[JaredL]

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"the world's greatest mathematician and game theory expert goes heads up against the world's greatest behavioral psychologist / people reader. both have average skills in the other person's expertise, and both have a good understanding of poker. who has the edge, and how much is it?"

If you use perfect game theory and have no physical tells, no one can have an edge on you head up.

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Wrong

This is a game of imperfect information in which the game theory guy does not know the type of his opponent. By type I simply mean the way any 'realisation of' the psychologist plays the game. In any optimal strategy chosen by the game theory wiz there will (almost certainly) be realisations of his opponent's type against which he is an underdog-It is possible that the psychologist can have an edge against Mr. game theory.

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Way Way Wrong. The optimal game theory strategy is the same against any opponent, regardless of how he is playing, and it is already proven to be unbeatable.

The term game theory is thrown around loosely in poker. You don't understand what it really means to play by optimal game theory.

But again, keep in mind the mathematician cannot play this optimal strategy because it takes too long to compute.

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Heres a simple example of what I'm talking about

Opponent type A: Bets 100% of the time he has nothing, Checks 100% of the time he has hit.

Opponent type B: Checks 100% of the time he has nothing,
Bets 100% of the time he has hit.

Do you still contend that there is a unique optimal strategy for Mr. Game Theory against these two types of his opponent, given that Mr Game theory does not know which type he is up against?

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I think that your problem is a semantic one. People for some reason in poker discussion continually throw the terms "optimal strategy" or worse the "optimal game theory strategy" when really what they mean is "an equilibrium strategy."

In your example, if the superhero theorist doesn't know the type of the opponent then she would not know the optimal strategy (using the standard definition of optimal). She would play an optimal strategy given the probability that the opponent is each type (assuming no other types exist). This strategy would be different from the strategy she would use if she knew the opponents type.

The point others have made is that if she played an equilibrium strategy for the game, it wouldn't matter. Either opponent type would lose money to her every single hand. However, her use of the equilibrium strategy would certainly not be optimal.

Jared