MIT 15.

S50 LECTURE 2
Wednesday, January 16th, 2013
OUTLINE: POSTFLOP PLAY
 1st Half: Continuation Betting, Fundamental
Theorem of Poker, Flop Analysis
 2nd Half: Implied Odds, Set Mining, Bluffing
(with draws), Bluffing Epiphany 1, Bluffing
Epiphany 2
A REMINDER ABOUT ATTENDANCE...
 YOU are responsible for ensuring your
attendance is marked down each class!

 Find the Attendance Person with your name

either before class, during the break, or after
class. I won’t set aside class time for attendance.
REMINDER: LIVE TOURNAMENT
TOMORROW

 1PM, will end around 5PM if you make it until

the very end.
 Baker House Dining.
 Baker House is an Undergrad dorm.
 Google Maps it.
 The front door is locked, but if you tell the secretary
you’re here for the poker tournament, they’ll let you
in.)
ALRIGHT, LET’S TALK ABOUT SOME
POSTFLOP PLAY. NOTE POSITION NAMES.
THE RAISE SIZE IS A BIT BIGGER THAN 2.25BB, BUT
THAT’S FINE SINCE WE HAVE A COMFORTABLE 40BB
BOTH BLINDS CALL.
SB CHECKS
BB CHECKS
CHECKING TO THE PREFLOP RAISER
 This is conventional. The SB and BB, regardless
of what cards they have, will usually check to the
preflop raiser.
 Why is this?
 The SB and BB cannot really threaten to ever
have a big pair on this flop, because if they had
AA, they would’ve re-raised preflop.
 On the other hand, HJ-1 could potentially have
AA in this situation.
 So if the SB and BB bet, they leave themselves
susceptible to get raised by HJ-1, and they’ll
usually have to fold, since HJ-1 could
have/threaten AA while they can’t.
HOW BIG TO BET?
SAME “SWEET SPOT” PRINCIPLES…
 Betting small always allows your opponents to
call profitably.
 Betting big risks a lot.

 Good rule of thumb: bet half the pot on the flop.

Slightly bigger % of the pot on the turn. Even
bigger % of the pot on the river.
CONTRADICTION?
 This slightly goes against what we said last class
about being able to bet smaller on the turn
because your opponent has worse equity with
their bad hands.
 However, on the turn and river, they have the
advantage of having to call fewer streets in the
future.
 With a marginal hand, they have additional
incentive to fold to a flop bet, because you can
threaten to bet again on the turn and river. They
may just call your river bet.
 We didn’t mention this last class.
BETTING SMALL IS STRICTLY WORSE
THAN CHECKING…
“CHECK-RAISING”
 Betting small never forces your opponent to fold,
but even worse, it gives them the opportunity to
check-raise!
 You just denied yourself the chance to see a turn
card and potentially hit one of your 6 cards.
 Remember – just because they checked doesn’t
mean they have bad hands! They’re often
checking REGARDLESS of what they have, for
reasons I described earlier.
IN THIS SITUATION, BOTH BETTING 200
AND CHECKING ARE FINE PLAYS
COMPARISON
 Advantages of Betting 200:
 Don’t give some “garbage” like KJ a chance to
outdraw you
 Advantages of Checking:
 See the turn card for sure; no risk of getting check-
raised.
 When you bet, you are only called by hands that beat
you.
BUT IF WE CHANGE OUR ACE TO A KING…
COMPARISON
 Advantages of Betting 200:
 Don’t give some “garbage” like KJ a chance to
outdraw you.
 Get hands like AJ, A7 to fold!

 Advantages of Checking:
 See the turn card for sure; no risk of getting check-
raised.
 The correct play is clearly to bet 200.
NOW CHANGE OUR KING TO A QUEEN…
COMPARISON
 Advantages of Betting 200:
 Don’t give some “garbage” like KJ a chance to
outdraw you.
 Get worse hands like 55, T9, A8 to call you!

 Advantages of Checking:
 Essentially none.
 The correct play is clearly to bet 200.
FUNDAMENTAL THEOREM OF POKER
 With the top hands in your range, you should bet,
to get them to call worse (but still good) hands
 With the bottom hands in your range, you should
bet, to get them to fold better (but still weakish)
hands
 With the middle hands in your range, you should
check, because by betting you fold out all weaker
hands and keep in all stronger hands
AQ IS STILL A BIT WEAK ON THAT FLOP, SO I
SAID BETTING IS FINE. BUT SAY WITH 77, YOU
SHOULD DEFINITELY CHECK.
ANOTHER TIP: DON’T BLUFF SCARY-AS-HELL
FLOPS, EVEN IF YOU HAVE COMPLETE TRASH
DON’T TRY TO BLUFF >=3 PEOPLE, EVEN IF
THE FLOP LOOKS SAFE
CHECK-POINT
 We just learned:
 General theory of when to bet postflop.
 How big you should be betting postflop (half pot-ish).

 Now let’s look a bit at calling bets postflop…too

many people are calling with hands way too
weak!
 Unless your opponent bets extremely small
(which they should not do), you should fold
MOST of your hands to a half-pot bet.
SITUATION: EVERYONE FOLDS TO BTN,
WHO RAISES TO 125
SB FOLDS, BB CALLS 75
BB CHECKS FLOP
BTN BETS HALF-POT. IF YOU’VE GOT NO
PAIR NO DRAW, JUST FOLD…
FOLD (ACE HIGH ON SCARY BOARD)
FOLD (ACE-HIGH ON SCARY BOARD)
FOLD (BOTTOM PAIR ON 3-HEART BOARD)
FOLD (JUST A 4-OUT STRAIGHT DRAW
“GUTSHOT”)
FOLD (8-OUT STRAIGHT DRAW, BUT
THOSE OUTS ALL SUCK)
FOLD (SMALL PAIR ON SCARY BOARD)
IN THESE “FOLD” SPOTS, WHAT IF I THINK
BLUFF-RAISING WILL WORK?

 When you are bluffing on the flop, it’s usually

because you have some kind of draw, that has a
small % chance of turning into a very good hand
 In all of the above hands, we basically had
complete junk, without any draws, so we should
ALWAYS just fold
CALL (ACE-HIGH ON PAIRED BOARD)
CALL (BOTTOM PAIR ON SAFE BOARD)
CALL (SECOND PAIR ON SCARY BOARD)
CALL (SECOND PAIR ON SAFE BOARD)
CALL (GOOD PAIR)
CALL (TOP PAIR WEAK KICKER)
CALL (TOP PAIR TOP KICKER ON SCARY BOARD.)
CALL (SMALL OVERPAIR)
NOTE
 NONE of these “Call” hands are good enough to
raise!
 If you raise, you give BTN an opportunity to re-
raise all-in, and you either have to fold a good
hand, or call and have your hand not be good
enough – both terrible situations.
 By calling, you keep the pot size under control,
with your medium-strength hands.
 On a similar note, with these “call” hands, if he
keeps betting (turn + river), assuming you don’t
improve by the river, you should fold by the river!
ANOTHER NOTE
 You could argue for check-raising in some of
these Call situations, especially the ones where
your hand was more vulnerable to overcards.
 Since by just calling, you are giving your
opponent at least 6 outs to pair their hand.
 However, vs. most opponents, the advantages of
calling still outweigh the advantages of raising.
 Especially when, say in the A3 hand, an Ace
could turn, and you could win a LOT of money vs.
AK.
JUST HOW GOOD DOES MY HAND HAVE TO
BE TO RAISE!?

 A reasonable rule or thumb is: raise whenever

you have two-pair or better.
OF COURSE, THIS DOESN’T COUNT AS TWO-
PAIR…
THIS TWO-PAIR IS COMPLETE TRASH…
AS IS THIS…
RAISE (DREAM SITUATION…)
RAISE (ANOTHER 3-OF-A-KIND;
ALTHOUGH YOU COULD JUST CALL)
RAISE (NUT FLUSH…ALTHOUGH YOU COULD
JUST CALL)
RAISE (BABY FLUSH, MUST RAISE)
RAISE (STRAIGHT ON SCARY BOARD)
RAISE (TWO PAIR)
DO I REALLY NEED SUCH A GOOD HAND TO
PUT ALL 40BB IN?

 There are some situations when your one-pair

hand is good enough.
RAISE (IF YOU DIDN’T RAISE AA
PREFLOP…AGAIN YOU COULD JUST CALL THE
FLOP TOO)
RAISE (TOP PAIR TOP KICKER ON A RELATIVELY
SAFE FLOP)
RAISE (TOP PAIR PLUS GOOD FLUSH
DRAW)
WHEN YOU HAVE ONLY 25BB, ANY TOP PAIR
(OR OVERPAIR) IS USUALLY GOOD ENOUGH
RAISE TO 350 AND BE PREPARED TO GO
ALL-IN!
SAME THING! RAISE TO 350!
SAME THING AGAIN!
BREAK…
A PREFLOP SCENARIO: DO YOU CALL?
DO THE MATH
 Need to call 2BB to win 5.5BB already in the pot
 2/7.5 = 27% equity needed

 Assume he’s raising top 25 percent of hands (see

right)
 Your equity with 72o is 28%

 Enough to call!
SAME SITUATION EXCEPT YOU HAVE MORE
CHIPS…
INTRODUCING REVERSE IMPLIED ODDS
 In the first situation, we called because we were all-in
and the equity calculation (which assumes that
players are all-in) said we could call with 5.5-to-2
odds.
 In this situation, even though pot odds tell us to call,
the correct play is clearly to fold.
 The reason is because, the hand is not over the
moment you call. You still have to play the flop, turn,
and river. With a hand like 72o, it is going to be
extremely difficult to play postflop. You are often
going to fold the best hand, or put in more chips with
the worse hand, which makes your 28% equity less
relevant.
 We say that in this situation your actual odds are
worse than 5.5-to-2 due to reverse implied odds.
SAY YOU HAD A2O…
REVERSE IMPLIED ODDS ARE VERY
IMPORTANT!

 I would still fold in this situation! Even though

your equity against his range is 43%, and you
only need 27% equity to all-in profitably.
 You will often lose a lot of money when he has a
stronger ace and an ace comes.
 You will often get bluffed off a pair of deuces,
when there are 4 higher cards on the board.
 To make things worse, you are out of position the
entire hand. You have to act first on the flop,
turn, and river, which causes you to make even
more postflop mistakes.
HERE, WE ONLY HAVE 37% EQUITY
INSTEAD OF 43%, BUT I WOULD CALL.
REVERSE IMPLIED ODDS DON’T WORK
AGAINST YOU HERE

 Even though your equity is worse than with A2o,

I could call instead of fold, because you will be
able to make much better decisions with your
remaining 60,000 chips.
 You can hit a straight, and get him to put in lots
of money with a good pair.
 You can hit a flush, and get him to put in lots of
money with a good pair.
 When you hit a 9 or a 8, it’s harder to bluff you
off the hand than if you had a pair of deuces,
because there will be fewer cards on the board
higher than 9 or 8.
 Yes, you are still out of position, but whatever.
IMPLIED ODDS
 Sometimes, reverse implied odds can work in
your favor! In this situation, we say that you
have implied odds.
 This can happen when you have a hand that
plays well postflop (suited connectors, pairs), and
you are in position.
SET MINING
ANALYSIS
 You need to put in 3BB, with 5.5BB already in.
 You need 3/8.5 = 35% equity.
 However, you only have 34% equity:
 I would definitely still Call:
 You are in position.
 You can win a huge pot vs. AA on a 752 flop.
 You can win a huge pot vs. AK on a A62 flop.
 Even though you will lose the pot most of the time, you will
rarely lose a big pot.
 You will flop a deuce (flop a “set”) 1/8 of the time.
 We say that you are “set mining”.
 Note: You need a LOT of chips (effective stack size
>50BB) for this to be a good play. Even with 30BB,
it’s sketchy.
ANOTHER HAND
CALL. WE HAVE IMPLIED ODDS (AND
HAVE ENOUGH EQUITY ANYWAYS…)
BOTH BLINDS FOLD AND CO
“CONTINUATION BETS”
CALL. WE DON’T HAVE MORE THAN 50%
EQUITY TO WANT TO RAISE, AND RAISING GIVES
HIM THE OPPORTUNITY TO RE-RAISE ALL-IN.
CO BETS AGAIN, AND BIG, ON THE TURN.
ANALYSIS
 Let’s assume that CO has at least a pair of Aces when
he bets again, and bets this big. Let’s assume that we
win if and only if we hit a diamond on the river.
 We need to call 8000 to win 20000 already in the pot.
 8/28 = 29% equity is what we need
 # of diamonds left = 9. # of total cards left = 46.
 9/46 = 20% equity is what we have – not enough!
 However, I would definitely still call. Because when
you hit your flush, you actually win more than 20000:
you win 20000 + the money to go in on the river,
which could be up to another 20000.
 So we say that you call because of implied odds.
THE SAME SCENARIO WITH DIFFERENT
CARDS…
HERE, YOU DON’T REALLY HAVE IMPLIED
ODDS TO CALL

 When you do hit the 4th diamond, the board will

have 4 diamonds on it, and it will be sort of
“obvious” that you have a flush when you bet. He
will only call with a decent diamond (Td, 9d),
which he is not that likely to have. So your
“implied odds” are a lot worse.
 You’re not even drawing to the best hand. When
the board has 3 diamonds and you have a J-high
flush, you’re only beaten by the Qd or Kd with
another diamond. Here, you’re beaten by the
naked Qd or Kd.
 Also remember, on paired boards, flushes can be
beaten by full houses! (Whereas on non-paired
boards, flushes are unbeatable.)
BLUFFING WITH DRAWS
 So far, we’ve played all of our draws passively –
that is, we either fold if we don’t have the implied
odds, or call if we have the implied odds and try
to hit our flush.
 However, draws are very potent when you play
them aggressively. In fact, “bluffing” is
equivalent to “raising aggressively with a draw”.
You should VERY RARELY be bluffing (before
the river) without a draw.
EXAMPLE
RE-RAISING ALL-IN PREFLOP IS ALSO AN
ALRIGHT PLAY, BUT I’D CALL HERE.
FLOP AN 8-OUT STRAIGHT DRAW (“OPEN-
ENDED STRAIGHT DRAW”)
HE CONTINUATION BETS.
HI-YA!
WHY DID WE DO THIS INSTEAD OF CALLING
AND TRYING TO HIT OUR STRAIGHT?

 When we just call, we can put our money in when

we hit, and not put our money in when we
miss…why did we raise all-in instead with ten
high!???
 The thing is, it doesn’t matter that we have ten-
high. He is never calling our all-in with a naked
Queen high or King high or Ace high. What’s
important, is we have 8 outs (or more) against
hands he calls with, ie. hands with Jacks (or
better). We have 8 outs even if he has JJ!
 Compare this to say 65 on this flop. Even though
we have a pair, we actually have fewer outs (5
outs) against a pair of jacks, and have close to
0% equity vs. JJ.
A BLUFFING EPIPHANY
 It doesn’t matter how “good” our hand is. It only
matters how many “outs” we have against the
hands he calls our raise with.
 This is why bluffing with draws is so good!
Because draws are hands that suck (ten-high),
but have many outs against the good hands in his
range.
 On the other hand, a hand like 77 is better to call
with instead of raise, since it beats most hands in
his range, but loses badly to the ones that call our
raise.
EPIPHANY CONTINUED…
 The next time you make a bluff, instead of
thinking “how good is my hand”, count “how
many outs do I have against the good hands he
could have”?
 How you do vs. his bad hands doesn’t matter,
because he’s folding all of them. That’s why
bluffing with draws is so good. Draws do
relatively well vs. his monster hands (vs. his best
possible hand, you still have 8 outs), and
relatively poorly vs. his “bad” hands (even vs. Q3,
you are losing).
ONLY MAKE BLUFFS WITH DRAWS ON THE
FLOP! THIS IS NOT “BLUFFING”…
WE CALL PREFLOP.
CHECK TO PREFLOP RAISER…
HE “CONTINUATION BETS”, AS EXPECTED
WE CHECK-RAISE FOR NO REASON HERE?
HE CALLS…
WE BET THE TURN WITH ABSOLUTELY
NOTHING
HE CALLS
WE GO ALL-IN ON THE RIVER AS OUR LAST-
HOPE
THIS IS “OPENING YOUR WALLET AND
GIVING YOUR MONEY TO YOUR OPPONENT”

 You should never be bluffing because “you feel

like it”. All big bluffs start with a draw.
 Bluffing is much better when a scary card just
came. When the flop is Jack-high, a turned Ace
can scare a player off the Jack they called with.
When the flop is Ace-high, it’s harder to turn a
card that scares them off the Ace they called
with.
 The “safe” 3c on the river isn’t a great card to
bluff. It’s much harder to bluff someone off an
Ace on a board with an Ace, than it is to bluff
someone off a Jack on a Jack-high flop with a
turned or rivered Ace.
…THIS IS BLUFFING!
SAME
WE HAVE FLUSH DRAW, INSTEAD OF
NOTHING
SAME
SAME
SAME
WE TURN A 15-OUT DRAW
SAME
SOME NOTES
 If CO shoved, we would have odds to call his all-
in (we have 15 outs in 46 cards; just barely have
enough odds).
 Note that by check-raising flop, betting turn, we
give ourselves the chance to put all our money in
on the river without ever having to bet absurdly
big. So we give ourselves a chance to double up
without having to do weird bet sizing.
 You should usually play draws this way because
this is how you would play your good hands (say
22) on this board.
RIVER IS KC; SLIGHTLY SCARIER THAN 3C
BECAUSE WE CAN REPRESENT QT
GIVING UP A BLUFF:
3-WAY POT…
WE CHECK…PREFLOP RAISER ALSO
CHECKS!??
CO BETS
GOTCHA WITH THE CHECK-RAISE!
ANALYSIS
 We have 4 outs to hit the nuts (8’s), 3 outs to hit
a higher pair than the 10, 3 outs to hit a lower
pair than the 10
 Furthermore, we have lots of back-door draws…

 If we turn a heart, now we have a flush draw

 If we turn a Queen, we have an 8-out straight

draw. If we turn a King, we ALSO have an 8-out
straight draw (“double-gutter”)!
 Notice that we can hit combinations of these
cards. Eg. Qh. This is what makes back-door
draws so relevant.
HJ-1 GETS OUT OF THE WAY
CO CALLS OUR FLOP CHECK-RAISE
TURN IS THE WORST POSSIBLE CARD…
ANALYSIS
 This card does not help us at all.
 Furthermore, this card is very “safe”. It doesn’t
really put his pair of Tens, or pair of Queens, or
whatever, in jeopardy. If he called with a 7 on
the flop, he now improved to 3-of-a-kind.
 A huge issue – we cannot have a 7 here! With a
7, we’d just call the flop, by the principle of “call
medium hands, raise strong hands and draws,
fold everything else”.
 We stop our bluff here. He’s not going to fold
much if he knows we can’t have a 7.
CHECK…
AND FOLD.
BLUFFING EPIPHANY 2
 Other than counting how many outs we have, it’s
important to analyze what we are
representing.
 When a 7 comes and we cannot represent a 7 by
our flop play, this is a bad spot to bluff.
 An Ace-turn would be better to bluff because it is
scary; also we can represent AJcc, A8dd, etc.
 A 6-turn would be alright to bluff too because we
can represent 98.
 When you were bluffing (with a draw) and a
different draw completes, this is usually a
good opportunity to bluff.
SUMMARY: POSTFLOP PLAY
 1st Half: Continuation Betting, Fundamental
Theorem of Poker, Flop Analysis
 2nd Half: Implied Odds, Set Mining, Bluffing
(with draws), Bluffing Epiphany 1, Bluffing
Epiphany 2