Re: Game Theory and Poker
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... game theory doesn't tell you how to win. It tells you how to not lose.
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Actually an equilibrium strategy doesn't even accomplish the minimal goal of not losing when there are more than two players. If everyone follows the equilibrium strategy than the EV of each player across an entire orbit will be zero and you won't lose. But one player not following the equilibrium strategy can easily place another "innocent" player in an unavoidable negative EV situation.
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Yes, and no. If player A departs from the equilibrium strategy in such a way that an "innocent" player (B) is in a "negative EV situation", then by definition, B has a different strategy they could follow that would be better than the equilibrium strategy they were originally following, and so can obtain a non-negative EV - this shifts the negative EV to some other "innocent", who can also switch to a better strategy, and so on.
Ultimately, all of the players can (in theory) switch strategies so that the negative EV falls back on the player who's playing a non-equilibrium strategy. The other players may not be able to guarantee a positive EV in their new equilibrium, but they can at least remain non-negative.
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