but not quite as good. We don’t care about their ability to create
gammons but we do care about their ability to create primes.

5. Slotting to build an inner board quickly is mostly wrong.

6. Plays where you run off an anchor to avoid being primed later are commonplace.

7. Escaping the back checkers is even better than usual.

Taking all this into account, it’s not hard to see that 13/7*(2) is even better at DMP than in a cash
game. It gains ground in a race while taking no risk of losing ground in the race. The point is useful
as well.

(c) Trailing 1-2 in a 5-point match.

Trailing 1-2 to 5, or ‘4-away 3-away’ as it is sometimes called, is a score where gammons matter
more than usual for the trailer. If the trailer wins a doubled gammon, he wins the match. If the
leader wins a doubled gammon, he still wins the match but some wastage is involved (he doesn’t
need the fourth point). As a result, the trailer needs to create positions where he has an elevated
chance of winning a gammon, at a reasonable cost. He doesn’t want to go crazy, he just wants to
take a little more risk for extra gammon chances.

Both 13/7* 6/3(2) and 13/7* 8/5(2) fit the bill here. They’re the second and third best plays in a cash
game, but here the extra inner point creates more gammons at a small cost in raw winning
chances. Which of the two is best? A rollout left the two plays in a dead heat. Playing 6/3(2) makes
a weaker point, but as compensation it unstacks a big stack and leaves fewer shots.

APR-15-2023 || BALANCED AND UNBALANCED POSITIONS

Apr 15, 2023 | Backgammon Problems: Middle Game
Center cube. Money game. White on move.
 Should White double? If he doubles, should Black take, drop, or beaver?
White seems to be doing pretty well in this position. He has a 4-point board, while Black as yet has
no new home board points made. Black doesn’t have an anchor yet. White can hit on the 4-point
with 18 numbers (all 4s, 3-1, 2-2, 1-1, 6-3, and 3-3.) He has a few more numbers to hit on the 1-
point, although that’s certainly not his top choice. White leads by a whopping 38 pips in the race.
Looks like White’s concrete assets and threats combine to give him a good double. Can Black
even take this? Over the board, a lot of players would drop almost instantly.

Before we pass final judgment on this cube, let’s alter the position just a little bit:

Position A: White on roll.

We’ve moved White’s spare on the 3-point back to the 6-point, where it’s active, and we moved the
third checker on the 8-point back to the midpoint. White has lost 8 pips in the race, but his
checkers are now where they belong and his position is much stronger.

Position A is a strong double for White and a clear pass for Black. (By the way, it’s not remotely
close to being too good to double.) Our original position, by contrast, is also a good double but a
clear take. White has threats, but he also has a number of bad rolls, and even when he rolls well to
start, his checkers aren’t sufficiently well-positioned to follow up.
Now let’s look at the two positions a little more closely. Position A is what I like to call a balanced
position. Given the underlying structure, White’s spares are well-placed and effective. Our original
position is unbalanced; here White’s spares are in the wrong places. The spare on the 3-point is
mostly useless. The extra spare on the 8-point doesn’t do much, and the broken midpoint is costly
in both the long and short term.

The difference between balanced and unbalanced positions is visually pretty clear, but the real
difference shows up when we examine White’s bad rolls. (The good rolls will play well anyway.)
Let’s list White’s worst rolls and see how they play in both the original position and Position A.

6-6: In the original position, this is a disaster; White is forced to play 13/1* 8/2(2), killing two
checkers. In Position A, this is a very good roll; White makes the 1-point.

5-5: In the original, this is another awful roll; White switches with 6/1*(2) and plays 13/3, killing a
checker. It’s not as bad in Position A, where White plays 6/1* 13/8 13/3.

6-5: In the original, White kills a checker with 13/2. In A, he plays 6/1* 13/7, much better.

6-2: White plays 3/1* 13/7 in the original. In A, he plays 23/15 because he owns the midpoint,
rather than having a blot there. Big edge to A.

6-1: In the original, White makes the 7-point, but gives up control of the outfield. In A, he gets to
play 23/16 as before. Another big edge for A.

5-3: In the original, he plays 13/8 with either 24/21 or 23/20. In A, he again takes advantage of
owning the midpoint by playing 23/15. Huge edge to A.

5-2: Same story. In the original he plays either 13/6 or 13/8 23/21. In A, he gets to play 23/16.
Another big edge to A.

5-1: In the original he plays 13/8 23/22. In A he plays the much stronger 6/1* 2/1.

3-2: In the original he gets to play 3/1* 23/20, activating the checker on the 3-point. In A he plays
the massively stronger double-hit.

2-1: In the original he plays 3/1* 2/1 as above, activating a bad checker. In A he gets to play 6/4*
23/22, hitting on the more important point.

As this listing shows, the difference between the standard-looking position in A and the inferior
position in the original isn’t slight; it’s actually huge. A lot of players look quickly at the original
position and actually “see” something more like A. But the exact placement of all the spares matter,
and it especially matters in the case of the bad rolls. In tough cube decisions, try to pay at least a
glancing impression as to how concrete rolls actually play, rather than get caught up in forming a
general sense of the position.

MAY-01-2023 || HIT OR MAKE A POINT?

May 1, 2023 | Backgammon Problems: Early Game
Cash game, center cube.
(a) White to play 3-1.
(b) Same position, White to play 3-2.
Here we see a typical sort of early game position where neither side has made much progress yet.
Black has played a 5-3 and a 6-3, making the 3-point and running a checker into the outfield. White
has rolled a 5-1, balancing his builders and splitting his back men.

The 3-1 and 3-2 rolls give White a choice between hitting and making a good point. Lots of players
hit automatically in these positions, not really believing that any non-hitting play can be good. But
that’s not right. Constructive positional plays are often better than hitting, especially in the early
game when boards are weak. Not always, however; sometimes hitting is, in fact, correct. Before
we address the particulars of this position, let’s take a general look at the rules that guide this sort
of choice. I’ll list a bunch of features of the position, and which choice each favors:

> A strong home board favors hitting; a weak home board favors building a point.

> A big disadvantage in the race favors hitting; a close race is neutral.

> The more ground you can gain in the race by hitting, the more correct it’s likely to be. Hitting a
blot in your opponent’s inner or outer boards is usually correct; hitting a blot in your own outer
board is sometimes a mistake.

> Strong threats for your opponent favor hitting as a tempo play or making a defensive anchor; few
threats favor making an offensive point.

> Stacks of checkers favor making a point; no stacks imply plenty of points already, which favors
hitting.

With those principles in mind, let’s start with Position (A). Here everything points to making the 5-
point as the best play. White has no home board and big stacks, and making the 5-point fixes both
problems. The race is close, hence relatively neutral. The blot to be hit is in White’s outer board,
only a modest argument for hitting. The stacks strongly favor unstacking and make the 5-point.
Black has only weak threats, which is an argument for structure.

The weight is strongly in favor of 8/5 6/5, which is in fact the best play with a 3-1.

Playing a 3-2 in position B is a different sort of problem. Now the question is hitting or making a
good anchor, so a lot of those arguments disappear, since White can’t do anything about his
stacks. Here the real question is: how badly does White need an anchor? The answer is: not much.
Black doesn’t yet have a strong attacking formation, and White’s rear checkers are already well-
placed. Hitting also works now as a tempo play, taking away half of Black’s roll and reducing his
offensive chances still further. The best hitting play is just 13/10* 23/21, keeping a spare on the
midpoint and preparing to make a good anchor later.

One more point before we leave this position. Players who go on long losing streaks often feel they
are rolling incredibly badly for long periods of time. In fact, what’s often happening is that they are
steaming and making mistakes in just these sorts of positions, taking the first play they see instead
of thinking the position through. Thus they tend to drift into bad positions more often than they
should.

MAY-15-2023 || HIT OR MAKE A POINT?

May 15, 2023 | Backgammon Problems: Middle Game
Cash game, White owns the cube.

White to play 3-1.

White has a simple choice in this position: hit with 13/9*, or wait and make a point with 15/12
13/12. Last time we looked at some choices between hitting a blot or making a point in the context
of early game play. This position occurs much later in the game, but, as it turns out, the very same
principles are still useful. Let’s again list the criteria we explained last time, and see how they apply
to this position.

Here they are:

> A strong home board favors hitting; a weak home board favors building a point.

> A big disadvantage in the race favors hitting; a close race is neutral.

> The more ground you can gain in the race by hitting, the more correct it’s likely to be. Hitting a
blot in your opponent’s inner or outer boards is usually correct; hitting a blot in your own outer
board is sometimes a mistake.

> Strong threats for your opponent favor hitting as a tempo play or making a defensive anchor; few
threats favor making an offensive point.
> Stacks of checkers favor making a point; no stacks imply plenty of points already, which favors
hitting.

White’s home board isn’t totally undeveloped, but it’s still pretty weak, with just two points and not
many point-making rolls on the horizon.

Unlike our last problem, here White trails in the race by 41 pips (149 to 108). That’s certainly a big
argument for hitting.

However, hitting here gains only 9 pips in the race. That’s not very much, which is some argument
for playing safe.

Right now Black has no strong threats; he’s just trying to get his rear checkers home over the
course of the next few rolls. That’s an argument for making a point, especially since Black retains
good coverage of the outer boards.

White has a big stack on his 6-point, which is hard to improve at this stage except by dumping
checkers in his board and then covering later. That’s a big argument for consolidating first.

One other factor comes into play which wasn’t relevant in our discussion last week: the strength of
Black’s inner board. Last time we looked at an opening position where Black’s board was weak.
Now it’s pretty strong. Obviously, that’s also an argument for playing safe, since being hit could be
disastrous for White.

The weight of all these considerations comes down strongly on the side of playing safe this turn
with 15/12 13/12. White still retains plenty of equity in the game since it will take Black a while to
get his rear checkers around the board safely. Meanwhile, White can build his home board in
peace and wait for a better time to hit.

How much better would White’s board need to be to make the hit correct? Not much, actually. Just
take two checkers from White’s pile on the 6-point and make any new home board point, even the
wretched ace-point, and White’s game is then good enough to hit!

JUNE-01-2023 || EARLY BLITZ CUBE – TAKE OR DROP?

Jun 1, 2023 | Backgammon Problems: Blitzes
Cash game, Center cube.
 Should White double? If he does, should Black take, drop, or beaver?
In this position we have an opening blitz with a few little twists we don’t always see in such
situations. Let’s quickly review the features of the position and look at which are important and
which are not.

White has his 5-point instead of his 6-point. This looks like it might matter, but it doesn’t. If Black
eventually anchors, there’s just a tiny difference between anchoring on the 6-point and anchoring
on the 5-point.
White has more shots at a second blot. This is a big deal. Take a look at the next position, which is a
more normal blitz.

Position A: White on roll.

Black ran out with an opening 6-4, White made two points with 5-5, and Black danced. Here White
has only 11 shots at a second blot. In our original position, White has 25 shots (all 6s, all 4s, 5-3, 5-
1, and 2-2). That’s a big difference.

White has three builders for his inner board. This is a small improvement over two builders as in
Position A. White picks up three new numbers (2-1 and 1-1) which don’t hit but which do make an
inner point.
White has a third checker back. This is a big negative for White, costing him 20 pips or so in the race
and reducing the number of builders that can quickly reach an attacking position.
Compared to Position A, White has one big positive (more shots at a second blot), one big
negative (a third checker back), and one small positive (a third builder in position). If we know the
equity of Problem A, we know that our original position is better than that for White, but not
overwhelmingly better.

Fortunately, Position A has been well understood for a long time. It was originally (in the 1960s and
early 1970s) thought to be double and big pass. Hand rollouts, however, revealed that it was a
clear double but a clear take, and it became a big money-maker in propositions against
unschooled opponents.

If A is a double and clear take, then the original position must be better than that for White. We can
certainly conclude it’s a big double and it’s only the take/drop decision that’s in question. In fact, it’s
a drop, although a small one. The extra shots at the second checker are very important, as are the
increased chances of making a fourth inner-board point. Put them together and Black can’t quite
squeeze out a take.

JUN-15-2023 || WHICH POINT TO BREAK?

Jun 15, 2023 | Backgammon Problems: Middle Game
Cash game, Black owns the cube.

White to play 6-2.

This isn’t a terribly tough problem but it does contain an interesting point.

First, let’s note that all the reasonable plays start with 23/17. Abandoning the checker on the 23-point by
playing 17/11 can’t be right in any universe I know about, so let’s play 23/17, then look for the best two.
Three candidates quickly appear:

a) 17/15

b) 10/8

c) 8/6

Play (a), 17/15, we have to discard pretty quickly, since it leaves two blots and a triple shot (5s, 3s, and 1s all
hit, while 3-2, 3-1, and 1-1 are double-hits). It’s true that none of these hits are immediately decisive. But
that’s also true of the blots that White can leave in the other variations. In addition, the anchor on the 17-
point is attacking both Black blots, which is a strong argument for keeping the point.
If White doesn’t play 17/15, then he has to break one of his outfield points and leave a shot. The obvious
break is 10/8, because we have learned from experience that breaking a prime from the back is usually
better. But this isn’t really a prime, and after White breaks a point, he should be able to play for a couple of
turns before he has to dismantle another point.

The right play is actually 8/6, for a couple of reasons. The first reason is just our old friend duplication. After
8/6, Black need fours to hit and fours to button up both outfield blots, so he doesn’t have many good
numbers at his disposal. The second and less important reason is that by breaking the 8-point but retaining
the 10-point, White gets some extra shots if Black rolls 4-1, 4-2, or 3-1 and decides to hit. This idea is often a
reason for breaking an interior point rather than the back point. Breaking the rear point is often right when
White is bearing home and the rear point is really the rear point; it’s sometimes not right when the whole
board is still in play and White need to keep his army from being disconnected.

JUL-01-2023 || MAKE POINT OR HIT TWICE?

Jul 1, 2023 | Backgammon Problems: Middle Game
Cash game, center cube.

White to play 4-1.

Is backgammon a simple game? No, not at all. There’s a lot you have to know, a lot of technique you have to
master, a few formulas to memorize. But some elements of backgammon are easy. At bottom,
backgammon’s about hitting blots, making points, and winning the race.

This position is about as easy as it gets for an early position that’s non-trivial. If backgammon is about hitting
blots and making points, then the right play practically jumps out: 9/5* 6/5, making the best point on the
board (White’s 5-point), hitting a blot in the process, and putting several builders to work on the next point to
make, White’s 4-point.

If our only concern were to avoid being hit next turn, then we’d play 7/2. That’s the safest play. But it’s also
useless and unconstructive, killing a builder while starting a weak point. If we’re so worried about being hit
that we have to resort to 7/2, shouldn’t Black be worried about being hit as well? If we’re afraid of being hit
when Black has no board and a weak outside prime, shouldn’t Black be terrified of being hit when we have a
3-point board and a bunch of builders bearing down on another blot? One technique for locating the right
play is to put yourself in the other player’s position and ask yourself “What play don’t I want my opponent to
make?” If you’re Black, are you more afraid of 7/2, or of 9/5* 6/5? If I’m Black in this position, I’m praying my
opponent plays 7/2.

Only one other play is worth considering, the double-hit with 9/5*/4*. It’s a decent play, much better than 7/2,
but it has the big disadvantage of not actually making any point. Even if White doesn’t get hit and then covers
next turn, he’ll have made the 4-point rather than the stronger 5-point. Better to simply take the 5-point now
when you have the chance.

JUL-15-2023 HOLDING GAME: LEAVE ANCHOR OR NOT?

Jul 15, 2023 | Backgammon Problems: Holding Game
Cash game, center cube.

White to play 5-2.

Here we have a position from the tail end of a mutual holding game. These positions typically arise as
follows:

> Both sides make an advanced anchor in the opening.

> Both sides bring down some builders from the midpoint and make a few blockading points.

Neither side ever rolls a big double that would allow it to escape the back men safely.
>Both sides slowly dismantle their blocking points and build inner board points behind the opponent’s
anchor.

> Crunch time! Both sides start to face tricky decisions about when to leave the anchor.

In this position we’ve reached crunch time. White has a small lead in the race (99 to 105 before the roll), but
it’s not hugely significant. If he runs with 21/14, Black can attack the checker he leaves behind on the 21-
point. If he doesn’t run, he has to either dismantle his last blocking point (9/4 9/7) or kill some builders in his
inner board (6/1 3/1 or 6/1 4/2). At crunch time, you’re usually faced with a bunch of unappealing choices,
and you’re looking for the least-bad play. It’s dirty work, but you have to do it.

Let’s list a few general guidelines for this sort of position, and see if they point us in any clear direction.
Sometimes they do, but often they don’t.

(1) If you can escape your back checkers cleanly, do it. This is the easiest case. If White rolled 6-5, for instance,
it’s massively correct to play 21/15 21/16. Nothing else is close.
(2) Being way ahead in the race is an argument for running. This is a pretty obvious point, but you need to be way
ahead for this point to matter much. Here White will lead by 13 pips if he runs – not enough to be decisive.
(3) The better your opponent’s attacking position, the more you want to keep the anchor as long as you can. The is
usually the crucial factor. A “bad” attacking position has stacked points or a weak inner board with blots. A
“good” attacking position has many pointing numbers plus an absence of inner board points. Here Black’s
attacking position is very good. If White runs, Black has 10 immediate pointing numbers (4-3, 4-1, 3-1, 4-4, 3-
3, 2-2, and 1-1) plus three more hits in the outfield (6-4 and 5-5). In addition, all the rest of his ones, threes,
and fours hit loose, putting White in an immediately critical position. Black’s only bad numbers are 6-5, 6-2,
and 5-2, and even these aren’t disasters.
(4) Having useful waiting moves is a strong argument for staying. What makes this a good problem is that White is
actually out of useful waiting moves. If he doesn’t run, he’s got to either kill checkers or break his last outfield
point, leaving a shot.
(5) If the only alternative is breaking your home board, running is likely to be right. This idea is important but
doesn’t come into play here.
(6) When in doubt, keep the anchor. If running is a mistake, it’s liable to be a big mistake. Staying, however, is
rarely a big error.
The key consideration here is (3). Black’s attacking structure is ideal. He has no stacks and no blots in his
inner board. But if White doesn’t expose himself this turn, Black will almost certainly have to weaken his
structure in some way next turn, after which White can run to better effect. For now, we have to discard
21/14.

We also have to discard 9/4 9/7. The 9-point is a great asset, leaving a blot is a bad idea, and leaving a blot
exposed to a deuce is especially bad since deuces don’t play well for Black on his side.

With those two plays out of the way, we’re reduced to 6/1 3/1 or 6/1 4/2. Here 4/2 is the right deuce, leaving
the 3-point slotted. This gives White a chance to make a 5-point board with a subsequent six, and a stronger
board will be a big asset in the later stages of this game.

A final point in favor of our play is that it holds off the cube! Black has a strong double after 21/14 (but it’s still
a take), a slightly correct double after 9/4 9/7, and no double after either 6/1 3/1 or 6/1 4/2.

JUL-15-2023 HOLDING GAME: LEAVE ANCHOR OR NOT?

Jul 15, 2023 | Backgammon Problems: Holding Game
Cash game, center cube.

White to play 5-2.

Here we have a position from the tail end of a mutual holding game. These positions
typically arise as follows:

> Both sides make an advanced anchor in the opening.

> Both sides bring down some builders from the midpoint and make a few blockading
points.
Neither side ever rolls a big double that would allow it to escape the back men safely.
>Both sides slowly dismantle their blocking points and build inner board points
behind the opponent’s anchor.

> Crunch time! Both sides start to face tricky decisions about when to leave the
anchor.

In this position we’ve reached crunch time. White has a small lead in the race (99 to
105 before the roll), but it’s not hugely significant. If he runs with 21/14, Black can
attack the checker he leaves behind on the 21-point. If he doesn’t run, he has to either
dismantle his last blocking point (9/4 9/7) or kill some builders in his inner board (6/1
3/1 or 6/1 4/2). At crunch time, you’re usually faced with a bunch of unappealing
choices, and you’re looking for the least-bad play. It’s dirty work, but you have to do it.

Let’s list a few general guidelines for this sort of position, and see if they point us in
any clear direction. Sometimes they do, but often they don’t.

(1) If you can escape your back checkers cleanly, do it. This is the easiest case. If White
rolled 6-5, for instance, it’s massively correct to play 21/15 21/16. Nothing else is close.
(2) Being way ahead in the race is an argument for running. This is a pretty obvious
point, but you need to be way ahead for this point to matter much. Here White will
lead by 13 pips if he runs – not enough to be decisive.
(3) The better your opponent’s attacking position, the more you want to keep the
anchor as long as you can. The is usually the crucial factor. A “bad” attacking position
has stacked points or a weak inner board with blots. A “good” attacking position has
many pointing numbers plus an absence of inner board points. Here Black’s attacking
position is very good. If White runs, Black has 10 immediate pointing numbers (4-3, 4-
1, 3-1, 4-4, 3-3, 2-2, and 1-1) plus three more hits in the outfield (6-4 and 5-5). In
addition, all the rest of his ones, threes, and fours hit loose, putting White in an
immediately critical position. Black’s only bad numbers are 6-5, 6-2, and 5-2, and even
these aren’t disasters.
(4) Having useful waiting moves is a strong argument for staying. What makes this a
good problem is that White is actually out of useful waiting moves. If he doesn’t run,
he’s got to either kill checkers or break his last outfield point, leaving a shot.
(5) If the only alternative is breaking your home board, running is likely to be
right. This idea is important but doesn’t come into play here.
(6) When in doubt, keep the anchor. If running is a mistake, it’s liable to be a big
mistake. Staying, however, is rarely a big error.
The key consideration here is (3). Black’s attacking structure is ideal. He has no stacks
and no blots in his inner board. But if White doesn’t expose himself this turn, Black
will almost certainly have to weaken his structure in some way next turn, after which
White can run to better effect. For now, we have to discard 21/14.
We also have to discard 9/4 9/7. The 9-point is a great asset, leaving a blot is a bad
idea, and leaving a blot exposed to a deuce is especially bad since deuces don’t play
well for Black on his side.

With those two plays out of the way, we’re reduced to 6/1 3/1 or 6/1 4/2. Here 4/2 is
the right deuce, leaving the 3-point slotted. This gives White a chance to make a 5-
point board with a subsequent six, and a stronger board will be a big asset in the later
stages of this game.

A final point in favor of our play is that it holds off the cube! Black has a strong double
after 21/14 (but it’s still a take), a slightly correct double after 9/4 9/7, and no double
after either 6/1 3/1 or 6/1 4/2.

AUG-01-2023 || SPLIT TO THE 18-POINT OR SOMETHING ELSE?

Aug 1, 2023 | Backgammon Problems: Early Game
Cash game, center cube.

White to play 6-3.

This position shows one of the most commonly misplayed early game situations.
White opened with a 43 and made the building play, 13/9 13/10. It’s the most
aggressive choice for an opening 43, designed to make a prime quickly and create a
complicated position. Black responded with a 44, making his 9-point and electing to
make an advanced anchor rather than hit. (Hitting is also very reasonable.) Now White
has a 6-3 to play.

White’s two blots are under attack, and he can deal with the problem in a few obvious
ways. Let’s look at their merits and demerits.

Play (A): Make the bar with 13/7 10/7. This play cleans up one blot while making the
bar-point. While not a blunder, it’s also not a play to get excited about. Once your
opponent has moved up to the 5-point anchor, the bar point doesn’t have much
value. It doesn’t give you the strength of an inner board point, and it doesn’t really
have much blocking value. In addition, it leaves the midpoint stripped, which is usually
a nagging weakness early in the game.
Play (B): Make the 3-point with 9/3 6/3. Compared to the bar-point, this play has a few
advantages. It makes an inner-board point, it unstacks the 6-point, and it leaves a
spare on the midpoint. However, the 3-point isn’t that strong at this stage, and White
still doesn’t have much of a game.
Play (C): Make the 10-point with 13/10 9/3. This is a better plan than the first two since
the 10-point has more blocking value. Although we haven’t left a blot, that’s not a big
deal. Black would have to break his great anchor to hit anything, so a blot would
represent a very small risk.
If these three plays were our only choices, we’d go with Play C. At this point, however,
we need to step back and look at the position as a whole. So far we’ve just been
focused on cleaning up our two blots in some way. Now let’s look at the position with
fresh eyes and see what’s really going on.

Black has both a great defensive anchor and a good building position. If we make one
of the plays above, next turn almost all Black’s rolls will make a good point on his side
of the board – either the 5-point, 4-point, bar-point, or 3-point. (Only 5-1 and 3-2 miss
altogether, while 6-4 at least makes the 2-point.) After Black makes a new point, we’re
going to have to get our back men moving before they get blocked in any further.
Maybe the dice will let us do that, and maybe they won’t. But even if they do, we’ll be
running at a time when Black’s game is even stronger than it is right now.

If we need to move our back men quickly (and we do) then we’re much better off
moving them now, while we can and before Black has any home board. The right idea
is therefore 24/18 13/10! This prepares to make a great anchor and covers one of our
blots, while ensuring that if Black hits our checker on the 18-point, he can’t also make
an inner-board point without throwing a perfecta. Although the play looks loose, since
Black can hit somewhere with almost every number, it’s hard for Black to make real
progress with such a weak inner board.

—–
The first commercial neural net to make an appearance on the backgammon scene
was Jellyfish, in 1994. When players started practicing against Jellyfish, one of the first
things they noticed was that it was almost impossible to pin Jellyfish behind a prime or
back in an ace-point game. Those were standard game plans in master play, but you
could play an entire session against Jellyfish without ever seeing those positions arise
(unless you were the one stuck in an ace-point game!) The reason were plays like
24/18 13/10. Jellyfish had a better sense than the players of that era of the importance
of splitting, even into apparently strong threats.
Here’s a simple idea to take away from this position: When your opponent makes a
strong advanced anchor quickly, you need to split more than ever and try to equalize
with an anchor of your own, even if the split seems to involve some risk.

AUG-15-2023 || DOUBLING BLITZES

Aug 15, 2023 | Backgammon Problems: Blitzes
Cash game, center cube.

Should White double? If he doubles, should Black take or drop?

We’re in the early stages of the game and White is contemplating a double. Some time
ago Joe Sylvester developed a rule for evaluating early doubles. Sylvester advocated
looking at three aspects of the position:
(1) Positional advantage (board strength, primes)
(2) The race
(3) Threats
A solid lead in two out of three areas usually translates into a good initial double. A
lead in all three guarantees a good double and brings the take into question. Let’s
look at all three features of the position in light of Sylvester’s Law and see what we
get.
(1) Positional advantage. No one really has a priming structure yet. White has one
more home board point and one more outfield point, but Black has his 5-point. Slight
edge to White.
(2) Race. Huge edge for White, who leads in the pip count, 118 to 152.
(3) Threats. Another big edge for White, who has five crushing doubles (1-1, 2-2, 3-3, 4-
4, and 6-6) plus another six rolls that make the 4-point (6-4, 6-2, 4-2). In addition,
White can at least hit loose with most of his other numbers.
A big edge in two out of three categories certainly implies White can double. At the
same time, Black has a pretty easy take. White only has three really crushing numbers
(2-2, 4-4, and 6-6). Everything else gives Black a chance to anchor on his next turn,
with a long game in progress. And of course, Black does have his 5-point, which is a
big asset in his favor.
SEP-01-2023 || ACTION DOUBLES
Sep 1, 2023 | Backgammon Problems: Middle Game
Cash game, center cube.

Should White double? If he doubles, should Black take or drop?

This position shows a pretty interesting middle game position. Both sides have an
anchor, and some points scattered around. White, however, is on roll and shooting at
a bunch of blots. He has a total of 27 hits: all sixes, all fives, 4-3, 4-1. 3-2, and 3-3.
That’s a lot of hits, so he’s naturally thinking about doubling, and Black is probably
worrying whether or not he’ll have a take if White ships the cube.

I like to call these positions “Action Doubles”, because there’s a big equity swing when
White hits one of his shots. If he hits, Black could be forced into some sort of back
game/holding game; if he misses, Black’s blots all become builders and he’s in decent
shape.

Let’s start by evaluating the double according to Sylvester’s Law: we’ll look at the
position, the race, and the threats.

(1) Positional advantage. Both sides have an anchor, although Black’s anchor is
superior. White’s extra inner-board point is offset by the fact that it’s behind Black’s
anchor. White has the outline of a blockade, while Black is hampered by the stack on
his 6-point. Slight edge to White.
(2) The race. White leads by 12 pips, 142 to 154. Given the amount of contact in the
position, a 12-pip lead isn’t a big deal at this stage.
(3) Threats. White is shooting at three blots and most of his rolls hit. Big edge to White.
White has a big advantage in threats and small advantages in position and the race, so
the double looks pretty solid. Now let’s consider the take.

In action doubles, most of the take decision hinges on whether the defender has an
anchor or not. If he does, it’s usually a take; if not, it’s likely to be a pass. Here Black
has a very good anchor, while in addition White’s board isn’t that strong. These two
factors suggest it’s a take, and in fact that’s right. Passing here is a big blunder, costing
Black almost 0.3 points/game. The most likely sequence on the next roll is that White
hits one blot and Black then reenters, after which most of Black’s troubles have
subsided. He’s down in the race, but he’s holding a great anchor and maybe one other
point as well, while White still has to bring his men around the board.

Don’t be afraid to take just because your opponent is likely to hit a blot. If you have an
anchor, your checkers are all in play, and the game rates to go on for awhile, it’s not
likely your opponent is a 3-1 favorite yet. Take the cube and make him win the game.

Benchmark Doubling Positions

SEP 15, 2023 | BACKGAMMON PROBLEMS: BLITZES
Cash game, center cube.

Should White double? If he doubles, should Black take or drop?

A key idea in understanding the proper use of the doubling cube on a practical level is
that of the “benchmark” position. A benchmark cube situation is a position where one
of the decisions (doubling or taking) is a toss-up, while the other is completely clear.
Properly understanding a benchmark position is very useful since it unlocks the key to
many related positions. Just compare your actual position to the benchmark, spot
what the relevant differences, and you should be able to make a good cube decision
over the board. Better players are aware of hundreds of good benchmarks, so they
can make their over-the-board decisions quickly and accurately.
This position shows an excellent benchmark situation. Black started the game with a
5-1, splitting his back men, and White responded with a 4-4, making two inner-board
points. (Not best, by the way; making the 20-point and the 9-point is better, with a
more enduring positional edge.) Black then danced, and White is now contemplating a
double.
A rollout indicated that the double/no double decision was in fact just a small double.
If doubling is theoretically close, then taking is, of course, hugely correct. Dropping is a
mistake costing almost one-third of a point. (As a practical matter, this means that
doubling is mandatory, since it’s theoretically slightly and might prompt a huge
blunder on your opponent’s part.)
Once we recognize this position as a benchmark position for early blitzes where White
has made a couple of points and Black has a checker on the bar plus a blot in White’s
board, we can use it to analyze related positions. For instance, take a look at Position
A:

Position A: Should White double? Should Black take?

In this case, Black again opened with a 5-1 but this time White responded with a 5-5,
making two inner points. (The correct play in this case.) Again, White is thinking about
doubling. Let’s compare the two positions and see what we should do.
First, we note that if our benchmark position was a trivially easy take for Black, this
must be also. The two positions just aren’t different enough to swing this to a pass. So
we’re certain Black should take, and now we’ll look at the double.
This new position differs from our benchmark in two ways, one favoring White, the
other favoring Black. The factor favoring White is tactical, the factor favoring Black is
strategic.
White is favored because he has two numbers to hit Black’s last blot (sixes and fours)
instead of just one number (fives) in the benchmark position. The extra direct shot
means that White has a slightly better chance of closing Black out.
Black is favored because White’s two inner board points are deeper, and the ace-point
is in fact behind Black’s blot. As a result, when Black does anchor White will have some
checkers out of play, so his alternative game plan of priming Black isn’t nearly as
strong. In our benchmark position, all White’s checkers are still in front of Black’s blot,
so if a blitz doesn’t work, White still has chances of building a prime.
Which feature is more important? In fact, White completes a closeout less than 30% of
the time in either position, so the long-term aspects of the position matter most. In
the benchmark position, White can play quietly for the prime, taking chances only
when he rolls very well. In Position A, White has to go for the closeout, but he stands
somewhat poorly whenever Black survives. White is actually substantially worse off in
Position A, so the theoretically correct play there is no double. (The correct play over
the board against anyone but a top player is to double, for the same reason as before;
many players are afraid of blitz positions and will pass them without much thought.)

Early Doubles
OCT 1, 2023 | BACKGAMMON PROBLEMS: EARLY GAME
Cash game, center cube.

Should White double? If he doubles, should Black take or drop?

In the last post we talked about the importance of cube benchmark positions —
positions where one of the cube decisions (either doubling or taking) was perfectly
marginal, while the other was completely clear. Learning typical benchmark positions
gives us the ability to analyze a wide variety of related positions over the board with
unusual accuracy.
This position shows us another type of useful benchmark. We’re currently just four
moves into the game. The opening sequence was
White: 5-3, making the 3-point.
Black: 4-3, bringing down two builders.
White: 6-2, hitting.
Black: 6-3, dancing.
With Black on the bar and White clearly having the upper hand, White now
contemplates a double. Considering Sylvester’s three criteria for offering an initial
double, here’s how White stands:
Race: solid edge for White. His hit and Black’s fan leaves White up 25 pips, 151 to 176.
Threats: small edge for White. He’s threatening to hit Black’s other blot, but White’s
weak board means this is really just a threat to gain a little more ground in the race.
Position: Small but solid edge for White. He has a 2-point board, while Black’s board is
undeveloped. White’s extra point, however, is just the 3-point, and there’s no prime in
the immediate future. White has almost escaped one of his back checkers, another
plus.
To summarize, White has a sizeable edge only in the race, while his other edges are
small. Rollouts show that this is a small but correct double, which of course means
that the take is very clear. White’s problem is simply that a big lead in the race isn’t as
significant as one might think if the inner board is weak. The most likely sequences in
that case are ones in which Black easily makes a good anchor or exchanges of hits
occur; either of these scenarios minimizes White’s racing lead.
If you were at all tempted to drop this position as Black, just remember that the
combination of a weak board, few builders, and an anchor for Black almost always
guarantees an easy take. That’s the case here.
Once you know the value of this position in a cash game, you can easily make some
practical adjustments for tournament play. If White were trailing in a match, this
would be an easy double. If White were the better player, it would also be an easy
double, since this will be a long game and White should expect to outplay Black in the
later maneuvering.