Calculating Expectation While Multi-Tabling

[Rookcifer]

In NLHE:TAP, the authors discuss expectation while playing the nuts on river, or value betting when you are X% sure you have the best hand and are Y% sure of the times he will call with worse hands.

If you have the nuts, then the following is all you need:

EV = (Pcall)(S)

where

P = percentage of time he calls
S = size of bet

However, value betting is a bit more complex because you must calculate the percentage of time he will call X bet with Y hand, and then calculate the percentage of times you lose the showdown.

Like the authors discuss on page 87, if you think there is a 20% chance he may have you beat, and you are contemplating 3 bet sizes -- one of which he will call 100%, one which he calls 50%, and one he calls 30% -- then the math is much more complex to do on a whim (not to mention determining what percentage of each bet size he calls -- this is tricky in itself).

Again from page 87:

If $200 is the smallest of the three bet sizes and he will call it 100%, but beat you 20%, the EV equation is:

$80 = (.60)($200) + (.20)(-$200)

I don't mean to regurgitate a book most of you have read, but here's my question: Does anyone here actually sit at a session thinking like this and then doing these calculations in one's head? When I am 8 tabling I just don't have time to do these calculations (and I think few people besides Kim Peek actually would do all of these calculations in a few seconds). Do these calculations sort of translate into a "feel" the more one plays? Does it become intuitive (even though one's intuition may not have razor precision). I am a pretty smart dude, and I suppose I could do the calculations but it seems tedious when multi-tabling.

BTW, the book is great, as I am sure anyone who can master all the techniques will have as close to a perfect theoretical understanding of what moves to make in any given NLHE situation that is possible. I think the book shows there is no "gimmick" techniques one can use to become a great player, it takes a lot of work and theoretical understanding. The authors are right, I don't think there are any cookie cutter plays one can "memorize."

[pzhon]

Don't try to do complicated calculations at the table. Remember the situation, analyze it later, and next time your intuition will be better while playing. This gives you a significant advantage over the people (even winning players) who refuse to think about the hands away from the table. See this thread, where I believe that my play was right by a lot over the "standard" play, while several people said, "How is this interesting? Just make the standard play. Next."

[Rookcifer]

Thanks, pzhon.

One point about the hand you posted in that link. I notice you mention game theory as one of the reasons you acted as you did, and I often hear poker players throw the term "game theory" around as if they possess some esoteric knowledge that gives them an advantage. I guarantee that 99% of them have no clue what game theory even is. (You are probably an exception as I do remember hearing you say that you hold a mathematics Ph.D).

I am sure you are aware that Von Neumann used "three card poker" as a model for the theory when he wrote his paper introducing the concept. This three card poker model is vastly more simplified than hold 'em is. Firstly there are only two players with one card each (with a card in the middle). Secondly, the theory assumes both players are making optimal plays based on the theory, whereas you can be assured this will never happen in real life.

I am sure you are familiar with "fuzzy logic" developed in the 1960's at Cal Berkeley. The developer of it was Lotfi Zadeh, who, of course, would be acutely aware of game theory.

This is what Zadeh said in an interview when game theory got brought up:

[ QUOTE ]
"There's a field called "Game Theory." Hundreds of books and thousands and thousands of articles have been written about it since the late 40s. Now you might think that by reading those books and articles and by taking courses, you would be in a better position to play games of various kinds. But the truth is, it doesn't do you a bit of good. Not one iota. Game Theory is concerned with models that are not tied to real games and only tenuously tied to real world conflicts."

[/ QUOTE ]

Likewise, Sklansky pretty much dismissed game theory in his book "Hold 'em Poker," as he said it is not applicable because there are too many cards exposed.

So, my question to you is: why do poker players keep discussing game theory when so many experts in the field claim it has no bearing on poker (at least not in hold 'em)? Is there something I am missing? I really would like to learn about its applicability to hold 'em if there is any applicability at all.

Take care.

[Gonso]

I thought MoP had a pretty good treatment of the subject, at least for non-mathematicians.

[pzhon]

[ QUOTE ]
So, my question to you is: why do poker players keep discussing game theory when so many experts in the field claim it has no bearing on poker (at least not in hold 'em)? Is there something I am missing? I really would like to learn about its applicability to hold 'em if there is any applicability at all.

[/ QUOTE ]
Zadeh was wrong, slightly. He overstated the case. Game theory has little to say about chess or backgammon, and Zadeh is also known for studying backgammon. (Combinatorial game theory has some remarkable applications to go. However, combinatorial game theory is not really a part of game theory, despite the name.) Game theory does have applications to a few games such as bridge and poker, including Hold'em.

The applications to poker often come in the form of solving a model which resembles some aspect of poker. For example, suppose it is general knowledge that you have the nuts or a weak hand, and your opponent has a bluff-catcher. How much should you bet? How should you bet if you can bet on two streets? The solution can tell you about way ahead/way behind situations, and other situations when you think your opponent views his hand as a bluff-catcher.

[ QUOTE ]
Secondly, the theory assumes both players are making optimal plays based on the theory, whereas you can be assured this will never happen in real life.


[/ QUOTE ]
Parts of game theory deal with optimal strategies against optimal opponents, but not all. Normative game theory results are still relevant when you play against imperfect opponents. The deviation from optimal play can tell you how to exploit a strategy, but if you don't know what optimal play is, it is hard to know the direction in which a player is deviating.

Many times, players say, "I hate play X. I would never do that. Anyone who does X is a fish." Ok, is that because X is unfashionable, or because it is really a bad play? You won't agree with all of the plays made by someone who is better than you, and some of them are better than your choice. If X is a bad play, how can it be exploited? Will it be exploited by typical opponents?

You should be aware of the ways in which you are deviating from optimal play, and the ways to exploit your play, so that you can watch for players who may be exploiting your strategy. For example, you might observe that players do not 3-bet frequently enough, so you tighten up on your 4-bets, and fold more to 3-bets. This leaves you vulnerable to someone who 3-bets lightly as a semibluff, or with hands that gain valuable information cheaply from whether you 4-bet or not with your tighter range, or with a normal range, who quietly benefits from your lack of 4-bets for value. If you find players who are exploiting your deviation too much, you may need to move back toward optimal play--which again may require knowing the optimal strategy.

One idea from game theory is that defending yourself from multiple stupid strategies simultaneously may defend you from smart strategies. For example, in rock-paper-scissors, defending yourself from the stupid pure strategies 100% rock, 100% paper, and 100% scissors, produces the optimal mixed strategy. In poker, knowing how to defend yourself from someone who always bets and raises (or someone who always bets when you slow down) is an important step toward playing well.

These applications of game theory generally do not involve the frontiers of game theory. They use relatively basic ideas, although solving the models is not trivial. Reading research papers on game theory generally will not help. Understanding the core ideas will.