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Isura

Sep
08
2008
Initial Thoughts on Game Theory
Posted in Theory | View Comments (4)
 

I will flush out my thoughts here on the subject. First, some definitions. An exploitive strategy is a strategy against a specific fixed strategy. For example, villain always bets $100 on the river as a bluff, so you call with all bluff catchers (the latter is the exploitive strategy, the former is an exploitable strategy). What we're familiar with is finding the maximally exploitive strategy (MES) (i.e. choosing the strategy to maximize EV against a particular strategy).

Optimal strategy is then derived from the idea of MES. We are hero, and suppose villain plays the MES against us. In other words, he adapts his strategy to maximize EV against our strategy. Hero's optimal strategy is the strategy with the highest EV against villain's MES. Equivalently, the optimal strategy makes villain indifferent between their various exploitive strategies (I'll leave it as an exercise. It is fairly simple to verify using the definition of optimal). This second definition (the exercise) is most useful in actually finding solutions to particular game theory problems.

There is an important property of optimal solutions worth stating. In practice, optimal strategies tend to be mixed. Mixed meaning that you choose action A X%, action B Y% instead of always choosing A or B. The key property is that the EV from any choice from a mixed strategy is the SAME. Say we're on the river and are deciding whether to bluff. If villain was exploitable we'd either bluff 100% or bluff 0%. If we don't know villain's tendencies we choose an optimal solution (against his MES). Something like bluff 30%. The key is that our EV is the same whether or not we bluff.

Thus, in the game theoretic approach to poker there is no value in choosing inferior strategies (i.e. -EV type plays for 'image'). Choosing inferior plays for future EV is a purely exploitive approach! Put more bluntly, game theory advocates believe that metagame is irrelevant.

I hope all that is correct. More to come.

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Posted in Theory
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Comments
09-09-2008
d2themfi is online now d2themfi
as far as i understand everything you said is correct. I think a lot about this stuff, have read and reread mathematics of poker. One part I dont quite understand yet is how this applies to current day online msnl 6max and HU. For one from what I can gather, optimal game solutions dont exist for multiplayer games. If this is true, then Im not sure how important it is to non HU games. Then as for current msnl HU games, Im still not sure how important balancing your overall strategy is, and how one can decide whether going with a balanced strategy is better than a maximally exploitative strategy which may exploit an edge that we are not totally sure exists. Meaning we may be trying to exploit a perceived leak from incomplete information.

Idk if that makes sense, but any thoughts u or anyone else has would be cool. Maybe even start a theory thread on the forums if you have enough to say on the matter!
09-09-2008
Isura is offline Isura
It still applies since you can reduce the multiplayer game to a collection of two player games between each pair of players at the table. There is some crossover, but that's not too important for practical analysis.

It's true optimal solutions don't exist. But looking at the game this way gives a lot of insight into exploitive strategies and how to spot and counter-exploit them. Also half-street games can be completed solved. River play when it's checked to you is often half-street poker in 100bb games unless the pot is small. In practical terms balanced strategies can probably come fairly close to optimal. By balanced I mean within some threshold within optimal.

Some would say that GTO is poker.. and the rest is a game of rowshambo with cards
09-09-2008
d2themfi is online now d2themfi
yea all good points. Is there anywhere you read /learn about this stuff, besides that book mathematics of poker? I havent found any other good texts dealing with poker and game theory yet
09-10-2008
Isura is offline Isura
No, I haven't read any other material. I hear U of Alberta does research on game theory and poker.
 
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