game theory in hold em - please help, math experts

[LuckYou777]

how do you use game theory in NL Texas Hold'em? I have a basic understanding of it in stud, but I have no idea how game theory can be used in a game where the opponent can see the board. (example- in stud, you are drawing to a flush, and your orrponent puts you on a flush draw. you miss youir flush, but bluff with one of your "key cards." your opponent folds. but suppose you were drawing to a flush in hold em. your opponent puts you on a flush draw. you miss your flush, and bluff at a key card on the river. your opponent, seeing that it is a blank, calls.) this seems to make game theory useless in hold 'em. but sklansky talked about using it in his heads up match with phil ivey.

can anyone provide me with thorough explanations as to how you use game theory in texas hold 'em, specifically no-limit? any examples would also be very much appreciated.

best of "luck".

/images/graemlins/club.gif monte green /images/graemlins/club.gif

[jgorham]

I guess I will make an attempt to tackle this. However I must warn before I begin that part of my motivation for writing this post is to make sure I understand it correctly - so criticize any and all errors you find please!

Ok, so the first thing you need to understand here is that game theory is a mathematical quantification of the decision making process. This process, in poker, is simple: bet, fold, check (or raise). All of these decisions are made for rational reasons - you think you are ahead/behind, you are bluffing, you have great equity on a draw etc. This is generally a very good thing - obviously you want your decisions to be the best possible decisions. But what if you are up against an opponent who understands your reasoning behind any decision, and therefore can read your hand quite easily based on your bets? If you continue playing your hands in the same way you will never beat this player.

Before I go further it should be noted that game theory is *only* useful against top players who you feel might be able to read you very well. Against bad players, just make the right move. If you find yourself heads up against Phil Ivey, you need to do something to take away this edge he has on you.

Second note: game theory is only useful if your opponent would *know* your cards based on your betting patterns. If you exhibit some physical tell that tells him/her your cards, then game theory wouldn't be effective, as it deals with varying your actions randomly.

Now, back to game theory. In the example you provided, you have alreadly lost. Your opponent knows you are on a flush draw, and the flush didn't come home. No matter what you decide to do on the river, you aren't winning the pot. but how did your opponent know you had a flush draw? At some point, your rationale was visible through your betting patterns, and your wise opponent picked up on it. This is where game theory comes in.

Lets say you hold A /images/graemlins/heart.gif5 /images/graemlins/heart.gif, and two hearts hit the flop. You decide to make a bet of one quarter the pot, so as to prevent your opponent from betting an unfavorable amount, and to possibly pick up the pot right there. Against most opponents this is a fine way to play the hand, but against an opponent who understands your rationale you just gave your hand away (most likely because he has been carefully watching what you do when you flop a flush draw heads up out of position).

But suppose you decide to play in the above manner 50% of the time, bet half the pot 25% of the time, and check 25% of the time. And lets assume if you flop a made hand you will bet half the pot 50% of the time, bet a quarter of the pot 25% of the time, and check 25% of the time. And with nothing you will check 50% of the time, bet a quarter of the pot 25% of the time, and bet half the pot 25% of the time. Even if your opponent knows you are making your decision this way, there is no possible way your opponent can know your cards, thus his edge is removed.

The essence of game theory is in crafting the percentages at which you should randomize your actions based on the situation, so that your expectation is positive no matter how your opponent acts. This is very difficult in NL holdem (perhaps even impossible in some situations), but you can still utilize the concepts of game theory to reduce your expert opponents edge over you by randomizing your actions.

In your example you talk about betting on specific cards - i.e. in a stud game where you are drawing to a flush you will bet your flush, or any ten or nine. That is the mechanism of game theory, not the theory itself. Other mechanisms you could use would be to look at the second hand of a watch (thank you Mr. Harrington), or squeeze one of your hole cards so you don't know what it is either.

In any case, the lesson to be learned here is not to be predictable, or if that is unavoidable than make your decisions randomly /images/graemlins/cool.gif

[LuckYou777]

excellent response, very much appreciated.

still a few questions- sklansky's game theory section in ToP, the one with the drawing to the wheel in single draw ace to five, he based his decision of betting so that pot odds offerered to his opponent were the same odds against him bluffing, calling it ideal bluffing strategy. do pot odds play a role in game theory usage in No-Limit hold em?

and any link to harrington's second hand of the watch quote, or example of how to use it? 'preciate it.

/images/graemlins/club.gif <font color="green"> monte green </font> /images/graemlins/club.gif

[jojobinks]

it has the exact same application to NL. ideal bluffing rate is always tied to pot odds.

harrington's second hand system is a way to randomize his betting patterns as well. different, but similar. by changing his betting patterns randomly (by his watch), he makes it impossible (or much much harder) to know what he's holding.

[Jdanz]

This is one incredibly small element of game theory. It's accurate, but the basis of all game theory is Utility (for poker: read EV) and there are far more uses for it then randomization.

All odds stuff is game theory, but that's asy stuff, if you want more difficult stuff bayesian theory is the game theory of hand reading and calculated what hand your opponent has based on hand ranges and probabilities.

There's pleanty of other stuff but it's kinda silly to go into it all as everything that takes EV into account deals with game theory in some way.

-JDanz

PS : The other most useful thing i've found is you can use game theory, in the form of mathematical EV calculations to see when it's profitable to push with what hands when folded to on the button in a SnG or Multi-table. The result it's very often correct to push with any two.

[LuckYou777]

well, you had me at hello, but lost me at bayesian theory.

there are plenty of game theory sites, but any specifically made for hold'em?

i appreciate all the great responses. good to know there ARE 2+2ers willing to help a lesser player.

best of "luck".

monte /images/graemlins/club.gif

[Mark1808]

jgorham, Excellent summary thank you! I am still unsure how to randomize my bluffing on the river because my previous betting pattern and the visable board give too many clues. Slansky's example used 5 card draw where there were not visable cards. I am wondering if it might be proper before the hand to use a random generator to trigger a bluff before the hand even starts. For instance if you want to bluff 10% of the time if your watch second hand is on the firtst 6 seconds before the hand you play it like you have AA no matter what. Just an idea. I have seen scarecely any material devoted to optimum bluffing strategy in hold em.

Anyone looking for a more complete discussion of these concepts should get "Theory of Poker" by Slansky, it is a must read for an serious poker player!

[Jdanz]

most common random generator is look at the second hand on your watch.

[Jdanz]

i don't know of any holdem sights, but if you look up poker and bayesian you might find something.

I'm exahusted right now so i'll give you a real quick example

Blind 10/20
Someone raises in EP to 75 you're in LP and reraise with Aks to 225 foldes to the EP player who pushes for 900, do you call?

bayseian theory calculates the change in probability of his holdings with each new action, let's say he's a TAG and could be raising ak-aqo,ak-ajs,kqs,AA-99 so you reraise but you know once he pushes he has either ak, AA,KK, or QQ

well there are normally 6(3*2*1) possiblity for pair hands and 16 for non-pair (4*4), but you have one ace and one king so there are 3 pairs of aces 3 pairs of kings, 9 possibilities of ak, and 6 of qq.

I could go farther and figure out all the probabilities but there are 21 possible hands against you and you figure out your EV vs each * the likely hood they have them (i.e. 6/21*EV of calling 625 to win 1305 for ak vs qq) and do that for all of them.

That was really rambling, but maybe you get it.

I'll explain it better later if there is interest.

Midterms= no sleep in days
-JDanz

[jgorham]

You are absolutely right that any poker decision is game theory in action, as a major premise of game theory is that every player makes any decision based upon their possible rewards. My explanation was for the specific scenario that was included in the original post - not meant to define game theory and all of its applications.

[Jdanz]

i didn't mean to imply at all that you weren't answering the OP's question, just that the uses of this framework (incomplete information, competative, zero-sum game theory) are in every deciscion made, so while it's easy for peolpe to get confused about randomized bluffing/raising strategies, they probably know more game theory then they think they do. Also the applications are at a poker table, well, endless.

-JDanz