1. Course Overview and Introduction

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visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: OK. So let’s get started. So before I get into
any poker I want to talk about the
mentality I want everyone to try to have when analyzing
poker in this class. So I call it the
decision mentality. I’m going to start with a story. Who here has heard of
credit card roulette? It’s like a game you play
at the end of a guy going to restaurants. So what happens
is poker players, they’re going to split
the bill by instead of everyone paying their
own bill, which is annoying. You have to keep track. You might have to Venmo
people after the exact amount. And sometimes the
waiter or waitress doesn’t want to split
the bill per person. So poker players get around
this by just picking one person at random to pay the bill. And we like making
this exciting. So what we do is we ask everyone
to put in their credit cards. And then we pull out the
credit cards one at a time. And if your credit card is
pulled out then you’re safe. And the last person in has
to pay for the whole table. So it’s a pretty fun game. Yeah, I think I’m pretty lucky. The biggest one I
lost was in Hong Kong. I once had to pay
around 1,200 USD. It was a pretty big table. But overall I’m pretty
good at this game. It’s a game of skill for sure. But sometimes this results
in some funny stories with non poker players. So this is something that
happened to some poker players. So poker pro Matt, he goes to
dinner with poker pro Steven. And that brings Emily, who’s
a close friend whom he also has a romantic interest in. So when the bill
comes Matt’s like OK, I’m going to pay for it Emily. So he puts in two credit cards. He’s like the second credit card
is for Steven– is for Emily. And then Steven
pays for himself. So Stephen puts in
one credit card. So they play credit
card roulette. And then Matt, being
a very lucky guy, pulls out both of his credit
cards before Steven’s. And Steven ends up paying
for all three of them. So now the question is,
who should Emily thank. So who would you thank if
you were in Emily’s shoes? Does anyone want to
say to thank Steven? AUDIENCE: Yeah. PROFESSOR: Because Steven
actually paid for the meal. So I think it’s a
totally reasonable thing to do as a reasonable person
to thank Steven who actually had to pull out his wallet. So in this class
we want everyone to think in terms of the
expected results and not actual results. So Emily should be thanking
Matt because, on average, Matt put in the card for Emily. And on average Matt is
going to be paying for Emily because Matt’s
going to be paying the one third of the time
that Emily would be paying. But at the time, Emily
thanked Steven for her meal and then didn’t say
anything to Matt. And then Matt was upset about
it and told the entire poker community. That’s how I found
out about this story. So we want to think about
in terms of on average what your decision
would have whether you would have made money in
expectation or on average. So roughly, the law
of large numbers says, over your
lifetime, the amount you end up paying for
credit card roulette is the same as you would have
paid from splitting the bill. So you know why split the bill? You might as well just
save a lot of time by playing this fun
game every single time. And over your
lifetime, the amount you pay in credit card
roulette is roughly going to be what you would
have paid from splitting. So all randomness
eventually averages out to it’s expected value. That’s what this is saying. So what does eventually mean? So basically when we say
a gamble is very risky I’m not mathematically
defining anything here. But I just want to throw
out some intuitive concepts. So a risky gamble
is a gamble where it takes a long time to
converge at your expectation. But the point is, no matter
how risky it is, eventually it will get you. So there’s a saying
that death, taxes are the two things that
eventually get you. As poker players, we would
like to think that three things eventually get you. It’s death, taxes, and
the law of large numbers will eventually– you’re going
to reach your [INAUDIBLE].. So here’s another
hypothetical situation. So let’s say you get off
at the wrong bus stop because you were distracted. And then you were
upset yourself you analyze how to not be
distracted in the future and get off at the
right bus stop. But then after you get
off at the wrong bus stop you find $1,000 on the ground. And then you immediately,
you’re no longer upset and you marvel at your riches. So this is sort of
an absurd story. But situations like this
happen all the time in poker. You’re going to
make a bad decision but bad decisions still get a
good result 49% of the time. And if you make
the right decision you’re still going to get a
bad result 49% of the time. So it’s very important
to analyze your decisions without being biased by the
actual outcome that occurred. So you really want
to be obsessed with this self-improvement,
analyzing your decisions. If you made $10,000
in a situation where you could have be $12,000
then that’s not good enough. So I want everybody
to think in terms of what’s the maximum
you could of made and analyzing what’s the best
decision you could possibly have made in every situation. And sometimes it’s hard because
if the result is exactly correlated with the
decision then you can just go back and
look at the result and know whether you made
a good decision or not. But that’s why learning
poker can sometimes be very, very hard because you
don’t have immediate feedback. You’re not sure whether
the decision you made is what caused you to make that
money or you just got lucky. So with that being
said, now let’s talk about some ways to
reason about poker hands. So roughly there’s three levels
of reasoning of poker hands. Level one my hand
versus your hand. But by this I mean, you can
see what your cards are. And you look into
your opponents eyes and you say, OK, I can tell
your cards must be pocket kings or whatever. Your hand must beat
this other hand. And you played your hand
exactly against your opponent’s specific hand because you
have a soul read on them. So let’s see the
example of this. So we’ll watch an episode
of Poker After Dark here. [VIDEO PLAYBACK] [MUSIC PLAYING] – Raise to 1,200. – I think you would call
it this time, Patrick. – Button raises. Never anything. NARRATOR: Contrary
to what Patrick might think Jennifer has a real
hand and it just got better. She’s flopped top set. Patrick flopped a pair of tens
with a gutshot straight draw. – I’ve got two pair. – Check. – Full house. – I can’t beat that. – I thought you
had pocket kings. – I almost thought I had you. [END PLAYBACK] PROFESSOR: So yes,
this is sort of well known poker term from
way that in the day. If you’re a Jennifer
Tilly hand– I’m sorry if I’m
making fun of her– but basically she put her
opponent on a specific hand. She looked at
Patrick and Antonius and had a feeling
that he had pocket kings for some strange reason. And then what happened was,
so she had pocket jacks here, which is a really,
really good hand. It’s a full house. And she just checked the
turn and checked the river instead of trying to
get Patrick to put more money in because she
was so certain Patrick had pocket kings. Just mathematically
speaking, out of all the possible combinations
of cards you have, to put your opponent
specifically on pocket kings in this
example is basically unfounded. So this gets to
level two reasoning. So level two
reasoning is my hand versus your range of hands,
versus your probability distribution of hands. And another name for this
is exploitative play. So let’s look at
a different hand. And I’m going to show
you how to reason about this hand using level
two exploitative reasoning. So I’m not going to go
through the whole hand. But this is actually a real
hand I played in Macau five, six years ago. So we get to the river and I
had ace 10 in this situation. So the pot is 21,000 roughly. And my opponent
bets 8,000– sorry, so the pot is 21,000 after
my opponent bets 8,000. So basically the pot was
13,000 and my opponent bet 8,000 making it 21,000. And I have to decide whether to
call with a pretty good hand. I have a pair of aces here. But I know my opponent is
[? Rain ?] [? Kahn, ?] who is a very tight player and
doesn’t really like bluffing. So I don’t think he’s
really ever bluffing. If I’m beating him
here it’s because he’s betting a hand that
he thinks is good but is actually worse than
mine, like ace eight basically. So I model my opponent’s range
as ace king through ace eight. I don’t think he has
something even stronger, like pocket nines because
he would have raised more earlier in the hand. So let me run through
this calculation slowly for those of you seeing
pot odd for the first time. So here basically, I want
to think of it like this. The pot, which includes the
8,000 he just put out, is 21. We’re considering calling for
8,000 so if we lose, if we call and her turns up ace king,
which is a better hand, then our net result from this
decision is negative $8,000. If we win and we get our 8,000
back as well as the 21,000 in the pot, so we make,
our net is plus 21,000. So therefore, our
win to lose ratio needs to be at least
8,000 to 21,000 in order for calling to be
positive expectancy. So we’ll do the
exact calculation. I’ll try to do it
somewhat slowly to show an example of how
to do this calculation. So essentially what I do
is I count the combinations of each hand that exists. So ace king, there’s
eight combinations because there’s two aces
remaining that I haven’t seen and there’s four
kings remaining. So it’s two times four,
there’s eight combinations. Same with ace queen,
ace jack, and ace eight. Ace 10 and ace nine, there’s
only six combinations each because I have the
10, which makes him having ace 10 less likely. And for ace nine there’s
a nine on the board. So ace nine is also
slightly less likely. So ace 10 we actually
get half the pot. So I’m just going
to roughly make that equivalent to us
winning three of those times and losing three of
those times, which is equivalent in expectation. So basically, if you
do this counting, there’s 33 combinations
that beat us, there’s 11 combinations
that we beat. And so our equity is
basically our probability of winning, which is
equivalently only the fraction of the pot that we own. So our equity in
this case is 25%. And the pot odds are 21 to 8. So we need we
basically 1 over 3.56. So 21 to 8 is 2.56 to 1. We need equity 1 over 3.56
to call, which is 28%, which we don’t. So I folded. So unfortunately, this
calculation is a bit ugly. You just have to do
it a bunch of times and convince yourself that are
doing the right calculation. Basically you got to remember to
add one when you’re converting the odds ratio to an equity. So it should be
fairly simple math. So in this case,
I folded because I didn’t have the desired. So is there any
questions about that? That was maybe a bit confusing
but I don’t know of a great way to show the exact conversion
from pot odds into equity. But I just want to
point out that they’re slightly different. One is a ratio of when to
lose and one is basically a fraction of win over
all possible outcomes. So just don’t get
confused by this. That’s all I’m saying. I’m going to quickly
interchange between the two throughout the course. And you should try to get in the
habit of being able to quickly complete between the two. So this is an example
of level two reasoning. And hand reading is about using
your opponent’s past actions and your knowledge
of their tendencies to tweak your probability
distribution of over what you think their hand is. So hand reading is not
about pegging your opponent on a specific hand. It’s a marketing message. Poker players, they
wear sunglasses, they have earplugs to prevent
people from reading their soul. It matters a bit, but
really, these things, things like I scratched my
ear before I raised, it should affect your belief
about my cards a very small amount, way less than what
Lady Gaga and the media makes it seem like. That’s how you reason about
a hand exploitatively. You build a model for
how your opponent behaves and you make the decision that’s
the most positive expectancy against that model. And you can go very, very
far with level two reasoning. You can basically build a career
out of level two reasoning. And it’s best targeted
towards individual opponents with specific
tendencies that you’re trying to take advantage of. So this sounds very good. This sounds like a
great way to play poker. I figured out what my
opponent’s doing right. I just figured out the
probability distribution and play in a way make
the most money from him. So does anyone have any problems
with this type of reasoning? So I’ve got some $20
Amazon gift certificates from [? Acuma ?] Capital. Someone can point out
potentially something you don’t like about
this type of reasoning I’ll give you this
gift certificate. AUDIENCE: You reveal
a lot of information about what your hand is
when you think like this. PROFESSOR: Right. But what if your model
incorporates the fact that they are going to behave
based on what they think is in your hand. Yeah. AUDIENCE: It might take you a
long time to build this model. And if the players leave
your table, or whatever, you spent like– because
before you have a model you can’t use this
line of reasoning. So it’s expensive to do it. PROFESSOR: That’s a good point. So first of all, level
two reasoning is not easy. Even though it has flaws, even
playing very good level two, poker is not easy. Building the model can be very
hard and you could be wrong. But that’s not really
what I’m looking for. Colin, yeah. AUDIENCE: Because if your
opponent knows your reasoning then he could maybe bet a
certain way to push it to 28%, where you’d only call if it’s– PROFESSOR: Right. OK. Yeah. I think that’s be good enough. I’ going to give a certificate. I’ll give it to you at the end. So essentially,
the problem is it’s this assumption– the
fatal flaw in every plan is the assumption that you
know more than your enemy. Does anyone know where
this is from, by the way? If you do I’ll have another
$20 gift certificate. Does anyone know where
this phrase is from? Yeah. AUDIENCE: Is it from Kasowitz? PROFESSOR: No. Yeah. AUDIENCE: The Art of War? PROFESSOR: No. No one knows. I’m going to keep
the gift certificate. That’s OK. So essentially, the problem
with this line of reasoning is your opponent does
not play according to a fixed, static algorithm. They’re also an
intelligent human who’s taking this class who’s
building all this for you and adapting the
strategy to beat you. So if you assume your opponent
plays with a fixed strategy, but what if they’re
doing the same for you? Now I’m going to get to the
third level of reasoning, which I call optimal play. So let’s analyze the exact
same hand using level three reasoning. So don’t get me wrong. Level two reasoning is great. If you can do level
two reasoning very well you can make a ton of money. But level three reasoning is
a completely different way to analyze this hand that can
also make you a lot of money. So level three reasoning I’m
going to think like this. Level three is my range of
hands over your range of hands. So instead of looking
at my specific cards and figuring out
what my cards are, I’m actually going to also
put a probability distribution over myself and myself, to
my opponent’s eyes, what is the probability
distribution of my hands? And in this specific
spot, let’s just say, I decide that my
range in this spot is ace jack through ace seven. So not including ace nine. It’s basically ace 10,
ace eight, ace seven. So this is the way to
do the calculation. So let’s just assume I know
my opponent’s propensity to bet 1 over 1.6% of
the pot on the river. So the pot was
13,000 on the river and I know that my opponent’s
going to bet 8,000. So I must call with
the frequency such that their EV from
bluffing is zero. So that’s essentially my
goal with optimal play. So essentially
what I’m saying is, let’s say they have
a really bad hand. They have like jack 10
for jack high, which is almost certainly going to
lose the pot if they don’t bet to try to get me to fold. Then I want to call
with the frequency such that with those
hands, regardless of whether they bluff,
their expectation is zero. So how do I do that? I just make my call to
fold ratio 1.6 to 1. Sorry, in all
these computations, to make it easier,
I’m assuming 1.6 is approximate for the ratio. It’s actually 13 over 8. It actually turned out to
be mostly Fibonacci numbers so the ratio is around
1.6 to 1 for all of them. [INAUDIBLE] So my call to fold ratio
needs to be 1.6 to 1 so that if they
have that a bad hand their expectation
from bluffing is zero. It doesn’t matter
whether they bluff. So if I do this calculation
then ace 10– sorry, there’s a typo–
ace 10 is definitely in the top 61.5% of hands I
can have so I need to call. So I’m not building a
probability model for them. What I’m essentially saying is,
if I’m not calling ace 10 here then they can exploit
me by bluffing too much and I’m just folding
all my hands here. And they’re going to be able
to make money off of me. To prevent this I must
call ace 10, which is a 61.5 percentile
hand in my range, so they can’t exploit me. So I’m going to make
an analogy with RPS. Rock, paper, scissors,
does everyone know how to play this game? So you either throw a
rock, scissors, or paper. So there’s no way that you
would not know this game. I know people, if you grew
up in a different background you might call it
something else or you might have different rules. But the rules I’m playing
with is rock beats scissors, scissors beats paper,
and paper beats rock. So exploitative play
you think like this. You say, since my
opponent just played rock three times
in a row I think they’re probably not
going to play a rock a fourth time in a row. So I’m going to play
scissors because I know I can’t be beaten. Optimal play just says
I’m going to memorize a sequence of random
bits and always play each a rock, paper, and
scissors with probably a third. So this is an analogy with
rock, paper, scissors. So one question I often get it
is, if when you play optimally you’re making all
your opponent’s decisions the same then your
opponent essentially is never making a mistake
because regardless of what they do it’s the same. Then how do you make
money playing optimally? In rock, paper,
scissors that’s true. If my strategy is just
play rock, paper, scissors, each with a
probability a third I’m never going to beat you
more often than I should. But in poker there’s
enough opportunities to essentially be inconsistent. For example,
sometimes you will see players fold seven six suited
and then, because later they’re bored and feel like
playing a worse hand, they’ll call six five suited in
the exact same situation, which is like basically making a
strictly dominated strategy. Or like check raising a
circling theory range. Essentially, a theoretical
optimal strategy you will still extract money slowly
from even the best players. Because even the best
players in poker right now, there’s going to be slight
inconsistencies that are not theoretically optimal. So the optimal strategy,
another way to think about it is a Nash equilibrium, if
you’ve heard of the term. Because the best response
to the optimal strategy is the optimal strategy itself. Whereas the best response
to any exploitative strategy is going to be a
different strategy. Whenever you play an
exploitative strategy you stand to bee beating
by a different exploitive strategy that re-exploits you. This is a defense optimal plays. We play each with
the same probability. Optimal play you’re indifferent
to your opponent’s move. So optimal play, you’re
making a lot of money when your opponent does
something strictly suboptimal. Whereas in exploitative
play you make a lot of money when you’re winning
the mind games and you lose a lot when
you’re losing them. So exploitative play
is sort of like I know that you know that I know
that you know that I know this. But you know that I know
that you know that I know that you know that I know this. You get into these mind games. And if you’re good at them
then it’s pretty good. If you’re playing
rock, paper, scissors against a four-year-old
child, probably you don’t want to play optimally. Probably you want to
look at their face and try and figure
out what they’re going to do and try to beat them. But if you’re
playing rock, paper, scissors against the rock,
paper, scissors world champion, which there is one
actually, then probably you just want to memorize
the sequence of random bits and play each
probability a third. So another good thing
about exploitative play is it’s intuitive. We sort of grew up thinking
in terms of exploitative play. I think that’s a fair statement. In most things it’s like what
do you think might happen? OK, if that might
happen, OK, I’ll do this. But optimal play is sort
of a weird mentality thing because it’s sort
of like I’m just going to analyze what my
opponent could potentially do. So you need an
opponent essentially. And then I’m just
going to perform an action that makes it so
that my opponent can’t really beat me. So that’s enough about
those two general concepts. I’m going to take a short
break right here since it’s good timing. So I’m going to continue and
we’ll get in some actual poker. But first we’re going
to play one last game. We’re going to play a
game called Who’s Taller? Anyone can join the
content for a dollar. We’re not actually having this
so don’t get out your wallets. And then the tallest
person who joined the game gets the entire pot. So all the people
who join the game, we’re going to measure
who’s the tallest, and then that person
gets everyone’s money. So again, let’s play. So everyone, close your eyes
so that you can’t look in here. Everyone close your eyes. No peeking. No peeking at how tall– So I want everyone–
close your eyes. Is everyone’s eyes closed? So put up your hand if you
want to join the contest. Put it nice and high so
that I can see if you want to join the content. So raise your hand high. It’s OK. There’s no embarrassment. The whole point of
poker is where– OK, cool. So now everyone open your eyes. So I think five people joined. So you guys come down here. Let’s see who– [LAUGHTER]
Let’s see who won the pot. AUDIENCE: [INAUDIBLE] PROFESSOR: That’s OK. It’s totally OK if you lost. So I think the four of you. Sorry, what’s your name? AUDIENCE: Justin. PROFESSOR: OK. Justin. So I think Justin voted one. So good job Justin,
you would have made $3. All right. Cool. So what’s the
point of this game? The point of this
game is so from a game theoretic point of
view no one really should be playing this game. So this is only known as the
k-beauty game from game theory. So how tall are you Justin? JUSTIN: 6’5″. PROFESSOR: 6’5″. So why did you play the game? Because he thought there’s
probably someone who’s going to be 6’2″ who might
play the game, right? But if everyone knew that
if you’re only 6’2″ you shouldn’t be playing this
game because someone might be 6’5″ then you wouldn’t play the
game because someone else is only going to play the
game if they were like 6’8″ or something. So let’s say we
played this again. Probably only Justin would play. Eventually this always
devolves into a situation where basically no
one is going to join. Because you know that no
matter– even if you’re like seven feet tall,
you’re LeBron James, you would know that
someone would only played this game if they were
the tallest person in the world essentially. So basically poker
without blinds, which is the money
that’s put into the pot at the start of every
hand, would essentially be like Who’s Taller game. So when you play poker you want
the motivation of every hand to be stealing the
blinds, stealing the money that was
forced into the pot without the choice
of the person. So you would always
fold king king, which is the second best
hand in poker pre-flop, if there were no blinds. Suppose we were to play
Who’s Taller again. But I told you that I’m going
to force Lee Marie to play. OK So now we’ve got
a game because now, even if you’re not sure
whether you’re the tallest person in the room, if
you’re taller then Lee Marie then you have a
chance of winning. So that’s essentially why we
need blinds to have a game. So you always want to
think how many chips you have in terms of the blinds. So having $400 in front of you
in a game where the blinds are $1 or $2, for our purposes,
is equivalent to having $4,000 in front of
you in a game where the blinds are $10 and $20. Because essentially,
everything you’re wagering is relative to stealing
the blinds that were forced into the game at the beginning. So in both of
these situations we say that you have 200 bets,
or 200 big blinds, or 200 BB. So that’s how to
calculate your stack size. But what’s actually
important isn’t stack size it’s effective stack size. So effective stack
size takes into account the stack sizes of the people
remaining in the pot as well. So I’ll give an example. So in this case, we’re the
player with the ace jack. And we decided to go all in. So what is our exact stack size? The big blinds is 2,000,
the small blind is 1,000. And we wagered in total 42,000. So what’s our stack size? AUDIENCE: 20– PROFESSOR: 21, right. It’s around 21. It’s around 21 big blinds. But we didn’t really risk
21 big blinds here, did we? Can someone– OK, I’ll give
a $20 gift certificate. How much did we actually
risk in some sense. Yeah. AUDIENCE: I can’t
see quite well, but I think 12 and
one half big blinds? PROFESSOR: Yeah, exactly. I’ll remember it. I’ll put it here. So we only risked 12
and a half big blinds because everyone in front
of us has already folded. And the true players behind the
small blind and the big blind, one of them only has 7
and a half big blinds and the other one only has
12 and a half big blinds. Can everyone see that? So even though UTG plus two
has 32 and a half big blinds could have
theoretically covered us and could have theoretically
taken all our money. But on this hand, because
they already folded, we’re essentially only
risking at most 12 and a half big blinds. That’s the most we can lose. So we can’t be eliminated
from the tournament this hand. So here’s another example. So here you see
this guy that I’m going to call Low
Jack for now, you see him go all in
for 16 big blinds. So in this case, technically
he could lose all his money because we have more than 16
big blinds and we do cover him. But in reality, I’d say
he’s probably not on average risking 16 big blinds because
most of the people who could call him,
other than us, have way less than 16 big blinds. Does that make sense? So essentially, there’s
not like an exact formula for effective stack size. But you want to sort of
think of it in terms of you look at the stack
sizes of all the people who could potentially
play the hand against you. And you want to look at
roughly how much am I going to be risking in this hand. That’s effective stack size. Does that make
sense to everyone? So the second thing I
want to talk about that’s very important is position. So position is basically
where you are at the table relative to the blinds. So how many players
are remaining to compete versus
me for the blinds? Essentially, the
fewer players that are left the less strong my hand
needs to be attack the blinds. So I’m going to give
names for the positions. Basically the thing
that matters is how far you are from the button. So in this example
with ace jack, when everyone folded
to you and you’re the dealer, which is
also known as the button, essentially to steal
the blinds, you just need to get through the
two blinds themselves. So that’s essentially
two players. And then if you’re in
one position earlier, when it was folded
to cut off, then he had to deal with three players. So you want to name everything
relative to the dealer essentially. So we can just quickly
go through the names. They’ll get more
familiar as time goes on. So the first person to act,
we call them under the gun. So that’s this guy here. And then we go around the table. It’s under the gun plus
one, under the gun plus two. There can be different
names for the same position. So in this specific hand, where
there were only six players at the table, you could have
called Low Jack under the gun because under the gun
is the first person to act to the left
of the big blind. But essentially, it’s
more clear to say Low Jack because when you
say under the gun you have to say under the
gun at a six-handed table. And then people will
know that means you got to get through five hands. But if you say Low
Jack it’s very clear. You have to get
through five hands. So under the gun and then
plus two, and then Low Jack. You can also call under the gun
plus two, Low Jack minus one, if you want. And then High Jack,
cut off, button. Don’t ask me where
these names came from. I actually have no idea. And then small blind, big blind. So that’s position. And the importance of position
is basically the later you are the fewer hands
you got to get through to steal the button, to steal
the blinds of everyone who’s already folded. So the third thing that matters
in a poker game is equity. So we talked about stack size,
we talked about position. The last thing is
actually your cards. So the equity of your cards is
basically your secret height for the Who’s Taller game. So you can think
of it like that. Your cards is like
your secret height. And the probability of
you winning the pot, or equivalently, the
fraction of the pot you would win once the
remaining cards are dealt is called your equity. So I’m going to give some
examples of calculating equity. So here’s an example where
we get it all on the turn. And so I have five four
states spades here. So I’m not in a great position. But let’s count how
many outs I have. So this one I want to just
name a river card that would help me win the pot. AUDIENCE: Seven of spades. PROFESSOR: Yes. AUDIENCE: Seven of spades. PROFESSOR: Seven of spades. So that gives me a straight
and a flush actually. So let’s go along those lines. So how many spades are
there left in the deck? AUDIENCE: There
should be nine spades. PROFESSOR: Right, nine spades. And then how many cards help
me make a straight here? AUDIENCE: Six more. AUDIENCE: Seven or a two. PROFESSOR: Right. A seven or a two. So it’s six more because
there’s eight sevens and twos. But I’m double counting
the seven of spades and the two of spades. So that’s nine plus six. And then I actually have
to subtract one more card. Does anyone see what it is? Yeah. AUDIENCE: The queen of spades. PROFESSOR: Right. The queen of spades
because that’s actually a disastrous situation because
then if it wasn’t all in I would probably put more
money in the river thinking I have a flush and
lose to a full house. So it’s 14 outs, 17 minus 3. Our equity is around 32%. It’s 14 over the 44 cards
that could still come. Did that make sense to everyone? So that’s one way of
calculating equity. It’s just a very simple
probability distribution over the remaining cards in
the deck that could come. And if you’re worried,
what if someone folded the queen of spades so
I shouldn’t be counting that? Essentially, you
just want to pretend that the cards that
are in the muck, like the cards that were
folded by other players, they’re essentially irrelevant
because they could have folded the queen of spades. But they could have also
folded an irrelevant card, like the jack of
hearts or something. So essentially you just
want to all the cards that you haven’t
seen, it’s easier to just assume that they
don’t affect anything. In theory they
affect things a bit because if you know that the
dealer button folded two cards, even if you don’t
know what they are, they’re probably
more likely to be really crappy cards, like twos
and threes rather than aces because if they had an ace
they would have played it. But I think not worrying
about that is fine. You don’t need to
worry about it. Another example of
equity calculation. So it’s the exact same
example as before. But in this case, the
probability distribution isn’t over cards
that could come. All the cards have already come. The probability distribution is
just over my opponent’s hand. So this is the same calculation. We calculated our equity is 25%. And that’s not a
probability distribution over cards to come. That’s a probability
distribution over our beliefs of
our opponent’s hand. So example three of
calculating equity. So this one you can’t
really do by hand. Let’s say you get it all in
pre-flop, with ace king suited against pocket twos. And you basically
need a calculator. There are certain websites
that help you do this. And ace king suited
against pocket twos, if they don’t have
a two of your suit is actually a very small
favorite which is cool. But if you have
the two of hearts then you’re actually
a slight underdog. So just make sure for
all the different things equity could mean. Equity could mean a probability
over river cards, probability over the unknown. A very good
calculator in general is PokerStove,
which all have lots of examples of in my slides. And you can download
it via this link here. So this is an example
of using PokerStove. You can put in
exact calculations. Let’s say you get it in with
two of diamonds, two of spades. So pocket twos on the flop of
5, 3, 2 versus a range where you know your opponent is
going to have a big pair, like pocket jacks plus,
you can actually run it and your equity is 85%, which
is actually surprisingly low, I think. Because it seems like
you’ve got three of a kind they’ve only got a pair. They have two chances
to hit one of two cards. But there’s a lot of random
stuff that can happen, like if they have aces
they can make a straight, they can make a back
door flush, the board could come two more
fives, which counterfeits, or three of a kind deuces. So this is another example
of calculating equity. So this is just a summary of
the different situations you might want to calculate equity. And I recommend you
download PokerStove. But you don’t really have to. And I guess one
question you could ask is how do you actually
do this at a table? So essentially, if you do
this a lot while you’re studying about
hands and thinking about poker, eventually– I’ve been able to– you just
memorize a lot of situations in general what the
probabilities are, or at least what the
correct decision is. So now let’s talk about raising
two win the blinds and antes. So the antes, an ante
is an extra small bet that each player must put
into the pot each hand. And these sum to
around a big blind. And they come in during the
later stages of a tournament. And they’re inexistant
in cash games. I stuck this under the rug
in the earlier examples. So in– let me go
back– so like in here. Do you see the
1,200 in the middle? So actually stuck
this under the rug. But that comes from
each player being forced to put in 200, which
is 1/10 of the big blind, at the start of every hand. And if you’re playing
tournaments then this would usually be the case. Antes will come in fairly soon. If you’re playing cash games,
where you just sit down and you can leave
whenever and you sit down and just play for
your own play money, then there’s usually no antes. But antes actually make
a world of difference in terms of what you want to do. It’s not just the stakes are
bigger when there’s antes because you don’t
want to just think of it like there’s extra
money in the pot every hand. It’s equivalent to the
blinds being bigger. That’s not true because you
also have to put in an ante. So if the blinds were
proportionally bigger to cover the antes you would
have to raise to a bigger size to try to steal the blinds. But with antes you don’t need
to raise to any bigger size to try to steal the blinds. So it’s actually
very action driving. It’s very exciting. It makes it so
that your basically want to play a very
wide range of hands. And you really just
want to be trying to win the blinds as often as
possible because winning one pot with the antes is so big. So this is what it looks like. So the first thing
I’m going to say is if you’re going to start
playing tournaments tonight is if no one has raised yet you
really, you don’t want to call. You want it to raise
to give yourself a chance of winning the
blinds without seeing a flop. So I’d say the most
common beginner mistake I see beginner poker
players make is not raising when no one has raised before. So in this case, it would
be just calling for 2,000 and trying to see a flop. But the main issue
is you’re giving the big blind they
can just check and see the flop for free. Whereas if you raise you
put them to a decision. And they might fold,
and you might just win the pot for
free without having to do anything essentially. So how much do you
raise when I say raise. The minimum raise
size you can do is raising to two big blinds. However, this is a
bit small because you give the blinds fairly good
odds to make a profitable call. Although, it’s
not even that bad. So let me just talk in
general about raising big versus raising small. So the advantage
of raising small is that you’re risking less. Like let’s say you raise and
then the next person re-raises, and then the next
person goes all in. So you know probably those two
people have pretty good hands and you want to fold. If you raise to a small
size then you can fold and you don’t lose that much. If I raise to five big blinds
then I’m losing a lot more. But what’s the
benefit of raising big is you give other people
worse odds to call. If I only raise
to two big blinds, let’s actually do
this calculation. Let’s say here, instead
of going all in I raise two big blinds,
which is 4,000. What odds am I
essentially giving the big blind you call to call? So this is actually, in
this very exact situation, this is a very common
mistake I see beginners make, which is you raise
to only 4,000. Yeah. AUDIENCE: So there’s
8,000 that’s in the pot and they have to call
2,000, so it’s 21? PROFESSOR: Right. So it’s 41. But there’s also a small blind. So there’s actually going to be
9,000 essentially in the pot. Yeah. So it’s going to be 8,800 in. It’s going to be 8,800. So approximately 9,000. And they only have to
call 2,000 to see the pot. Does that make
sense to everyone? So the odds are
actually 4.5 to 1. And ace jack off-suit
is a great hand. But there’s no
hand that ace jack off-suit is more than a
4.5 to 1 favorite against. So in some sense, basically,
even if they have jacks two, or whatever, ace two, think
of the best possible case, you’re still not doing
better than the odds you’re giving them. So on the other hand
though, it is really risky to raise more than 2.25. So a reasonable rule
of thumb, I’d say, is to raise to the 2.25
big blinds in tournaments. I know it’s pretty close to do. If you just raised to two
it’s probably not that bad. But roughly speaking,
I think this is a reasonable rule of thumb. Earlier you could
try to raise to more. I think that’s
sort of customary, although I don’t think
it’s theoretically optimal. You’ll often see
players raise to like three blinds, especially
when you watch pro players. They’ll raise to bigger. But the main reason
is because they’re the better player by
a lot and they’re just trying to make big pots,
which is reasonable. If you’re trying to
just play big pots and win big pots then raising
to the bigger size is fine. But I don’t think there’s
any theoretical reason to raise to more than 2.25
big blinds in most situations. Other than when in cash
games, where all players have a lot of money, then
it’s a bit different because also in
cash games you’re not worried about risking
more because you’re not worried about losing
out of the tournament. So the other thing is instead
of raising you should just go all in if the effective stack
size is 12 big blinds or less. So recall, the rational
for raising big is to prevent others
from calling for cheap. But the rational
for raising small is to lose less if we get
re-raised and have to fold. But 12 big blinds is sort of the
point where it’s small enough that you never really want
to fold after committing 2.25 big blinds. So if I only have 12 big
blinds, I raise 2.25, I’ve only got 9.75 left after. OK, fine, if I get raises and
re-raised maybe I’ll fold. But even if I get
re-raised once, if I’m raising in
the first place my hand is going
to be reasonable. If it’s a Who’s
Taller game I’m not going to raise in
the first place if I’m 5 feet, or something. So your hand will be reasonable. So this is beginner mistake
number two is being too scared to go all in pre-flop. So that’s why this ace jack
hand, I actually cheated a bit. So technically here, the
effective stack size is– the big blind has 12
and a half big blinds but the small one
only has 7 and a half. So I roughly said, the effective
stack size is less than 12, and I just went all in. So that’s definitely a
beginner mistake number two in tournaments is to be too
scared to go all in pre-flop. So what your goal essentially
should be– oh, sorry. I should say the rule is– so all of the numbers I
said assume there’s antes. If there’s no antes you should
change to 10 big blinds. So the threshold
for going all in should be less because
when there’s no antes you want to be risking less
because the pot is smaller. So overall, when I
talked about position I talked about stack size. Essentially what I’m trying
to get the point across is if you’re just
starting out, players tend to make all decisions
based on their cards. It’s just like, I
have a pair of jacks. I see my pair of
jacks on this board. I have a pair
that’s pretty good. And you sort of tend to ignore
what the effect of stack size is, how much you’re
wagering, and position. But experienced
players, the cards actually matter much,
much less to the. In fact, if you’re
doing optimal play you don’t care in some
sense what your cards are. You just care what your range
of cards are at that point. So experienced players, they’re
willing to raise the blinds with much weaker hands
from good positions rather than early positions. And they’re going to
risk going all in a lot more frequently with
a lot worse hands if their stack size is low. So I want you to
think about that. So if you’re just
starting out that’s fine. If you’re still
trying to figure out whether you have a straight and
stuff like that, that’s fine. And it’s totally fine
if you try to play based just on your cards. But I want everyone’s goal
by the end of the class to be able to play based
on these other factors more so than your cards. So that being said,
I’m going to give you some concrete suggestions
for those of you who might want to start
playing tonight of what hands you should be playing
from each position. So most of the tournaments will
have nine players per table. So this is going to be roughly
a range I recommend to open. So these are the
range of hands you should be playing from
the worst position, so under the gun at
a nine-handed table. So there’s eight
players left behind you. You can pick up
really good hands. So it’s aces, kings, queens,
jacks; ace king off-suited; ace king off-suit; 10s; ace
queen suited; ace queen off. So that’s basically
the list of hands. These are only premium hands. This is like 6.2%
of hands, I think. It’s a very premium range. So note how tight this is. Because the thing to
remember is only the best hand out of nine hands at the
table is going to get the pot. When there’s nine hands, even
though the average hand is really bad the best
hand out of nine hands is always going
to be pretty good. So to even think that you have
a chance you need to start out with a very premium hold ’em. Roughly, what do you add
as you go around the table? So for the second position– I’m going to post all these
slides before the tournament starts, by the way. So you don’t feel
that you scramble to write all this down. I’m going to post it. From the second position,
I put in black the hands that I would open from
the previous position. And I’ve put in red the
hands that I would open from that position in addition. So second position
there’s one less player. OK. I’ll gamble with sevens, ace,
jack, king, queen, ace 10 suited. So we’ll get around
the table and then the range will slowly increase. Also note that these are
very conservative ranges. If you watch high stakes
poker, probably the players will open a lot more hands than
what I’m recommending here. But my general
experience has been when you’re just starting
out to play poker it’s much easier to err
on the side of being too tight than being too loose. Because it’s in some
sense a lot easier to play pocket aces
than seven five suited. With pocket aces
you’re always going to have a pair of
aces or better. You just back that bet. And then with seven
five suite you need to be able to
bluff very carefully, you need to sometimes be able to
try to get value when you just hit a pair of sevens. And it’s just a lot harder. So the ranges I’m
suggesting are very tight by most poker standards. By tight I mean conservative. But I think that’s
the right side to err on when
you’re just starting. So these are the ranges. As we get to the later
positions, so this is Low Jack, we’re opening more hands now. Any two suited Broadways. So that’s hands like jack
10 suited, queen 10 suited. It’s basically
any two cards that are the same suit and
both 10 or higher. So maybe I should just
run through this quickly. So why is having your
cards be suited good? AUDIENCE: You get a flush. PROFESSOR: Right. So if it suited you’re more
likely to make a flush. But if have two unsuited
cards then there’s two different flushes
you could get. If you have queens or
diamonds, 10 of spades is going to make a diamond
flush or a spade flush. Essentially, that
argument is wrong because there’s two
reasons why it’s wrong. One is it’s not more of a
play because you need four of the suit to make a flush. And two is, when you make the
flush it’s also more obvious you have the flush. like If you only have
one diamond, even if it’s the ace of
diamonds, once there’s four diamonds on the
board it’s way more likely that you have a flush. So you’re going to
get paid off less. Whereas if you have two
diamonds in your hand and there’s only three
diamonds on the board it’s less susceptible
that you have a flush. So high jack is
three to the button. So this is what I
would recommend. So any pair, pairs
are pretty good. Any suited ace, so
suited ace means any card with any hand with an ace and
another card of the same suit. Any suited connector. By that I mean hands
like basically two cards that are next to each other and
also the same suit, like 10, 9– 10 of spades, nine of spades. Or any two unsuited
Broadway cards. So I do use a lot
of terminology here. So yeah, please stop me
if something is unclear. You can google most
of these, I think. And suited connectors are good. So like a hand like
seven, six suited is often better than a
hand like 10, 6 suited, even though the trend
is bigger than the six because ten is sort of a
small enough card where it’s not that relevant, the
fact that it’s a big card. But the fact that
seven, six is connected and can hit a lot more
straights is very relevant. So we’re if we’re
cut off I’m just going to show you on
PokerStove because there’s too many to list. But the thing I want you
to know is the percentages. 30%. So remember, under the gun
I recommended playing 6%. So we’ve multiplied
how bad our hand could be for us to play by five. And I think this is what I
really want you to try to do. And I think what a
lot of new players don’t do enough is they always
play the same cards regardless of their position. And then even crazier,
on the button, if everyone in
front of you folds, I recommend them playing
about 55% of hands. This is huge. I want you to play
jack three suited. Who thinks jack three
suited is a good hand? Or king four off-suit,
or queen six off-suit. What hands do we play
from the small blind if it’s folded to you? So let’s compare opening from
the small blind to opening from the button. So for small blind it’s
a bit different now. So I should mention
this because when you’re raising from the button,
from the dealer, if you get called you get to
act last post-flop. So I’m going to talk more
about this in future lectures. But this is basically called
having position post-flop. And having position
is basically good. Yeah. AUDIENCE: For all
these hands, are you assuming that everyone’s
folding behind you? PROFESSOR: Yes, yes. If people haven’t
folded, essentially, I’ll talk more about this
in future classes but essentially what
you need to do if– so let let’s say this guy
raised and you’re the button. Essentially you need to
consider what his range is and calculate your equity
against his range, which you can do– AUDIENCE: The calculation
is completely different. PROFESSOR: Right. So the calculation is
essentially completely different. So essentially the
first guy who raised determines what the barrier
to entry to the pot is. Because essentially
the first guy that raises, if it’s from under
the gun, he’s telling you, my range is pocket eights plus. Even if he’s sort
of loose it’s still going to be pocket fours plus
and queen 10 suited plus. Basically it’s saying, if you’re
playing eight six suited then you’re basically in
idiot, because my range is way better than that. So essentially the first guy
who plays this hand sort of sets the tone on how good
your hand needs to be. Thanks for that question. So I’ll talk more about
this in a future lecture. But essentially that’s
what you need to do. So from the small blind let’s
compare opening the small blind from opening the button. So the issue with
opening the small blind is if the big blind
calls you actually don’t have position post-flop. The big blind gets to
act after you post-flop. Pot. So it’s actually a lot
worse in some sense than opening from the
button because you don’t get you act last. But it is better in the sense
that there’s one fewer person to get through. And also, you have less to
wager, which is actually really relevant because
from the button, if the blinds are 2,000 or 1,000
or OK, let’s just dictate it. So if the blinds
are 20, 40, if you want to steal the lines from the
button and you want to do 2.25 you need to put in 90. You raise me 90 and
you need to wager 90. But if you’re raising
from the small blind you only need to put in 70 more. So you’re actually
paying a smaller price to try to steal the blinds. But the fact that
you’re out of position is a very important negative. So I’d say all these
factors balance out. And you can roughly play
the same range of hands from the small blind as you
would from the big blind. I think that’s a
reasonable rule of thumb. But the fact that
you’re out of position hurts a lot less as stacks
get shallower, essentially as effective stack
sizes get a lot smaller. So you could really
drastically increase this range if you only have 10 big
blinds from the small blind. So let me just give a
few caveats about this. So actually, I’ll
leave it to you guys. If someone comes up with
a very good complaint about these recommendations
I’m giving you I’ll give up the
last $20 gift card. So what are some problems? Normally I get lots of
complaints in this section. You already got one
but you can answer. Yeah. AUDIENCE: They’re very
predictable so it’s unusable. PROFESSOR: Good. That’s a very good point. A lot of people ask me,
why would you follow these? If I follow these everyone
knows what I’m doing. Well the point is, for most
of these, even this range, it sort of encompasses
enough hands. So this is where I’m talking
about optimal balance play. I think even though humans
haven’t solved poker, I think roughly,
if you want to ask, I would guess that roughly
the optimal range of hands you open from this position
is something like this. It’s going to be looser. But it’s something
roughly like this. Probably you want to
probabilistic play some smaller cards just so when the
flop comes 2, 2, 4, you can potentially have a two. But essentially you’re
not doing bad here because if the flop comes
three small cards then you were going to be
doing pretty well with all your big pairs. And if the flop
comes the big cards you’ve still got ace king, ace
queen, ace jack in your hand. But not that is
a good complaint. So in theory, it’s
in theory optimal to play seven seven some
fraction of the time, six six some
fraction of the time, and two two some
fraction of the time. But that’s making things
really complicated. I don’t want to add
two two to the list because if you play two
two every single time then that’s way too loose. You’re just spewing money
by raising with two two against this many
players behind. So ideally maybe
with two twos you should do a random
number generator and 10% of the time you play two two. That would probably be
theoretically optimal. OK, good. That would have gotten this. But OK, I’ll give it to– Yeah. AUDIENCE: I think another
problem with playing really tight all the time is that
you are also very easily bullied around the table. If someone bets and you
really want to play, you really want to stick to
your tight range, you’ll fold and you’ll maybe
miss out on something that you shouldn’t
have depending on your position,
and things like that. PROFESSOR: OK. Good. So yes, these are
pretty tight in that it does give the other
people incentive to raise a lot
because everyone’s going to be folding a lot
because you are just waiting for these really good hands. OK. That’s good. Are there any other questions
about these suggestions I gave you guys? Or are there other
potential complaints? I’m going to give this
gift certificate to you unless someone thinks that
they have another complaint. So I’ll give this
to you at the end. This is one thing that
I didn’t really address. I talked about going all
in as well as just raising. So how do these ranges differ? The answer essentially is
they don’t really differ. So let’s say, here, these are
the hands I told you to play. Let’s say you were
sort of small enough, you only had 12 big
blinds with antes and you were
supposed to go all in instead of raise, which of these
hands do you go all in with? It’s roughly the same range. I think that’s a
decent rule of thumb. If you just go all in
with the same range you’re not going
to be doing badly. But when the effective
stack size is much smaller, like let’s say you only
have three big blinds, then you can drastically
increase this range. So when your
effective stack size is actually say 10, or let’s
say your effective stack size is five big blinds, intuitively you
might think, I can wager a lot, I can wager a lot
wider range of hands. So here’s the argument. The argument is I’m only
risking five big blinds. In the other case I was
risking 12 big blinds. I should be way more
aggressive with five big blinds than 12 big blinds. So that’s the argument. But the reason why
that argument is wrong is because with five
big blinds you’re going to get called every time. With five big blinds
you can’t just go all in with
seven two off-suit because your opponent has
such good odds to call, they’re going to call you. Whereas with 12 big blinds,
even though you’re risking more you also have more chances
of getting everyone to fold. So even though it seems like
you’re risking way more, in some sense you’re not. Because the more chips you
are risking the more likely it is that everyone else folds. Does that argument
make sense to everyone? So make sure you don’t
get tricked by that because it is easy
to get tricked. But the fact that when
you’re risking more you’re getting
people to fold more means you’re
actually not risking as much as you think you are. And that’s a common fallacy. So we’re near the last
part of the class. So are there any
other questions? I know some of you probably
want to start playing tonight, and I definitely did not
address everything you need. But are there any
other questions roughly, in terms
of opening and going all in that you might want to
know before playing tonight? Because I do think we have
maybe five extra minutes. So I can answer some questions. Does everyone not know what
the term “bluff” means? I said bluff a
bunch of times but I realized I never explained. So bluffing essentially
means you have a bad hand and because you have
such a bad hand you know the only way of winning
that is to get your opponent fold. So basically you bet big to
hope that your opponent folds. If you have a better hand,
like an average hand, often you actually
don’t want to be betting because there’s no point. Because when you bet you’re
essentially just getting adversely selected, where
your opponent calls you when their hand is better
and you lose more money to a better hand. And your opponent folds
when their hand is worse so you’re not making any
money from a worse hand. And then with your
best hands, you want to bet to try to get your
opponent to call and increase the amount that you win. And we call this value betting. So I’m going to get more
into this in future lechers. But essentially in poker,
the paradigm you want to play is you want to value
bet your very best hands and then you want to
basically check and try to get to show down, like try
to show your hand on the river with your medium hands. And also bet with your bad hands
to try to get your opponent to fold better hands. I’m going to get to
the last part now. So quick test. So here what would you do? It’s folded to you. You’re in the high jack. You have ace, five of clubs. So someone want to
suggest what would you do? What would your play be? AUDIENCE: Call. AUDIENCE: Bet. AUDIENCE: Raise. PROFESSOR: Raise. OK, good. Raise. So not call. That was mistake
number one to not do. You always want to raise
the blinds if it’s folded. But it’s fine, it’s fine. That’s fine. We’re all here to learn
about these hands. Now should I go all in
or should I just raise to 450, which is 2.25? I should go all in. OK. I think it’s not terrible
if you just raise to 450. But I said if it’s 10
big blinds– there’s no antes so you need 10 or less. And you have 10, so going
all in I think is fine. So we decide to go all in. So there are Nash calculators. They’re complicated. But if you run this through
a Nash equilibrium calculator this is roughly what you
should be going all in with. So we go all in. So this range is a bit different
than what I showed you before. This is an actual Nash
calculation just not just my recommendation. It’s going to be wider than what
you saw before but that’s fine. So now you’re this guy. You’re seat nine. So I’m going to show you how you
do a quick calculation of what equity you need to call here. So what equity you
need to call here. A straight up pot
odds calculation says you’re getting
23 to 20 or 1.15 to 1. So roughly you need 46.5%
equity to call as this player. But there’s two players behind. There is a graphics glitch
because seat one has not folded. Seat one and seat
two both has cards. So you actually
need more than 46.5% equity because the
calculation of 46.5% assumes seat one and seat two
can’t wake up with pocket aces. PokerStove is very
good for this. And you can do this right now. I’ve taught you everything you
need to do these calculations. And PokerStove is also easy
to figure out how to use. You can essentially
just plug in. You look at pocket
fives, it has 48%. You need 46.5%. And I said you need a bit
more than 46.5 due to the fact that there’s two players
behind so pocket fives, it’s good enough. Well, I’ll call ace nine suited. I’ll call. So I’m just showing you some
calculations on PokerStove. It really is a really good tool. So you can do some calculations. So basically they call. And the hands I showed
you here is actually sort of the worse hands that
it’s plus CV to call with. Pocket fives, ace
nines suited plus. So aces nines suited plus means
ace nine suited, ace 10 suited, ace jack suited, all the
hands that are strictly better than ace nine suited. Ace 10 off-suit,
king queen suited. As the last player here, do you
call with king queen suited? It’s just a rough guess. How many of you
intuitively would call with king queen suited? Two players have
already gone all in. So most of people would fold. Oh, you guys would call. So it turns out,
at least according to the Nash calculator– So here you calculate
the pot odds. And this is an exact calculation
because there’s no more players behind. So just calculate, do
I have 29.5% accurate? Basically if I assume that
player one and player two are playing according to Nash
equilibrium or optimal ranges, you actually have
way more than enough. You actually have 34%
where you only needed 25%. So this is a trick
question I set up. The trick was king queen suited
doesn’t seem like a good hand. But against two other hands it’s
actually relatively a very good hand. Against one other hand,
they could just have a pair and you’re behind. They could have an ace most
of the time and you’re behind. But against two other
hands you actually have really good equity because
when you hit a king or queen you have the big pair. You can also hit
straights and flushes with king queens suited. And your equity against two
other hands is very good. So you have way more
than enough so they call. So we’re going to get
in this all in freefall. So who are the people
I gave these cards to? You guys can come
up to the front and I’m going to
hand you your cards. The people who I gave these
gift certificates to, I said. AUDIENCE: Do you want
me to stay up here? PROFESSOR: Yeah. Stay up here. So what I want you guys to do– these are the hands
people went all in with. Who was the first
person to answer? OK. So you get to pick. Which hand do you want? AUDIENCE: I’ll go
with jack jack. PROFESSOR: OK. So Colin is going to jack jack. Sorry, what’s your name? AUDIENCE: Kevin. PROFESSOR: Kevin. Kevin, which hand do you want? So he took jack jack. Which of these remaining–
you were second, right? Yeah, you were– OK. AUDIENCE: I was last. PROFESSOR: OK. Which hand do you want? AUDIENCE: I want king queen. PROFESSOR: OK. So he’s going to
take king queen. So you’re going to
take ace five plus. This is sort of mean but
I want to show you guys this how poker works. When you’ve already
won, you’ve won $20. You guys are going
to put in your hand and whoever wins this hand
is going to get all $60. [LAUGHTER] We’re going to go for it. So this is the free
flow of equities. So it is pre-determined. So it looks like you
guys did very well. You guys picked correctly. You got to pick first. You picked the best hand
with equity of 34.73. You got 32.95. You’re only a bit
behind with 31.1. So the flop is 6, 7, 8. So let’s look at the
probabilities now. Jacks is still ahead, ace five
has picked up a lot of outs. King queen of diamonds
is not looking too good but they did pick
up one diamond. Notice the nine of hearts. So, sorry. Like Queens. I’m sorry. So you’re out of the running. AUDIENCE: He needs a 10. PROFESSOR: 2 to 1 to cheer. Is there any card
you’re hoping for? What are you hoping for? AUDIENCE: I think a 10. AUDIENCE: A 10 or a heart. PROFESSOR: So you
want to be screaming. I’m going to press it
on the count of three. You want to be
screaming 10 or higher. And you want to be screaming– AUDIENCE: Anything else. PROFESSOR: So I guess
you got all three of us. There’s going to be
more of these good card stories in class. So participate in
class, you’re going to get gift certificates
courtesy of [? Acuma ?] Capital. All right. Thank you guys. [APPLAUSE]

Posts created 2633

21 thoughts on “1. Course Overview and Introduction

  1. AYYYYYYYY! Now I can learn about quantum physics while I feed my crippling gambling addiction! Thanks MIT

  2. @MITOpenCourseWare could you write the title of the course in the video title? F.e., this course in my feed just says "1. Course Overview and Introduction". Overview of what? Introduction to what?

  3. Will Ma – as a fellow MTG player, I'm disappointed that nobody recognized the iconic flavour text on Mana Leak. Reply to this comment if you're reading this!

  4. At 34:08 how did you calculate the outs? if you have 52 cards in the deck and you have 4 on the table, 2 in your hand and you put the oppoint on QQ that means there are 44 cards left in the deck to draw from. Then you take the cards you need to make a good hand (your outs) you need to subract that from the remaining cards, so you have 14 outs subtract that from 44 and you have 30 cards left giving you ~30:14 out odds, reducing that gives you ~2.2:1 odss so ~32%.. is this just another way of calculationg the odds not the %?

  5. At around 11:20 (the example ov level 2 reasoning), why are only AK through A8 considered? Hands like AA or A3 could change the outcome quite profoundly.

  6. J Tilly gets a bad rap for that infamous hand because she stated that she thought Patrick had Ks, which was unlikely considering the betting sequence.   But K-T, K-J or K-7 would have her beat as well, and he could easily have slow played that from the flop with a pair and K kicker, waiting to see if she would show her strength on the turn.   When she didn't, he could've stolen the pot by betting on the river by making her think he had one of those hands, or even K-x if he didn't put her on a boat.   So yeah, the stares from Ivey and J Harman were funny, but Antonius could've and maybe should've stolen that pot when she fast checked on the river.

  7. I think the first person should have gotten the giftcard because thats roughly what he meant with "you reveal alot of information about what your hand is" – Since your opponent also builds ranges for you, you are readable to if you play that structure.

    Great video overall tho

  8. I'm confused from the part where the class starts to the end. But I guess if you know what Texas holdem is you won't be confused.

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