2. Introduction to Postflop Play


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visit MIT OpenCourseWare at ocw.mit.edu. WILL MA: All right, guys. I’m going to get started. If you haven’t done attendance
yet, you can do it at the break or afterwards. I think it will work. OK, so just a few
quick announcements. So, homework 1 is
posted and due Friday. I have it up on here. Are there any questions
about homework 1, or anything about the procedure? So, Lee Marie’s going to
have office hours shortly after class, 4:30
to 5:30 in E51-145. So if you have any questions,
you can ask her as well. Or you can ask me
now if you think they’re applicable
to the general class. OK, cool. So, OK, so I’m going
to proceed then. So I hope– so
most of you I think have started playing in
the online tournaments. I hope you guys–
if you haven’t, I hope you plan on starting soon. Yeah, I hope they’ve
been fun so far. OK, so today, I’m going to
focus more specifically on poker itself. I know last class, I talked
about a lot of general concepts on decision making
and how to think about exploiting your opponent
versus playing within a Nash equilibrium way. Today, I’m going to
focus mostly on poker, and try to give a
lot of hand examples. And I’m going to
introduce post-flop play, which I didn’t really
talk about last time– so basically, what happens
after you see the flop. OK, so I’m going to just
start with an example hand. So, we get ace-queen
offsuit in hijack minus 1, so I think I called it
lojack in the earlier slide– in last class, but basically,
it’s four away from the button. So it’s how many people– the thing that matters is how
many people behind have cards and could be left to act. So we raise a bit bigger
than 2.25 big blinds, but I’m not going to
nitpick that for now. So, we’re a bit
deeper stacked, so we want to build a bigger
pot because we think we have an advantage, I guess. OK, so, it’s folded
to both blinds. And both blinds call OK? So, the flop comes on 9-8-deuce. So we sort of missed the flop. And the small blind checks,
and the big blind checks. OK, so what happened
is clear so far? OK, so now, we have a
decision here, essentially. So first, I want to talk
about checking to the preflop aggressor. So this is sort of– this is
sort of a conventional way to play. So, they both checked, so we
were the preflop aggressor. So in this case, I mean
by preflop aggressor, the person who put in
the last raise preflop. And the reason why
this is significant is because in some sense, we
have a stronger range of hands than they do because we
could potentially have pocket aces, which is the best hand. And it’s going to be good
hand on pretty much any flop. Whereas it’s much harder– it’s
much more unlikely for them to have pocket aces, because
if they had pocket aces, it would be a good play,
and a tempting play to re-raise preflop. So basically,
they’re sort of just recognizing the fact
that on average, we’re going to have a
better hand than them. So they’re going
to check us and let us bet because in general,
on average, they would prefer if the pot was smaller. And we would prefer
if the pot was bigger because our range is better. Yeah, so they both check to us. And right, so, like let’s say
they had a pretty good hand. Like, let’s say small blind
had 10, 9 suited or something, which is the top pair– so the
highest pair on this board. That’s a pretty good hand. But that’s still a hand
that loses to pocket aces. And there’s still the risk
if he bets out with 10, 9, we could just raise. And then he has to
be worried, you know, do we have pocket aces? There’s basically always going
to be this worry of pocket aces and pocket kings,
and just big pairs that he has to worry about that
we have to worry about less. Occasionally, someone
there probably should slow play pocket
aces preflop and just call. But most of the time, it will
be a better idea for them to re-raise to get
more money in preflop. So that’s why they
both check to us. So now, we have the opportunity
to bet or to check back. So, let me first
check what– how big to bet if we decide to bet. So here, we bet 200 into 375,
which is about half the pot. And so, between betting
big and betting small, it’s sort of the same principles
I talked about last class between raising big and
raising small preflop. So the advantage
of betting small– so, the disadvantage
of betting small is that you give your
opponent better odds to call. So like let’s say they have, I
don’t know, like Jack, 10 here, a hand that’s losing to you. They have the better odds
to call and a cheaper price to call to see another
card to try and beat you. But on the other hand,
our hand isn’t amazing. Our hand isn’t good
here, essentially. We’ve missed the flop. We haven’t paired our hand. And if we get raised, we’re
probably going to have to fold. And the more we bet, the more
we lose when we get raised. So it’s the same
sweet spot principles. If you bet too small,
you get called too often by worse hands that just
have good odds to call. And if you get too
big, you’re just losing a lot when
you get raised. So a good rule of thumb is to
bet half the pot on the flop and then like a slightly
bigger percentage on the turn, like 60%, and then an even
bigger percentage on the river, like 70% or something. Something like that
is about reasonable. You could bet up to like
100% of the pot on the river. So I’d say just somewhere
between 50% to 100% of the pot is a good amount to bet. And the fraction should increase
as you get closer to the river. So this might seem
slightly contradictory, because what I
said last class was you were able to–
last class, I said you want to give your opponent–
you don’t want to give your opponent great odds. But in some sense, if
we get to the river, right, all the
cards have come out. There’s no more unknown cards. So either they had
the better hand or we have the better hand. But there’s going to be no
uncertainty in what cards could still come. So in some sense,
you might think it’s more intuitive to bet
smaller on the turn and river and bigger on the flop,
because on the flop, they have more
chances to outdraw us, whereas on the turn and
river, they have fewer. But let me just find the– all right, now I don’t
have to stand there. OK, so this might seem
contradictory, right? So I’m saying that bigger on
the river, but on the river, they actually have
in some sense– on the river, there is– it’s more determined whether
their hand is good or not. So why is this? Why do we want to bet bigger
on the turn than the flop, whereas on the flop, any hand
sort of has closer to 50% equity, because anything can
still happen with two cards to come? So the main reason is because
when you bet the flop, they’re not just deciding
to call your flop bet for the equity there. They also potentially have to
call a turn bet and a river bet. And essentially, this factor–
the fact that they have to, you can threaten to bet again
on the turn and bet again on the river, and they have
to call all these bets, is a bigger factor than
the fact that they have– there’s slightly better
odds to call on the flop. OK, so another important thing
to say is when I said bet between 50% to 100% of the
pot, I mean I think that’s– it’s very important to bet at
least some fraction of the pot, especially when
they’re checking you. Because in some
sense, betting small is strictly worse than checking. Like in this case, you get 50,
which I guess isn’t nothing. But imagine you bet $1 here. The issue with this is the
rules of betting safe, right, if anyone bets any
positive amount, then the guys who checked now
have a chance to check-raise. So if you’re
betting small, which is almost the same as
checking, all you’re doing is giving your
opponent a free option. You’re allowing them
the opportunity to say, OK, I couldn’t just– like if
you check, you see the turn, and the turn comes. But by betting, now they
have the opportunity– a second chance to bet. Yeah? AUDIENCE: How does this
change if you have the nuts? Should you bet? Like, you want calls
at that point, right? WILL MA: Right, right. Exactly. Yes. So, I’m going to
get to that, yes. So if you have a good
hand, yeah, you’ll bet too because you want calls. Right now, I’m just talking
about a general strategy to play with your
entire range of hands. And in general, I
guess that’s all I’m trying to encourage
people to think about poker in this class. Like instead of thinking
about what cards do I have and what cards do
my opponent have, I try to talk in terms of
what is the probability distribution over
my opponent’s hands, and what’s the probability
distribution over my hands in his eyes, essentially. So I’m just talking about
a general scenario, yeah. OK, cool. So, right. So you never want to bet
too small, basically. It’s better just to not bet. There’s no point to bet. Really, it’s not, because
you’re giving away free option. OK, so yeah. So this is what I just
said, essentially. Because remember, just because
they checked doesn’t mean they have bad hands. They’re often checking
regardless for the reasons I described earlier. OK, so in this situation
with ace-queen offsuit, I think both betting 200 and
checking are reasonable plays. And let’s analyze the advantages
and disadvantages of both. So the advantage
of betting 200 is that you don’t give some
garbage hand like king-jack a chance to outdraw you. So in this situation,
if we bet 200, probably if someone
had King, Jack, they’ll probably just fold
because it’s almost one of the worst hands
on this board. And if we bet 200, then
they’re going to fold. And then we could just
win the pot right there. If we don’t bet, maybe the
turn will come a king or a jack and they could beat us. So what’s the
advantage of checking? The advantage of
checking is we get to see the turn card for sure. We can’t get check-raised. Like right now if we
bet we get check-raised, we probably have to
fold with no pair. But if we check, we might
see a queen or an ace on the turn that
should be great. And another advantage of
checking is, in some sense, when you bet in this
spot, you’re only called by hands that beat you. You’re going to get king-jack
to fold, which is still fine, because they have six outs. But you are ahead of
them, so it’s not the end of the world to just check him. If the turn comes like a
deuce, you’re still ahead. And if it checks all
the way to showdown, like all the way
to the point where you have to flip
over your cards, you’re going to beat king-jack. Whereas when you bet,
you’re essentially getting all the hands
you’re ahead of to fold. Like if they have ace-7,
which you’re also ahead of, they’re probably going to fold. And pretty much all the
hands that beat you probably aren’t going to fold. Like, maybe someone will
fold pocket 3’s or something, but for the most part, you’re
going to get called by a 9. You’re going to
get called by an 8. So it’s this idea sort
of adverse selection. You’re getting called only
by hands that beat you, and you’re just folding
at everything else. So overall, I’d say these
about balance out and you can– I think betting or
checking are both fine. OK, so now let’s suppose
it’s the same spot. And we had king-queen. We had king-queen
instead of ace-queen. So pretend all the
action was the same. All the preflop action, the
flop action– everything was same, except just
our cards change. So in this case, if we do
the same comparison again, we’ll see that betting has
a bigger advantage now, because we can get hands like
ace-jack and ace-7 to fold. Those hands previously we
were beating with ace-queen. But now, we don’t want to risk
getting a situation where it’s checked to showdown and
everyone flips over their cards, and we lose to
ace-jack or ace-7. So I’d say in this case,
now with king-queen instead of ace-queen, betting
has a lot more advantage because we’re getting
better hands to fold. OK, and this is what
you were talking about. Yeah, what if you have the nuts? So in this case,
if– so suppose now we change our king to a queen. So we actually have
a really good hand. We have pocket queens,
which is an overpair, a pair above any card on the flop. So now, let’s look
at the advantages of betting versus checking. So now, one advantage
of betting that we never had before because we
always had bad hands is, now we can get
worse hands to call us. If they have 10-9 or ace-8
or pocket 5’s, they’re probably going to call. And we’re beating them, so we’re
just going to win more money. And the advantages of
checking is essentially none. So the correct play,
I think, is clearly to bet in this situation. So, essentially what I’m
trying to get at is– so I call this the
Fundamental Theorem of Poker. It’s sort of a made-up term. But essentially– so
one of the main things you should realize when
you’re betting postflop is that a bet basically
accomplishes one of two things. So with your good
hands, you want bet because you can get them to
call with worse, but still good hands. And we call this value betting. So with the pocket
queens, this is– what you’re doing is value
betting when you bet. And then with the bottom
hands in your range, you should bet to get them
to fold better but still pretty weak hands. So in this case, when
we had king-queen, we would be betting to
get them to fold ace-jack. So, this is called bluffing. So essentially,
the point of a bet should either be a
value bet because you have a really good hand,
or a bluff because you have a really bad hand. And you want to sort of
think in terms of that way. And if you ever find
yourself making a bet and you’re not sure whether
it’s a value bet or a bluff, then chances are you maybe
shouldn’t be betting. So with the middle
hands in your range, you should check
because if you bet, you fold out all
the weaker hands and you keep in all
the stronger hands. OK, does that make sense? So this is like the
fundamental concept in poker, essentially, that we
should try to realize. OK, so I sort of
made this diagram. So, the best hands are at
the top of the rectangles. The worse cards– the worst
hands are at the bottom. So once again, we’re thinking
in terms of our entire range of possibilities. So postflop, we
want it sort of– so that’s on the left. Postflop, we want to
bet the best hands, bluff the worst hands, and then
check things in the middle. And then preflop, basically
we fold all the bad hands and then we raise, or if
someone’s already raised, we re-raise the best
hands and we just raise the pretty good hands. I’ll talk more about preflop
playing in a future lecture. But I just wanted
to contrast this because I don’t want
someone to think, you know, if I have 7-2 offsuit
preflop, I should be bluffing. Because it’s a
different scenario. Because preflop, you’re choosing
what percentage of hands to play. And it’s strictly better to just
choose the best 30% or the best 40% instead of choosing the
best 10% and the worst 10%. OK, so going back to
this principle, with 7-7, so it’s still the
same situation. So I’m analyzing the same
situation many, many times with different cards. With 7-7, the right play
is definitely to check. Because so, with ace-queen, it’s
in a similar spot to ace-queen in that it’s also you get
called only by better hands and you mostly only
fold out worse hands. But with ace-queen, at least
there was the advantage that if they called with like
an 8 or 9, we could turn– we have more chances
to beat them. We could turn an ace or a
queen and win more money, or alternatively, we
could turn a jack which gives us a straight draw,
and try to bluff them off [INAUDIBLE] or something. Whereas with pocket 7’s,
there’s less room to play. So, I think with pocket
7’s, you should definitely check on this flop. So, OK, so some other stuff
about continuation betting on flops. I wouldn’t bluff
super scary flops. By super scary, I
essentially– mathematically, it just means there’s
a lot of uncertainty because so many
things are possible. And basically, this
happens when there’s three cards of the same suit
and they’re all connected. So whenever the board is
like this, it looks scary. It looks very coordinated. But mathematically speaking,
it’s essentially saying, anything can happen. And no one should fold if
you have anything at all. Because you know,
if you have any 10, you have a chance of
making a straight. If you have a
reasonable heart, you have a chance of making a flush. Just any hand is going to
have a reasonable chance. Same as, you know,
even if you have like an ace, like
I guess as we do, you have a chance of
turning a higher pair. So I would just check, and
basically give up on this flop. Or check, and hope you hit
an ace or a queen, I guess. And another thing is
continuation betting into too many people,
if you have nothing, it can be an advanced
play in certain situations if everyone else also recognizes
that if you’re continuation betting into five
people, you just have such a good
hand that they’re going to fold a hand as good
as say, like, pocket 8’s here. But for the most
part, in practice, I would say if the pot has
like six or seven people, I wouldn’t try to
bet on the flop with overcards to try
to get everyone to fold, because someone’s going
to have two hearts, or someone’s getting have a 7. Someone’s going to have a pair. OK, so I talked about sort of
when you want to bet postflop. So now, I’ll talk a
bit more about when you want to call bets postflop. And I’m going to try to give
a lot of different situations. So now, let’s look
at calling bets. And I think newer
players especially tend to call with hands
weaker than you need to. So the general rule of thumb
is, unless your opponent bets extremely small,
which they should not do by what I explained, you
should fold most of your hands to a half-pot bet. So in some sense, most
hands miss most flops. And when you miss,
there’s really not a reason to do anything
other than to fold. There’s a lot of tournaments. See I always play
the next tournament and get dealt and new hand
and try to have a good hand, so, OK. So now, I’m going to change
this situation up a bit. But once again, I’m going
to analyze the same betting situation over different hands. So now, it’s everyone folds
to– is folds to the button. We’re still 40 bets deep
because the blinds are 2,550 and we have– we have 2,000. And so the button
makes it 125, and we decide to call with our hand. OK, so let’s say we have
queen-9 suited in this case. And, OK, let’s say
the flop is 10-7-2. So, we check. We check as a form of respect
to the preflop raiser. And then they bet half-pot. So here this is
a situation where we’ve got no pair, no draw. I guess we have an overcard. We have an overcard
in the queen, and we can turn a pair of queens
to beat a tier of 10’s, but that’s only three
cards that help us. Basically, the correct
play is just to fold. You essentially
have nothing here. You know, you have some like,
speculative straight draws where if you hit a
jack and then an 8, like if you have two cards
that come for you, then you get a straight. But for the most part,
we’ve got nothing. We just fold. Here are some other situations
where you should just fold. So here, we have
ace-high but the board has three pretty big cards. And there’s a decent chance
he’s going to have one of them. And if he doesn’t,
he’s going to have like queen-10, or
10-9, or something with straight [INAUDIBLE],,
or some kind of straight draw with a lot of outs. So there’s just no reason
to play hands like these. So it’s totally fine if
you lose a lot of hands, as long as you win more chips
on the hands that you do win. So, just fold this. Not much reason to play. Here, you have this. This board is a
bit better for you. You have ace-9 high
on a 6-high board, but there’s a lot
of straight draws, and there is a flush draw, a
spade flush draw on this board, so I would still fold. Here, we even have
a pair, but this is an example where
I think I’d fold even though you have a pair. So we have a pair of 9’s
here which is decent, but once again,
there’s three hearts. And it’s easy for him to make
a flush or make a straight. And even if he
doesn’t, we’re going to be– we’re going to have
to check to him on the turn, check to him on the river. And then they can
bet, and then we have to decide whether
we call it or not. So, just overall, there’s a lot
of– it’s an [INAUDIBLE] play. And this is why what– I’m talking about
being out of position. So where we have to act
first on every straight, so it’s going to be tougher
to make good decisions. OK, so now, we’re getting
some better hands. But I think I would advocate
still folding these. So here, our hand is– it’s not bad. We basically got a four-out
straight draw, which is usually called a gutshot. You hit an 8 to turn a straight. And also we’ve got diamonds. If we get two diamonds in
a row, we can make a flush. But overall on this
spot, I would still fold just because
even though we’ve got four outs to our gutshot,
we’ve got no combinations– we’ve got no other
combinations to help us. Like, a 9 is essentially useless
when there’s three higher cards on the board. Turning a 9 doesn’t
help us at all. Turning a 7 doesn’t
help us at all. And furthermore, even if we
turn an 8, it’s possible. So if we turn an 8, then
queen-9 makes a better straight than us. And also, king-queen, which
already has a straight, is a better straight than us. So even when we hit
an 8, it’s not even– we’re not even 100% sure
we’re going to win the hand. And we could just put our
chips in after hitting an 8 and lose all our chips. So, I would fold this as well. A four-out gutshot
is bad unless you have other stuff to go with it. OK, so in this case, we
have a better straight draw. So in this case, we have
an eight-out straight draw. Because an 8 gives
us a straight– 8 through king. But a king also
gives us a straight. We have 9 through King. But in this case,
I would still– I would still
recommend folding just because if a king comes then– you know, we do have a
straight, but we lose to an ace. So, 10-jack-queen-king-ace
is going to just be a higher straight than our 9
through king straight, so even though we
have a lot of outs, the outs aren’t that good,
and it’s possible we just once again, we make a
second-best hand, which is the worst
possible situation in poker because you’re going
to put a lot of money in and you’re going to lose. OK, so this is another
example I would fold. Pocket 5’s on queen-jack-10. You have a small pair. You started with a small pair,
but you didn’t improve at all. The flop did not help
your hand at all. And it most likely helped
your opponent’s hand. OK, so, here’s a
question you can ask. So in all these
spots, I say fold, but what if I think
bluff-raising will work? You know, what if I think I
can get him to fold if I raise? So what I want to-
what I want to say is, when you’re
bluffing on the flop, it’s usually because you
have some kind of draw or some kind of nice
speculative hand that has a chance of
turning into a good hand. In all the examples I showed,
not only are our hands bad, there’s not that many
good cards for us, with the exception of maybe
this 7-9 hand, where if you turn an 8, it’s pretty good. But yeah, even this– even this hand, if you turn
an 8, it’s not that good, because the board is then
going to be 8-10-jack-queen. So we’re only playing with
one-card straight, which is still fairly easy to put aside. OK, so before we get to spots,
or maybe we want to raise, potentially
bluff-raise, let me just go– let’s go through
some spots where I think calling is a pretty good play. So here, I think calling
with ace-9 high on this board is reasonable. In the example where I
said you should fold, the flop was 6-5-4, and
there was a flush draw. So there were straight
draws and flush draws. In this case, the board is
paired, which really helps us because there’s just fewer
combinations of pairs that he could make. And a 3 is a pretty
small card, so it’s pretty unlikely they have a 3. So ace-9-high is
pretty good here. You have two overcards. You even have a diamond
[? back your ?] flush draw. So I would call here. OK, so we would get–
so getting better, here, this hand is even better. We have ace-3. We have bottom pair on this. Pretty safe flop. It is three different cards, and
they could have a jack or a 5, but just overall
against a range, we have tremendous equity here. So I would call. So note, when I say
call, do not raise. I’ll give you examples of
how good, roughly speaking, our hand has to be to raise. All right, so
here, I would call. The board is very scary,
but we have second pair. And I think second
pair is just– second pair with the
best kicker would be ace. So that’s definitely
good enough to call. With ace-9, I think this
would be borderline, whether you call. I think calling is
OK, but not mandatory. OK, here’s another example–
second pair on a safer board. This is a pretty good hand. I mean, if they’ve
got an ace, we’re not drawing to that many outs. But if they don’t
have an ace, they’re not drawing with that many outs. So it’s because whenever
big cards come on the flop, like an ace and a
king, in some sense, even if there’s flush and
straight draws, more of the– more of who’s going to
win has been decided. Because if you’ve
got a big pair, like if you’ve got
an ace or a king, then there’s not like an even
bigger card that can come in to try and beat you. And if you don’t have
it, then, you know, it’s like if you have 10-9,
even if you turn it’s hand, you’re not going to
outdraw an ace-7. So here, I would just call. Here, you have a pretty good
pair, pocket 8’s on 9-3-3. Obviously, you have a
very good hand here, but I just think,
in this case, where there’s no flush draws–
no straight draws, there’s not really
that much reason to raise because
it’s not like you’re going to get called by
worse hands that often that I would still only call. Even though in some sense, your
hand is very, very strong here. Like, I would expect you to have
the better hand more than 80% of the time. But the problem
is when you raise, they’re only playing
the 20% that beats you, which is hands 9’s, hands with
3’s, and pocket 10’s plus. So here, I would also
recommend calling even though we have top pair. So top pair, the highest
pair on the board. It’s a pair of
aces, which seems– you know, it seems like we have
a good hand we should raise. But once again, our other
card, which is very relevant, is very small in this case. So we’re going to
lose to ace-queen– any kind of big ace. And furthermore, there’s
not that much reason to raise because
we’re not that scared of letting them see a
turn card with, say, 10-9. Because even if he turns a 10 or
a 9, he’s not going to beat us. So, right– so, the
reason you raise is essentially to not let
your opponent see more cards and give them outs. But they don’t have that many
outs if we’re ahead of them. So I would– so this is,
you can say this is like, a way-ahead,
way-behind situation. That’s some terminology
that you might hear, which basically means you’re
either way ahead because they don’t have an ace,
or you are way behind because they’ve got ace-queen. And when you’re way
ahead or way behind, you don’t really want to be
raising because he’s just going to call you when
you’re way behind, and he’s just going to
fold when you’re way ahead. OK, so here we’re getting
some pretty good hands. Ace-jack and jack-10-9
with a flush draw. I think if you raise, it’s not– it wouldn’t be the
end of the world. The issue is I think 2,000 chips
when the blinds are only 2,550 is still a bit much to put in
your entire stack on this flop. And just because even though
you have top pair with the best kicker, there is a
lot of straights. And even if he’s– like even if let’s say they
have queen-9 of hearts– I think that’s behind of you
currently because they only have a pair of 9’s. There is just going to be
so many straight and flush outs they’re going to have that
you’re never really getting it in ahead of equity by that much. So I would just call and
see what the turn is. But that’s maybe the best– one of the examples
of the strongest hands you can have where I
would still recommend calling. In this case, we’ve
got a small overpair. But I would still call
even though, once again, we have the best hand probably
80% plus of the time. But once again, when
you raise, you’re only getting played back at
by the 20% that beats you. So, OK. Yeah, so, and notice there, when
I went through these examples, the stack size was
very important, right? So in the first class,
the important things are position, stack
size, and cards. In this case, the
position was the button. The cards– I’ve showed
you what the cards are. But the stack size–
the fact that you’re playing for potentially 2,000
chips, is very important. And if you’re playing
for fewer chips then you can risk gambling a lot
more, as I’ll show you later. OK, so another note
is you could argue for check-raising in some
of these call situations especially the ones
where your hand was more vulnerable to overcards. So let me just quickly
run through them again. So, I’ll describe what they are. So this is one of
them, because here, you could argue, OK, I want to
raise because if I call, what if he has jack-10? Then he has 6-7, right? Here, this is another example. What if they have 10-9? They can turn a 10
or 9 and beat us. Here, this is not an example. Here, I think calling
is clearly correct because the only bad
cards are like a queen, because an ace
gives you two-pair. So, there’s just
very few scary– the board is already scary and
there’s not that many overcards that can come. This is another example
because in this case, there’s actually no
scary cards in subsets. No card is– there’s
no card that you’re afraid of giving him. This is an example where
you could argue for raising. You know, you don’t want
jack-10 to see another card. That’s reasonable, yeah. Here, there’s no risk. It’s completely safe,
so I would never raise. Here, I guess there are some
bad cards, but if you raise, they can just call with your
draws anyway try to hit. So here, this is
an example where you could argue for raising to
not let them see a turn card. OK, so, yeah. These are reasonable
arguments and I think raising some
of these call hands would not be a terrible play. But I think for most of these,
the advantages of calling still outweigh the advantages
of raising, especially if your opponent is also
capable of bluffing. Because let’s say
you check-raise. So let’s say they make it 150. You make it 400. And then let’s say
they go all in. But they’re going to go all
in not only with hands that beat you, like pocket 7’s plus. They’ll also occasionally
do this with hands like ace-3 or ace-4, hands that
have an overcard in the ace, but also have a
gutshot straight draw. Like ace-3 or ace-4
can make a straight. Then you’re just in
a very tough spot. Basically if you call, you’re
not in a good situation because you’re often behind. But if you fold,
then you’re also folding to a lot
of weaker hands. So there’s just a lot
of ways for the hand to go badly if you raise
because your hand sort of– it’s too– it’s not good
enough to raise and call if they re-raise. Yet, it’s too good to sort of
waste as a check-raise bluff and just fold if
they re-raise, right? Like let’s say my play
here with pocket 6’s is to check-raise and fold
if they do anything else. But then you could argue, why
am I doing this with a hand as good as pocket 6’s? Why don’t I do this with 10-9? Because it’s going to
be a similar result most of the time. They’re going to
either fold and I’m going to win the pot with
10-9, or they’re going to raise and I’m going to have
the fold with 10-9. Occasionally, they’ll call, but
you could argue in that case, I would almost rather have 10-9
than pocket 6’s because pocket 6’s I’m going to always lose. And 10-9, who knows? I can turn a 10. So, anyway, so the
long story short is I would just
recommend just calling with most of those hands
although there’s definitely lots of arguments you
can make for raising. Yeah? AUDIENCE: I didn’t get
why we’d assume once– should re-raise if you have
the top pair, the top kicker of either because if
you give them the draws, at least once you make
the shorts bigger, then it will turn out all right. WILL MA: You’re talking
about this situation? AUDIENCE: Yeah, it is. WILL MA: Yeah, yeah. OK, yeah, that’s a good point. So, yeah, I think
that the main reason is just your overall
equity against their range is pretty low on
this board compared to an average situation if you
have top pair or top kicker. Like if the board is jack-7-2,
your equity against their range is probably something like 85%. Whereas on this
board, your equity is just overall a lot less. There’s a lot more
hands that beat you. So there’s a lot
higher probability that if you raise and call
and put all your money in, that you’re behind, basically. So there’s just a
huge risk of that. So, but yeah, I do agree. It does feel very
unsatisfying to only call and let them see those cards. But I think it’s sort
of the lesser of two evils in this situation
between putting all your money in with
his hand versus letting them see some cards. Yeah. All right, cool. OK, so just how good does
my had have to be to raise? And the question depends on
the effective stack size. But when the effective
stack size is fairly deep– so let’s say 40 big blinds,
I think it’s about the cut– 40 big blinds or deeper So, you
know, you have a lot of chips. You’re playing for a lot of
chips relative to the blinds. You need a pretty good hand to
want to put all your money in. So a general rule of thumb
is two-pair or bigger. And yeah, once again,
this is only applicable when the effective
stack size is large. And a lot of the
online tournaments, especially the ones where
the blinds go up quickly, the effective stack size can
be around 10 or even lower pretty quickly. Yeah? AUDIENCE: How much do
all of these decisions depend on their position
or your position? WILL MA: OK, that’s a very
good question, actually. Right, so in this situation– so the answer is essentially–
yeah, it depends a lot in this. The examples I gave are
specifically for the button. Yeah, so, I would say if they
were under the gun instead of the button, you need to
play somewhat differently because they’re going to
have– because on the button, they’re going to
have 55% of hands. And let’s say, here, like
10-9 is a possibility. But actually, maybe
a better example is– now, I think this is a board
where it’s really different. Because against a– if
they raise from the button, you know they could
have 55% of hands. And ace-3 is a pretty
good hand here. But if they raise from under
the gun and they’re pretty tight and their range is– pocket
8’s are better and ace-queen, ace-jack, ace-king, then
you’re doing a lot worse. Yeah. So yeah, so it
definitely matters a lot. And yeah, I mean– yeah, so I guess I can’t
go through every single possibility, right? Like this position, this stack
size, with this [INAUDIBLE].. So yeah, so you do have to
do a bit of extrapolation. Like if they’re– right
now in these examples, they’re the button. If they’re the
cut-off, their range is going to be a bit stronger. If they’re the
hijack, their range will be a bit stronger, yeah. Yeah, that’s a
very good question. Yeah, very, very good point. Yeah, because in all
the analysis I just did, I’m assuming their range
includes hands as bad as like, 8-7 suited
and stuff, which isn’t going to be the case if
they were an earlier position. OK, so– all right, so
how good does my hand have to be to raise? So, two-pair or
better, but by two-pair or better, I mean two-pair where
both of your cards make a pair. Here, where one
pair is on the flop, I wouldn’t count
this as two-pair. And this two-pair
is complete trash because any card beats you. So I wouldn’t go on here. This one is also pretty bad. So, OK. So now, when would we raise? OK, so I think this is what–
this is basically the best thing that can happen to
you in poker, pretty much– almost this exact situation. So here, we’ve got
three of a kind. And there’s also a lot of draws. So we’re going to get played
back at a decent amount because you could have hearts. He’d have like queen-jack. There’s just so much stuff
that isn’t going to fold, and we’re always going
to be way ahead of him. Pretty much always
going to be way ahead. So, it’s sweet. I actually think this is very
close to the dream situation. Does anyone have an idea of
why this situation is almost, in some sense, even better
than say, we had pocket 10’s? Yeah? AUDIENCE: If you have pocket
10s, that’s why you tap a 10? WILL MA: Exactly. OK, I’m going to
give you a $20 boost. [CHUCKLING] No more playoffs today. So you’re going to see– OK, right. So it’s almost even
better in some sense you have pocket 5’s
because as Ben said, if you have pocket
5’s, he could have a 10 and put in a lot of money. If you have pocket 10’s even
though you’re crushing even harder, it’s almost like you’ve
taken all the good cards away and then he’s just
always going to fold. So, OK, here’s another situation
where your hand’s very good, although I think you can make
a case for just calling here. Yeah, I don’t want
to say you have to raise because your hand
is just so invulnerable. And even though
the chances that he has that the remaining ace and
a better card to go with it is pretty small, there is
still a lot of, I guess, adverse selection in this
case because there’s no draws. When you raise, he will
fold a lot of stuff. And the stuff that
he does play– it’s not going to only
include the remaining ace. Like, he will call with
pocket 7’s almost certainly, but it does include– it does significantly
make his range more likely to be the
ace that beats you. So, I think just calling is OK. Here, obviously, you have
the best possible hand. Although, once
again, I think just calling as a sort of
a trap is reasonable. Although I would
advocate just raising. I think it’s the simpler play. You know, a calling– I think you’ll see a lot of high
stakes players do as a trap, but it’s a very,
very tricky play. I think raising definitely
has lots of merits because if they’ve got
king– like even ace-king, they’re not going to fold. They just want to
get all the money in. Because they’re probably going
to think you’re more likely you have a single
heart than two hearts. So if they had
ace-king, especially when it’s only 40 big blinds,
they’re probably just going to be happy putting
all the money in, and before you can
see a fourth heart. So, like in this
case, even though you don’t need a fourth
heart to make a flush, a fourth card is a
really bad card for you, because that sort of
kills all the action that you’re getting
from a king– from a pair of
kings or something. Yeah, OK, so this is
a similar situation. Although in this case, I would
say a raise is mandatory. In the previous case, I
think it’s not mandatory because your hand is so safe. If you decide to try
to trap your opponent, you’ll never end up
trapping yourself. Whereas here, if they just
have any heart higher than a 6, if a fourth heart comes,
they are beating you now. And worst of all is,
let’s say they have 10 of hearts, 9 of diamonds. If you raise, you
could have easily gotten them to fold that
10 of hearts, probably. Although, that 10 of hearts,
9 of diamonds is a bit good. Let’s say like 9 of
hearts, 8 of diamonds. They almost certainly would’ve
folded their higher heart, and now you just lost an entire
pot because you didn’t raise. So here, I would raise. You have a straight. You are drawing dead
if they have a flush. But with only 40 big blinds,
I think the chances of a flush is unlikely enough
that getting in is OK. With 100 big blinds, you could
still raise, but probably not go all in. Two-pair– the board
is sort of scary, but two-pair is definitely
good enough here. So– All right, so, these
are examples where you had really good hands. And I said you should just
raise and get the money and then be happy about it. So do I need such a good hand? There’s some other situations
where a one-pair hand is sort of good enough. And so, coming back to the
ace-jack example, you asked. So, we’ll see some of that. OK, so in this
case, I think if you have pocket aces,
that’s definitely good enough to get it in. Although, you shouldn’t
have pocket aces that often here because most
of the time, you should be re-raising preflop. But if you decide not to
raise pocket aces preflop and you end up with it here,
then I guess raising is good. You’re going to be
having the better hand. Although, if you were
trapping them preflop, maybe you just want to trap
them again and call again since there’s not
that many scary cards. So here’s an example of an
ace-jack situation where I think getting in is fine just
because there’s still draws and there’s still lots of
worse hands that will give you action, but overall, your
equity against their range is much, much higher on
jack-7-deuce than jack-10-9. So I would just raise and be
happy getting in 40 big blinds here. Here’s a similar example– king-jack. But we’ve also got the
second best flush draw, so it’s just very
hard to get in back. OK, so we’ll see some examples
where we have fewer chips. So in the last
case, all the hands, we essentially had 40
big blinds– essentially had a lot of chips. So, OK, so now, let’s
look at a situation where all the players– so we only have 1,250
to start the hand, so that’s 25 big blinds. And, OK, so in this
case, even if you’ve got top pair with
a mediocre kicker, I would just be prepared
to go all in because we risking a lot fewer chips. We’re risking a lot fewer
chips relative to the blinds. So here, I would just go all in. So here are some– yes, so
I’m showing you some examples where if I’m 40 or
more big blinds deep, I wouldn’t be happy
getting all my money in. But when I’m only
25 big blinds deep, I’m very happy to
get all my money in. This is another example–
top pair, top kicker. It is a scary board
in some sense, but you’ve just got to gamble
for it when the pot is already so big on the flop
relative to your stack. Same thing again here. So earlier, I had some
examples of this on– similar to this where I
said, you just call it, but when you’ve only got– when you’ve only got four
to five times the flop– I’m sorry, 45 times
the pot on the flop, I would just go for it. OK, I’ll quickly run
through this section. This is a slightly more
advanced play where– it’s where you don’t check
to the preflop raisers. So this whole time,
I’ve been talking about checking to preflop
raiser as a form of respect– respecting that the preflop
raiser’s range contains aces and yours probably doesn’t. So when do we want to lead? So from a theoretical
point of view, so from a
trying-to-play-optimally point of view, essentially we want to
lead flops that hit our range better than his, even though
his range contains aces, which is like a
universal best hand. So they’re rare,
but they do exist. And I think it’s OK
if you never lead, but I’m going to run
through this section showing some examples where I
think leading is fun. But I think it’s an
advanced, unnecessary play. So, OK, so here’s an example. I hope this is visible. So we won’t– we’re
pretty shallow here. So most of the situations
where leading is good, you’re fairly shallow. So a cut-off two [INAUDIBLE]. So one from the button
makes it 1,200 at 300, 600. And there’s antes. So, we call with 9-deuce suited
with 4 and 1/2 to 1 odds. OK, so– and so,
here, we flop 2-5-6. And I lead a third of
pot, planning essentially to get all my money in
because we’re so shallow. Like, I only started the
hand with 10 big blinds. Essentially any pair is
going to be good enough to get all my money
in, although, maybe not if you raise
from under the gun. But from cut-off, I’m
happy to put all my money in against this. So what’s the rationale? So, our hand’s good enough
to put all our money in. And it’s essentially a
better flop for our range because we’re short enough
where the immediate equity preflop means so much
to us what we’re calling a very wide range of hands. Basically, a lot of hands that
includes 2’s, 3’s, 4’s, 5’s, and 6’s, whereas his range,
he opened from button– sorry, he opened from cut-off. You know, even though it
contains more monstrous hands than ours, like pocket aces,
it also just contains a lot of hands like
jack-10, queen-10– basically, hands that don’t
connect with this board. Because if he had 6-5, he
probably isn’t going to open, at least, I don’t think
by my recommendations he should be opening 6-5. Whereas we could
have hands like 6-5, we can have hands like 4-3. So I’ll lead here. So it’s basically
essentially saying, you know, I’m no
longer respecting you because the flop came
in a very specific way where now my range of
hands is actually better than your range of hands. So I’m essentially
the preflop aggressor. I’m going to bet and
try to make the pot big and force you into a tough
situation with your weaker range. And yeah, and we can play
like this with our good hands and with our bad
hands, like 7-3. We have a gutshot, but
we can bluff a bit. So here’s another example. So, under the gun raises. We call with ace-9
suited, which I think is a bit
speculative, but whatever. We just had to call. And we lead a 10-7-5 flop
where we have a flush draw. And once again, I
think it’s reasonable. So it’s deep– it’s fairly
deep, but we can have– even though they can have aces,
we can have more hands like– we can have more
pocket 5’s, pocket 7’s. Tighter hands than him. He might not open those. And also, he almost
certainly isn’t ever going to have 9-8 of
diamonds or jack-9 of diamonds– hands that are
basically monstrous draws, whereas we can. So once again, I’d bet
because I don’t really want him to check back ace-king
or pocket 8’s or something, which he probably will,
because if they have ace-king, they’re going to think
the board is fairly scary. They’re probably not going to
fold that much because there’s so many draws if I bet. So they’re just going
to check back ace-king. And that essentially has– that essentially
has two problems, is we’re not beating
ace-king unless we improve, so by betting, we basically
we just make the pot bigger against ace-king and 9’s,
and we can get them to fold. Whereas if we check, it
might just checked down. And yeah, so– so yeah. One caveat about
leading though is if your opponent knows leading
is part of your strategy, then your range is significantly
weaker when you actually check. So as a result, if
your opponent knows you’re the type of
player who, let’s say, on a– you know, so
this is really getting higher– next and next level. But if they know that
you’re the type of player you will lead a
lot of your hands on a 2-5-6 flop in this
specific situation, then when you check to them
with a hand like jack-10, they can basically
just bet and know you’ll almost certainly
fold, because you’re leading a lot of your good hands. So that’s another
caveat about leading. It’s very tricky to
balance correctly because you need to– you
know, if you’re leading bluffs, you need to also lead some
good hands to balance it out. But then you also need to check
some good hands occasionally to balance out all
the bad hands you’re checking so that your opponent
can’t just bet for free. So it’s a very tricky play. I wanted to quickly run through
it to just say it’s out there, and when you watch poker and
you see people not automatically check to the preflop
aggressor, just sort of giving you an idea of why. But it is a fairly
advanced and tricky play. And it’s easy to make mistakes
leading, which is why I think– you know, I think it’s fine
if throughout this course you never lead. OK, so now we’re going to
talk get some implied odds and reverse implied odds. So, OK, so here’s a situation. So note that– so we have
the worst hand in poker. We’ve got– we’ve only
got three big blinds, OK? And hijack raises to 2,400. So the question is, do we want
to call in this situation? So we’re putting in 1,600. So we can do a quick
equity calculation. So if we call, we’re all in. So the only thing that
matters is the equity of our hand against his range. That’s essentially
the only thing that matters because he
has no more decisions. So optimal play doesn’t
even matter in this case. It’s a strict mathematical
expectation calculation. And we’re actually–
so basically, we need a call two big blinds. So 1,600– that’s
two big blinds. To win how much is already in
the pot is 5 and 1/2, right? 5 and 1/2 big blinds. So they made a big raise here. They made it 3x. So we need 2 over 7.5,
which is 27% equity. And if we put him on
a reasonable range for that position,
we have 28% equity, which is enough to call. So I think calling
is a fine play, OK? I’m not winning in
front of this person who I think probably was me. So, yeah, calling’s a fine play. And so, now, but I
want to emphasize, OK? So if calling is a
good play because it’s positive expectancy,
why don’t we call when we have more chips? So in this situation,
if someone called, they would probably
be ridiculed, right? Why are you calling with
2-7 offsuit against a hijack raise that isn’t even
giving you good odds, because they raised it
3x, which is a big raise. So why is it bad in this case,
when you have more chips? And the reason is
essentially what’s called reverse implied odds. So in the first situation, we
called because we were all in, and the equity
calculations said we could. But in the second
situation, even though the equity
calculation is the same and we do have the right
odds to call preflop, the hand isn’t over. There is still potentially
46,000 more chips to be put in postflop. And with a hand like
7-deuce offsuit, not only is it a weak hand,
it’s very hard to play. When we hit a pair,
we hit a small pair. We’re often not going to be
sure whether we have the better hand. We’re going to have to decide
whether to fold or call them down. And we’re often
going to be wrong. So, it’s a very, very easy
fold in this situation even though you have the odds,
because these reverse implied odds hurt you so much when
there is still potentially 46,000 to play for postflop. OK, so here, let’s say
instead of 7-2 offsuit, I had ace-2 offsuit. I would still fold. So if you do the same
equity calculation, we actually have 43% against
his range, which is tremendous. But you only need 27%
equity to all in, right? So, why would we fold
when we have 43% equity and we only need 27% equity? That reason is because, once
again, reverse implied odds. So, there used to be
actually be this way you could cheat in online poker. So they had this thing
called disconnect protection which is
someone disconnects– this is really stupid. I got cheated by
this so many times. Basically, if you disconnected,
instead of your hand getting folded, essentially
there’s no more betting and all the cards are dealt.
And the person who wins the hand just wins the pot. OK, so essentially
by disconnecting, you could say, OK, screw you. There’s no more betting. We’re just going to
see until the river, and whoever wins the hand is
going to win the whole pot. So basically, you could
cheat in this situation even if you had 7-2 offsuit,
by just calling and then disconnecting immediately. And then none of this
reverse implied odds exist. But you can’t cheat
like this anymore, so don’t try to make that play. So yeah, so in this case, even
though you have 43% equity, I would fold. Here, with 9-8 suited, it’s
a whole different story. We only have 37% equity,
which is worse than 43%. But I would call. With 9-8 suited,
you can make a flush and make a better hand than him. You can make a straight and get
him to put in a lot of money with a good pair. And yeah, you’re
still out of position. You still have to act second. But overall, it’s just
a much better situation. OK, so now, I want to
talk about implied odds. So with the 9-8 suited, you
know, I sort of talked about– the implied odds, the
fact that you still have to play for more chips
after on the turn and river almost works in your
favor because you can make straights and flushes
and have a very good hand and be fairly certain
you’re winning, and get him to put in more
money with a worse hand. So implied odds is
basically, yeah, it’s when the odds
are in your favor because you’re playing a hand
that plays well postflop. OK, so– OK, so let’s
look at an example where implied odds,
I think, are good. So this is called set mining. This is a play that’s, I think– so, I’m going to go through it
even though it’s a play that’s sort of dying in poker. I think it’s a play that
no longer works that well in practice nowadays,
at least at like, at fairly high stakes. But it’s in theory, I think it
teaches you a very good thing about implied odds. So, in this case, under
the gun raises to 3x– 2,400 when the
blinds are 400, 800. And we decide to call. So if you do the calculation,
we don’t have enough equity to call, but why do we call? So essentially,
we’re in a position because we have the button. And also, we can win
essentially a huge pot when we hit a third deuce. So now, this only happens a
small percent of the time. And if you do the calculation,
this happens roughly 1/8 of the time. You’re going to hit a third
deuce 1/8 of the time. And essentially when
you don’t hit a deuce, you’re against an
under-the-gun raise, so he’s going to have
a really strong range. You’re going to lose
the pot 7/8 of the time, essentially, roughly speaking. So what this is
essentially saying is if I’m only winning
the pot 1/8 of the time, I need to win on average 8
times as much as I lose for it to be worth it, right? But the point is, at least
back in the day in poker, you essentially do, because
when you do hit the deuce, they just– they’re going to
have pocket aces or pocket kings or, you know, the
flop will come ace-6-2 and they’ll have ace-king. They’ll just have a
tremendously good hand that’s still
crushed by your hand so often that you definitely,
essentially, 1/8 of the time, you lose 2,400 chips, and– I’m sorry, 7/8 of the
time, you lose 2,400 chips, and 1/8 of the time, you
win their whole stack of 80,000 chips. Essentially, it’s what
the best situation is. So, yeah, so you need
a lot of chips for this to be a good play. You know, even if you have
40 big blinds which is, by our standards, fairly
deep, it’s still not that good because, once again, you
only win 1/8 of the time. So, you really need to
win a lot when you win. And like when you hit
a 2, it’s not 100% sure that he’s going to
put in all his money. So the fact– so
basically, you’re only winning a huge
pot even less than 1/8. Like you need to hit a
2, and you need to have– you have aces or kings. So you know, that’s going
to be like 1/20 or whatever. But the point is if
the stack is so deep, then it’s still worth
it, essentially. And the reason why it’s
sort of dying in poker is because I think
nowadays, players are good enough where even if
they have aces under the gun, they realize the
optimal strategy isn’t to always put all your
money in on a 7-5-2 flop. But yeah, long story short,
I think this is a fine play. I think it’s fine if you do
it in the current league. Because it’s tough to fold
aces on a 7-5-deuce flop. And yeah, I think it’s a good
play to know about at least. So, here is another hand. So, cut-off raises to 2,000. We have jack-10
suited on the button. So once again, we don’t
have direct odds to call. But we have good implied odds
because we’re in position and we’ve got a
suited connected hand. OK, so I’m going to go
through the whole hand because there’s going to be more
examples of implied odds here. So both blinds fold, and
the preflop aggressor, the cut-off continuation–
that’s about a bit less than half of pot. And we have a flush draw here. So, what is the
effective stack size? Even though we started
the hand with 80,000, they only have– they only
started the hand with 30,000. So the effective stack
size is only 30,000. So we’re definitely not folding. We could call or we could raise. The problem with raising is when
we raise and they go all in, we’re sort in a really
crappy situation where our hand’s too good to
really want to fold, but too weak to have the
odds to call his all-in. So I think just calling
is the right play. And yeah, and raising gives him
the opportunity to re-raise on. If we call, he can’t say,
oh, because right now, I’m putting in more chips, right? So, OK, so we miss on the
turn, which kind of sucks. And they bet fairly big. They bet 8,000 into 12,000. So let’s do an analysis. So, OK, so if I’m
simplifying an assumption, let’s assume they have it, OK? Let’s assume we modeled
them most fairly tight. When they’re making this
bet, they’ve got us beat. We’re not going to win the hand
by rivering a jack or a 10. We need to river a diamond. So essentially, let’s assume
they just have ace-king, or they’re going to have
a pair of aces, at least. So we need to call 8,000
to win 20,000 in the pot, so we need 8 over
28, or 29% equity. And if you count, there’s
9 diamonds out of 46 cards, so we only have 20% equity,
and we need 29% equity. But I would still call. So, because when we call
and we hit our flush, we can actually– we can
bet on the river, and there’s a decent chance
that we’re going to get called. Whereas if we call
and we miss our flush, we can just happily fold. Does that make
sense to everyone? So we don’t really have
the odds to call here. But we call because
if we hit our diamond, we can go all in on the river. And there’s a decent chance
they’re going to call us, and we’re going
to win more money. So we actually do have
the odds, essentially. We have the implied odds. OK, so here’s a
similar scenario. So pretend the same
thing happened, but this was the situation instead. In this case, I think we
should definitely fold. So what changed was
instead of having two diamonds on the board
and two diamonds in our hand, now there’s three
diamonds on the board and one diamond in our hand. So it’s worse for
many, many reasons. So one is when you only have
one diamond in your hand and there’s three
diamonds on the board, if they have
ace-king, it’s going to be more obvious that
we probably have a flush if we bet on the river and
they have like ace-king. So they’re probably just
going to fold this king. So, we’re not going to get paid
off when we hit the diamond. And even worse, we’re not
even drawing to the best hand. Like, what if they have ace-king
with the king of diamonds? Then we’re just crushed. We’re drawing dead
in this situation. There’s no cards
that can help us win. So that’s just such a huge risk. So, yeah, and also, a small
thing, but the board is paired. So it’s possible they have
like pocket aces, or ace-5. They already have a full house. And even if we hit the best
flush, we’re not going to win. OK, so– OK, so, that was
a good example, I think, of when you have
the implied odds to call with your
draw to try to hit. When you don’t have the
implied odds to try to hit. But we can also
bluff with draws. So in all the
examples I gave you before where you
check-raised the flop, we had a good hand, right? But obviously, this
is predictable. If they know that we only
check-raise their flop that with two-pair
or better, they can just fold whenever they
have one-pair or worse, right? So draws, not only are they good
for implied odds purposes where you call and then only put
in more money when you hit, they’re also very good for
bluffing in certain situations. So essentially,
what you’ll realize is bluffing sort of
equivalent to having a draw, in some sense. Because the hands
you want to bluff with are the hands that
have some draw value. So, here’s an example. The button raises to 1,600. So we’re 20 big blinds deep. And one of the big
blind with 10-9, and we call with
our 4.5 to 1 odds. OK, and the flop is jack-10-5. So we’ve got what I would
consider a good draw. So a good draw, I would
say, usually means either an open-ended
straight draw. So four-in-a-row do a straight. So there’s eight potential cards
that complete your straight, or a flush draw, which
it usually has 9 outs. OK, and then they bet 2,500. And then we go all
in in this situation. Essentially, we’re bluffing. We’re hoping they fold. But why is this a good play? So, you know, it seems
pretty sane to just call instead, right? Because we can call, we can
have perfect information of when we hit, when
we don’t, and only risk more money if we do. But it’s actually also quite a
good play to go all in because even though it looks
like we have a bad hand to be risking all our chips
because we only have 10-high. The point is the
fact that we have 10-high doesn’t matter
because they’re never calling our all-in with a naked
queen-high or king-high, right? They’re not to call
with a random hand. So what matters isn’t how good
our hand is, in this case, 10-high. What matters is how many outs
we have against the hands that they called. So in this case, we’re
always going to have 8 outs. Even if they have the
best possible hand, like pocket jacks, we’re
still going to have 8 outs. So, this is a great hand to
bluff with because if we call, we might just lose the pot
to queen-high by the river. Whereas if we
check-raise all in, it’s essentially
the opposite of what I was talking about before with
like being averagely selected. Here, it’s just essentially
being beneficially selected because all the hands
that barely beat you, he’s going to fold. And if they have a hand
as good as j– ugh. When they have a hand
as good as jack-jack, it’s almost, like,
wasted, you know? They haven’t– they got
their jack-jack with– if they had jack-jack,
they’re hoping we have like, pocket 8’s that only has
one out against them. But here, we have
a much worse hand than pocket 8’s with
8 outs against them. You can contrast this
with having, say, like 6-5 on this flop. 6-5 is a really bad
hand to raise with. You just want to be
calling because it’s sort of the opposite. Any hand that beats you is
going to be crushing you, and you’re going to
fold out the hands that are already using to your 6-5. But yeah, so 6-5, if you’re
against like ace-jack, you only have five outs. And you have close to 0%
equity against flopping jacks. So, right, so this
is essentially the bluffing epiphany. So when you’re
bluffing, the– when you’re bluffing before
the river, the thing that matters isn’t how good
our hand is, it’s how many outs we have. OK, so– right, OK,
so this is essentially just me talking about
the bluffing epiphany. So you want to always
bluff with hands that have a high number
of outs against the hands that you get called by. So, here’s an
example of something that’s not bluffing, OK? So the cut-off raises to 90 and
we call with 7-6 of diamonds on the big blind. And this happens randomly. You know, sometimes you’ll
see someone make a play like, what if ends– You’re going to– so someone
will make a play like this. And it’s going to work. And they’re going to
look like a genius. So, we check to
the preflop raiser. We’ve got nothing, but we have
a read that they, like, scratch their ear or something. So, we check-raise
hoping that they fold. So we get called. And, you know, we still got
absolutely nothing here. And we bet on the
turn because that’s the only way we could
potentially win the hand. And they call. And then we still have nothing. And then as a last resort,
we go all in on the river. And, you know, a good
percent of the time, they’re going to fold. And we’re going to look like a
genius for making this bluff, right? So basically this is not– so
yeah, this is not bluffing. This is essentially
opening your wallet and giving your money
to your opponent. So when you’re
check-raising, you’re essentially– the
reason why you were check-raising in the
first place as a bluff is because you had some chance
of making a good hand. And essentially, a
bluff is because your– the hand that you could
have potentially made, the flush that you
potentially could have made, didn’t get there. It’s not because you started
with a hand that could never make anything on this board
and it didn’t get there. So, OK, so here’s
a similar situation where I think it makes
a lot more sense. So it’s going to
be a similar board, but we have 10-9 of hearts. And here, we check-raise
their flop bet. So this situation’s
a bit different than the jack-10 diamond
situation from a while ago, where we only called
with a flush draw. The reason why
raising here is better is because the stack
sizes is deeper. So with the jack-10
of diamonds hand, the problem with
check-raising was there’s a risk they would go all in. And we would fold because we
don’t have good enough odds, yet our hand is so good. Here, our hand is similarly
good, but because it’s so deep. So, we actually started
the hand with, I think, 100 big blinds instead
of 40 big blinds. They’re pretty
unlikely to go all in. So here, check-raising
10-9 of hearts has a lot lower chance of
getting blown off the hand. OK, and we get a called. And we turn a 15-out draw. So we had 9 outs here, right? But the jack now
essentially gives us 15 outs because it gives us
the 8 open-ended straight outs, plus the 9 flush outs, minus
the 2 from double counting– so 15 outs. And we bet 650 here. So it’s the same
hand as a 7-6 suited. It’s the same hand
as the stupid play. We’re betting here. And we get called. So, some notes. Here, our hand was
good enough where even though when bet 650
into the pot on this turn, they could go all in. If they have like
ace-jack, they’re probably going to go all in. And you know it’s going to suck. But we have good enough
odds in this case, because we have so many
outs, that we can even call an all-in. So it’s fine. We can just call. And yeah, so, note that
by check-raising the flop, betting turn– so the good thing
about playing draws like this is that now, if
we play draws like this, we can also play our good hands,
like ace-8 or pocket deuces like this, and get
paid off a lot more. So, OK, so we get called. And then the river is a king. It’s not the scariest card, but
we can have queen-10 of hearts. We could easily get
a queen-10 of hearts. So we go all in here. And even if the king
wasn’t scary at all, like even if the king
was like a 3 or a deuce, I’m fine with just going all
in because that’s the only way we can win the hand. But it’s a fine excuse here
to go all in with 10-high on the river, and say that’s
the only way I could’ve won the hand because there was
a reason I was check-raising and representing all the
strength on the flop at turn, right? It’s because I had a heart draw. My heart draw didn’t
get there, so now, I need to desperately, to have
a chance of winning the hand, go all in. But it’s reasonable. The reason why I got to this
situation, this bad situation, is because essentially
I got unlucky, right? I had a chance of hitting
a flush, and I didn’t. It’s not like the
7-6 case where I knew I was going to get it in
this situation, which is not a good situation. But here, I got a bit unlucky
to get in this situation. OK, so– all right, so I think
this is the last example. So, last example of when
you give up on a bluff. So sometimes, you’re bluffing. You don’t have a great hand. But sometimes, you just give
up because you figured out your opponent’s not
folding, or the board comes out in a way where
it’s not theoretically a good idea for you
planning to fold. So hijack minus 1 makes it 90. Cut-off calls. And we’re 100 bets deep. We call with jack-9 of
hearts from the big blind. OK, so the flop is a 10-7-deuce. And so we have a– we get a decent flop. So once again, you know, we
have a reasonable draw here. We have some reason
to be bluffing. We don’t have nothing. We have some reason to be
bluffing because even though– essentially, we’re
hoping to turn 8, even though the chances that is
only 4 out of 47, which is low. But it’s still something. And it’s much better
to bluff with a 4 out of 47 chance of making
a monster hand than a 0 out of 47 chance. So, OK, so here,
this was interesting. The preflop aggressor
checked, which is fine. As the preflop aggressor, you’re
not forced to grant the flop. So, but this– but note that
the preflop aggressor is not the guy who got the flop. So the cut-off bets the
flop, but the cut-off was not the preflop aggressor. OK, so the cut-off
shouldn’t have pocket aces. They could occasionally, but
it’s less likely than usual that they have pocket aces. So they bet, and we decide
to check-raise here. And yeah, I think this is
a very reasonable play. So what are the reasons? One– so yeah, we
have something. We can try to turn an 8. And also, turning
a jack is fine. We also turn a heart. And so we had lots
of backdoor draws. We can turn a heart. That will give us four hearts. And we could turn even
like a queen will give us an open-ended straight draw. A king will also give us an
open-ended straight draw. So that’s the weird case where– so if the turn is a king, then
the board will be king-10-7. And we’ll have the jack-9. And then an 8 or a queen
will give us a straight. It’s one of the rare cases. It’s called– it’s
called a double gutshot, or a double gutter. So it’s one of the weird–
it’s one of the strange cases to watch out for. It’s possible that you have
an 8-out straight draw, even though you don’t
have four to a straight. So one example is
where you have like– it’s like this one, where you
have a king and then jack-10-9, and then 7. And another example is where,
let’s say you have like, king-jack on an
ace-10-7-6 board. Then essentially the board– essentially, it’s
ace-king-blank, jack-10-blank, 8-7. So then you have it
hit a 9 or a queen. So there’s a couple of weird
straight draws you can have. But anyways, the point is– so yeah, I think this
is a good play, not only because we have a crappy
hand that’s basically– so basically, a crappy draw is a
really good hand to bluff with, but also the fact that their
range isn’t particularly strong here. Because they can’t
really have aces. So, I mean, they can have pocket
7’s or pocket deuces, I guess, but also we’re attacking the
fact that he’s not the preflop raiser. So their range
isn’t that strong. OK, so, so, hijack minus
1, the preflop aggressor, gets out of the way. And then cut-off calls us. And then the turn is a 7,
which is basically the worst card in the deck for us. I’d say the 7 of clubs. Even if it was like
the 7 of spades, it would’ve been better. So, why is this the worst card? So first of all, it doesn’t
help us at all, right? It doesn’t give us any kind
of better straight draw or better flush draw or a pair. And furthermore,
it’s fairly safe. You know, even if
the turn was an ace, we could at least
pretend we have an ace. The 7 is a fairly safe card. If they have a
pair 10’s, they’re not jeopardized
because of ace-king. Furthermore, the main
issue is his range is going to be a lot more likely
to contain a 7 than our range. Because, remember
what I said earlier, you don’t really
want to be raising– check-raising the flop with
your middle-of-the-road hands. Because your middle-of-the-road
hands, you want to just call. Because when you raise, you’re
getting called by worse– sorry, you’re getting
called by better and you’re folding out worse. So, probably if I had
a 7 on the flop here, I’m never check-raising. So basically, I
can’t have a 7 here. And furthermore, they’re a
lot more likely to have a 7. So this just really hurts us. Essentially, it’s
just a bad situation where their range is a lot
stronger than our range. And basically the best thing we
can do is just fold our hand. There’s no point–
you know, there’s no point to try to
continue bluffing. Like, it’s sort of like
playing the “who’s taller” game where you don’t
get to see my height, but you know that I was
like malnourished as a kid. Like you just know,
on average, there’s no way I’m going to
be taller than you. So the right thing to do
here is just stop our bluff. And it was like the
worst card that came, but we just give up the
hand, which is fine. And then they take down the pot. Right, so, bluffing
epiphany 2 is basically, other than counting
how many outs we have, it’s important to analyze
what we’re representing. What else is in our range? You know, we’re bluffing. We don’t have a good hand. But what’s the good hand
that we could potentially have in some other
parallel universes that we’re representing? And in this case, there
just really isn’t anything. So yeah, so like an
ace-turn would’ve been fine. Even a 6-turn
would have been OK, because we could
have represented 9-8. So, one of the best times to
bluff is when your draw missed, but a different draw completed. So like if you had
a straight draw and you were bluffing
the flop, and then the turn completes the flush,
it’s reasonable to bet. I mean, you do run into the
risk that they have the flush, but also it’s just they’re going
to be more scared of the flush. And similarly, yeah,
like if you have a flush draw and the straight
completes, you can also bet. OK, so, yeah, so I’m running
through a lot of poker concepts today. So that’s the end. I’ll give a quick summary. So hopefully, this will
give people more ideas on how to play online. I know I sort of left you
guys in the dark last time. I mean, I ran through
things pretty quickly this [AUDIO OUT],, but hopefully,
as you play more, it’s OK if you didn’t understand
everything immediately. But hopefully, as
you play more, you’ll be like, ah, implied
odds, or you’ll be reminded of examples
from this class. So yeah, so we covered
continuation betting, the preflop aggressor getting
the respect, being able to bet, the Fundamental Theorem
of Poker about how you bet your good hands
and bluff your bad hands. We analyzed different
flops, and I tried to give you a general
idea of what sorts of– how good your hand needs to
be on certain kinds of flops. And yeah, so when I showed
you the different flops, you know, what I told you– I didn’t like mathematically
prove that calling is good or raising is good. It’s basically just
like from experience and from doing calculations,
I know roughly your equity is good enough. But I didn’t like,
mathematically prove it. So you essentially
just have to trust me in that sense for the example
flops that I showed you, because I didn’t show
any calculations. Yeah, we talked
about when to lead. We talked about implied
odds, reverse implied odds, set mining, bluffing with
draws, and then the two bluffing epiphanies. And yeah, so it’s important to– so basically, it’s much
easier to play good hands than bad hands in
poker in some sense, because when you
have a good hand, you just bet and
hope everyone calls. But it’s important to know how
to play bad hands, a.k.a bluff, so that your opponent
also might call you when you have a good hand. Because if you’re the type
of player who never bluffs, then the game is
uninteresting, right? So, because then, your
opponent just always folds whenever you do anything. So that’s why it’s important
to think about the bluffing epiphanies. OK, cool. Yeah, thanks. And hope you continue
to play online.

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2 thoughts on “2. Introduction to Postflop Play

  1. This isn’t bad but I expected more from an MIT lecture… this feels watered down.. Flopped bottom set on an extremely wet board isn’t a dream situation exactly. Trapping with a flopped nut flush out of position isn’t too tricky of a move either.. I didn’t even watch enough of the video to know if he talks about things like balancing your calling/3betting ranges or your bluffing/value betting ranges, but those are some higher level poker strategies….

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