Re: Fictitious play for multi-player games
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I think the difference lies in the definition of the "game." Fictitious play will work (I've used it) if you assume the current hand is a one-shot deal. There are no more interactions after the current hand. However if you extend the definition of the game to cover multiple hands then it gets a lot more complicated.
A perfect example is when there is a big stack bullying the table near the bubble. Nash says the big stack should raise almost every hand and the small stacks should almost always fold. However just being in this situation is -EV for the small stacks. It would be in a small stacks long-term interest to call more liberally and punish the raiser. This will attempt to get the big stack to stop his bullying. But you have to take a -EV move now in order to try and stop being in continually -EV situations in the future.
But that would be way too complicated to figure out with a computer...
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Yep, I guess this would require expanding the game tree out to be able to see the blinds moving and the big stack getting into more and more +EV bullying situations. Perhaps it could be expanded into the next hand (or even next few hands) and still be computationally tractable? Not sure how much better the solutions would be though.
Juk [img]/images/graemlins/smile.gif[/img]
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