Developing counting skills

Ever wonder why good bridge players seem to be able to

see through the backs of your cards? Why they are so
successful in finding the right lead, locating missing
honors, guessing the distribution of their opponents’ cards?
The answer is that they are usually not guessing. Whether
they’re defending or declaring, good players are constantly
gathering clues from the bidding and play and using them
to make logical assumptions about the location of the
unseen cards.

This exercise – some call it a talent -- is often called card reading, and it’s a skill that
even beginners can develop. It involves determining the overall layout – the length
and strength (honor holdings) of each suit in each of the two hidden hands. The first
and most important step in card reading is counting the hand, which focuses on
figuring out how many cards each player holds in each suit.

Counting one suit

At its most basic level, counting involves keeping track of the cards your opponents
play as you’re leading one suit. If you're declaring a suit contract, you use this simple
count when you’re drawing trumps. If you’re declaring a notrump contract, the first
suit you count is the usually one that offers you the greatest number of potential tricks.
This is probably your longest fit, and the suit you lead first.

As declarer, there are two main techniques you can use to keep count of the cards
remaining in a suit:
(1) Count up from the number of cards you and dummy hold in the suit. If
you have a total of 8 cards in a suit in your hand and dummy, you would start
your count at 8 and then mentally count up to 13 as the opponents play their
cards in the suit. If both opponents follow to the first lead of the suit, you would
count 9-10, then 11-12 on the next trick. Subtracting the last number from 13
will tell you how many cards the opponents still hold in the suit.
(2) Count down from the number of cards that are missing. With an 8-card
fit, you would start your count at 5 and then mentally count down to 0. If both
 opponents follow to your first lead of the suit, you would count 5-4. The next
number in the sequence is the number of cards the opponents still hold.

Most players find #1 the easiest, but it doesn’t really matter which approach you use.
Anything you're comfortable with will work fine.

You can use the same counting technique as a defender, with only minor variations.
Start your count with the number of cards you and dummy hold in the critical suit. In
some cases, you'll already know how many cards partner holds in that suit (from his
lead or from the bidding), so you’ll have a full count on the suit before any cards are
even played.

Counting two or more suits

Once you master counting one suit, you’ll want to move on to figuring the distribution
of two or more suits. To do this successfully, you need:

 The ability to count to 13 at least twice (4 times, if possible).

 Memory skills, which can be developed with practice. (See Developing your
Card Sense for tips on developing your bridge memory.)
 A basic knowledge of the meanings of bids, leads and defensive signals.
 Technical skills – knowing how to use “discovery plays” and other techniques
that help you collect clues about each player’s distribution.
 Concentration. You have to put some energy into counting. Pay attention to
every trick and modify your picture of the unseen hands as you collect new
clues.

Collecting information
From the bidding:
Whether you're defending or declaring, use what you know from the bidding to
come up with an initial picture or one or both opponents' hands. You can start with
very simple assumptions, such as the minimum length promised by an opening bid or
response. If an opponent opens 1H, for example, you can "see" at least five of his 13
cards. If that opponent makes subsequent bids in the auction, you'll learn more about
his other 8 cards and you can often build a fairly accurate -- or sometimes perfect --
picture of his hand pattern.
You can also use the bidding to determine what a player does not hold in a suit, which
will lead you to conclusions about his length in other suits and, in some cases, his
partner's length in a suit. For example:

 If an opponent opens 1D and then does not support his partner's major-suit
response, it's guaranteed that opener has 4+ diamonds (because the only time he
would open 1D with a 3-card diamond suit is when his distribution is exactly 4-
4-3-2).
 If the opponents' auction goes 1H-1S-1NT, you'll be able to narrow down your
picture of opener's hand to one of three patterns: 2-5-3-3 or 3-5-3-2 or 3-5-2-3.
This conclusion is based on three logical assumptions:
(1) Opener showed a balanced hand with his 1NT rebid, but he did not raise
his partner's 1S response (so he has exactly 2 or 3 spades);
(2) He did not rebid his heart suit (so he holds exactly 5 hearts); and
(3) He did not show a second 4+-card suit (so he has at most 3 cards in each
minor).

Before you lead or make a critical play during the hand, try to process everything you
know from the bidding. Count one hand at a time, and keep your focus on the number
13. Mentally repeat each fact you've learned about that hand and ask yourself what
logical conclusion you can make from it. Then apply what you know to the other
unseen hands. Your thought process may go something like:
"Declarer opened 1S and then bid clubs twice, so he has 10 cards in those two
suits. That gives him 3 cards in the red suits. If he's 2-1 in those suits, that means my
partner has ... . If he's 3-0, then my partner has ...".

From the opening lead:

The opening lead will sometimes pinpoint the leader's exact length in the suit. If
it's a notrump contract, for example, and your partner or an opponent leads the 2 of
spades (or the lowest spot card), you'll know he has exactly 4 spades (assuming 4th-
best leads). The opening lead can also tell you something about the leader's holding in
other suits. A defender will usually choose his longer, stronger suit for an opening
lead to a notrump contract, so if there are other unbid suits, you can figure that the
leader's holdings in those suits are shorter (and/or weaker) than the suit he led.

Other leads can suggest:

Shortness in a suit -- a high spot-card lead to a trump contract, for example.
A specific honor holding -- the lead of a queen from a QJ holding.
The lack of an honor combination -- a lead of a low card (especially to a suit
contract) usually suggests that the leader does not hold touching honors (AK, KQ, QJ,
J10).
From the play:
As each trick is played, look for evidence and clues that will help you refine your
picture of the hand (or hands) you're counting. Many of these are obvious, such as
when a player shows out of a suit. Others are more subtle and require you to make
negative inferences -- why declarer isn't leading hearts, why an opponent didn't return
his partner's suit, why he's pitching clubs instead of spades.

Watch the defenders' count and attitude signals. They will be signaling each other
about their length and honor holdings in specific suits, and you can use this
information to count their hands.

Discovery plays: If you're declaring and you have an important guess to make in one
suit, you may be able to collect extra information by using a discovery play before
you attack the critical suit. A discovery play involves leading another suit (cashing its
high cards or trumping its low cards) and keeping track of how many cards each
opponent holds in that suit. This will help you complete your picture of the
opponents’ length in other suits and lead you to a more informed decision about how
to play the problem suit. See "At the Table" below for an example of how to use a
discovery play.

General tips for counting:

 Memorize the common patterns of the 13 cards in a suit -- 4432, 4333,
4441, 5332, 5431, 6322, 7321, etc. (Note that all the patterns of four
numbers fall into one of two even-odd combinations: three even numbers and
one odd, or three odds and one even.) Drill yourself on the patterns and become
so familiar with them that you won't even have to think once you get a partial
count. If you discover that each opponent has 4 cards in a suit and you hold 2
cards, you won't need to do any arithmetic to know that partner holds 3. The
4432 pattern will instantly pop into your head.
 Concentrate on how the unseen cards divide. Once you become adept at
recognizing the common patterns, start thinking not just about the number of
outstanding cards in a suit, but about how they might break. If your hand and
dummy have 8 total cards in a suit, try to focus on the possible divisions of the
5 missing cards. With practice, it will become second nature for you to go
beyond thinking "5" and start thinking "3-2, 4-1, 5-0".
 Memorize the original layout. Whether you're declaring or defending, study
the dummy at trick one and create a mental picture of its distribution. Commit
it to memory by repeating the pattern in your head (for example: 3-5-3-2, or 35-
 32). Do the same with your own hand. Later in the play, if you can't remember
how many cards have been played in a suit, you can often reconstruct the play
-- and figure out how many times the suit has been led -- by recalling your
mental picture of the number of cards you and dummy originally held in the
suit.
 Mentally review the bidding before you play to the first trick. If possible,
come up with a picture of each player's general hand pattern and high-card
strength. Consider not just what the hidden hands actually bid, but what they
did not bid.
 Focus your count on just one unseen hand. The easiest hand to count will
usually be the player who made the most bids during the auction, or who made
the opening lead. Use what you know about that hand to figure the distribution
of the other hidden hand.
 Consider the skill of your opponents. The more experienced they are, the
more reliable their bidding and carding will be ... and the easier it will be for
you to make accurate assumptions about their hands. Popular bridge author
Eddie Kantar observed, "A madman's hand is particularly hard to count, but
he's usually in the wrong contract, which evens things out."
 Practice, practice, practice. It will take time and lots of practice before you
can process all the information available and make the right conclusions. You
can speed your progress by making a concentrated effort to count at least one or
two suits on every deal you play, even on those where it appears you can't
affect the result. The more hands you play and the more suits you count, the
more adept your brain will become at remembering the cards.
 But ... don't overload your neurons. Early in the play, try to decide which
suits are critical and concentrate on counting just those suits. If you're declarer,
your count will usually be focused on your longer fits -- the one or two suits
where you and dummy have the most cards. If you're a defender, try to start
your count with the suit you or partner led, then move on to figuring the
distribution of one of the declaring side's longer fits.

Tips for declarers:

 Study the opening lead. Try to make some conclusions about the opening
lead. Does the card led suggest length or shortness in the suit? Does it pinpoint
the leader’s exact length (and therefore his partner's length)? Does it show an
honor combination or the lack of one? What does it tell you about the leader’s
possible length or honor holdings in other suits?
 Play on one suit at a time. Once you begin drawing trumps or establishing a
suit, stick with that suit. If you have to lose a trick, resume leading and
counting the critical suit as soon as soon as you regain the lead. Resist the
 temptation to cash high cards in other suits unless you have a clear purpose in
doing so (you need them for entries, for example). When you're done cashing
tricks in the first suit you’re counting, move on to the next suit and start a new
count.
 Watch the defenders’ count and attitude signals. Be aware, however, that
you can’t trust these implicitly. If an opponent thinks a signal will be of more
help to you than to his partner, he may not give an accurate signal, especially
late in the play.
 If possible, delay your important decisions. Collect all the information you
can about the defenders' distributions before you decide how to attack a critical
suit. Run your long suit or cash a few extra trumps (if you can do so safely) and
see what you can learn from the opponents' discards. Use discovery plays to get
a count on side suits. If you have tricks to lose, consider giving the defenders
the lead to see if they'll provide you with a discovery play.
 Play the odds. If, for example, you have a two-way guess for the location of a
queen, use your count in the suit to decide which way to finesse. If you
determine from the bidding or play that one opponent is likely to have more
length in the suit, finesse that opponent for the missing queen. (See "At the
Table" below for an example of this situation.)

Tips for defenders:

 Watch partner's signals. They tell you about his length and possible high-card
holdings in key suits.
 Give partner good signals so he can count out the hand, too. Use your
judgment here, though. Some signals help declarer more than they help your
partner, so it’s sometimes right to withhold a count signal if you think it will
tell declarer how to play a suit.
 Find a time to add up what you know. Think while declarer or partner is
thinking or when it's your lead. If possible, avoid long thought when it’s your
turn to follow suit. Make your decisions early and be ready to follow smoothly
when declarer or dummy leads.
 Beware of falsecards -- especially those that won't fool declarer, but will fool
partner. If you hold QJ2 of a suit and play the 2 and then the queen when
declarer cashes the ace-king, you’ll lead partner to believe that your original
holding was Q2. If he’s trying to count the hand, this clue will lead him astray.

Tips for dummy (yes, dummy):

Your stint as dummy is the perfect time to practice your counting skills. Even though
you can see only your own hand, you can work on developing a mental picture of the
distribution in the other three hands. Analyze the bidding and opening lead and add up
what you know about each player’s suit length. Then watch the played tricks and the
defenders' signals and try counting the number of cards each player holds in each suit.
This is great practice because there's no pressure; if you make any errors, they're
"free", and no one will know.

At the Table
Here's an example of how to use a simple inferential count to make an intelligent
guess:

RHO wins the heart ace and returns the 9. You win the king and LHO
follows with the heart 2.

Your only hope for 9 tricks is to score 4 diamonds, and that will
Dummy: K6
require you to find the queen. You can finesse either opponent for that
J84
card. Is it a pure guess, or do you have a clue that will help you make
K1084
the decision?
K653
There's no discovery play available here, since cashing your other
You: A643
tricks first is unlikely to give you any helpful information. All you
K7
have to go on is your count in the heart suit, which you've already
AJ93
determined by watching the cards played to the first two tricks.
A42
Here, LHO led the heart 3 and then followed with the 2, so he's shown
You Partner
that he holds 5 hearts (Qxx32). RHO therefore has 3 hearts (A9x).
1NT 3NT
When you're in doubt about the location of a specific card, the odds
Opening lead: Heart 3
favor it being in the hand that has the most "room" to hold that card.
Your count in the heart suit tells you there are 8 chances that LHO has
the diamond queen (he had 5 hearts, so has 8 unknown cards) and 10
chances that RHO has the queen (he had 3 hearts, so has 10 unknown
cards). So your best play is to cash the diamond king and lead the 10,
planning to finesse RHO for the diamond queen.
Here's a defensive quiz where you can use the opening lead and the bidding to come
up with the right play:

Dummy (RHO):
K9765 Opening lead: 2 of clubs
Q7
J95 Declarer plays low from dummy and you win the club ace. Now is the
J64 time to add up all the evidence. It's often right to return the suit partner
led, but you'll change your mind if you stop to count out the hand. Try to
You: J1082 answer these questions before you make your decision:
A65 How many clubs does declarer hold?
A742 How many diamonds?
A3 How many hearts?
How many spades?
LHO RHO How many points does partner have?
1D 1S Which card will you lead at trick two?
1NT Pass

Focus your count on declarer's hand.

How many clubs does he hold? Exactly 4 (because the lead shows that partner
holds exactly 4 clubs).
How many diamonds? At least 4 (because he didn't raise spades).
How many hearts? Exactly 4. Declarer didn't open 1H, so he has fewer than 5
hearts. It appears that partner also has fewer than 5 hearts, since he surely would have
led a 5-card heart suit rather than a 4-card club suit. The 8 hearts that you can't see
must therefore be divided 4-4 in partner's and declarer's hands. (Note that you also
have a clue that partner doesn't hold a heart honor. Since partner is 4-4 in hearts and
clubs and he chose clubs for his opening lead, his clubs are probably stronger than his
hearts.)
How many spades? You've counted declarer's hand to be 4-4-4 in the other three
suits, so that leaves him with one spade. That means partner has three spades with at
least one honor.
Note that without a count, you probably wouldn't have expected opener to have a
singleton for his 1NT rebid. Many players, however, prefer this approach when they
have a 1-4-4-4 pattern. The alternative with this hand is to bid 2C (showing a minor
two-suiter), which is also a distortion.

You can also add up the high-card points here. Declarer's minimum notrump rebid
tells you he has 12 to 14 points. (If he had 15 pts., he would have opened a 15-17
1NT.) Add declarer's points to the 20 total points in your hand and dummy, and you
can determine that partner holds from 6 to 8 high-card points.

Did you find the killing shift? It's right to lead a low spade at trick two. Partner wins
the spade ace and returns a spade for down one. Your side will eventually score seven
tricks -- three spades, the AK of clubs and the two red aces.
Declarer's hand was: Q KJ109 KQ106 Q1085
Partner's hand was: A43 8432 83 K972

Here's a deal where you can use a discovery play to collect extra information:

Opening lead: Jack of hearts

Dummy: AQ9
765 RHO overtakes the heart jack and cashes the AKQ. LHO
A432 pitches two small clubs on the second and third hearts. RHO
K102 exits with a spade and you cash the AKQ. RHO follows with
the J74 of spades. LHO follows with the 32 and pitches a
You: K10865 small club on the third spade.
842
K7 Your contract depends on guessing the location of the club
AJ5 queen. With nothing else to go on, you might finesse RHO for
the queen just because he opened the bidding and is therefore
RHO You LHO more likely to hold the missing high-card points. If you're
Partner counting the opponents' cards, though, you might come to a
1H 1S Pass 4S different conclusion. And if you use a simple discovery play,
you may be able to guarantee three club winners.

Your thought process:

Focus your count on opener (RHO).
So far, you know 9 of his 13 cards -- 6 hearts and 3 spades.
You've seen 10 of his high-card points -- the AKQ of hearts and the jack of spades.
Did he need the club queen to open the bidding? No. He could hold the diamond
queen or QJ, which would give him 12 or 13 points.

Extra insurance -- the discovery play:

Before you make the critical play in the club suit, play on diamonds to gather more
information about RHO's distribution. Cash the king and ace and trump one of
dummy's small diamonds. RHO will follow to all three diamonds, so you now have all
the information you need to take three sure club tricks. You may also see more of
RHO's high-card points on the diamond tricks, but the most important information
here is his distribution.
You now know 12 of RHO's 13 cards -- 3 spades, 6 hearts and at least 3 diamonds.
That leaves him with a void or singleton in clubs, so you have a "marked" finesse.
Cash the club ace, just in case RHO has the singleton queen. If the queen doesn't fall,
finesse LHO for his known queen by leading a low club to dummy's 10.

Additional practice
Read bridge books.

How to Read Your Opponents' Cards by Mike Lawrence

Counting at Bridge, an interactive computer program by Mike Lawrence

Countdown to Winning Bridge by Tim Bourke and Marc Smith.

Count, count, count

The one that got away