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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]

Yea! Now with fixed sound. =D We'll get the subtitles added in a moment.

where is the lesson titled "probability and statistics of phil hellmuth getting owned"?

This is a class? What?

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

I love this

MIT is so disappointing

@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?

You ask for donations and put out a video on Poker. 😆. Sad

brought to you by pokerstars.fuck….

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!

This is so entertaining.

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 %?

I have a problem: how do you keep all that data in your head?

Count how many times he says "essentially."

Thank you for this great workshop. I appreciate the effort of both MIT and the great teacher!

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.

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.

I can't believe more people don't know about this. Thanks for creating it.

Why is 21:8 = 2.56:1?????

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

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.