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I was just making an informal remark, but reading your comment: > I think that the optimal mixed strategy for each hand is immune to bluffing (over many hands

I was just making an informal remark, but reading your comment: > I think that the optimal mixed strategy for each hand is immune to bluffing (over many hands it will have larger expected winnings against a bluffer). If that wasn't the case, there would exist no Bayes-Nash equilibrium for the game, contradicting Nash's theorem. I believe that's true. I know for sure that heads up limit hold'em has been solved. That said, I think this context is similar to the iterated prisoners dilemma contest. There's certain to be an equilibrium, but what's interesting isn't the perfect strategy in a min/max sense, but rather a slightly suboptimal strategy that can detect and exploit suboptimal behavior in other players. It sounds like you know this area well, perhaps you can shed some light if I'm on the right hunch?

algorias 10y ago
Yeah I think you're right. just playing an equilibrium is suboptimal in the sense that it doesn't extract maximal value from the opponent. You want to be playing a best response to the opponent's strategy. That's what you see online poker players do. They model their opponents (in the sense of labeling them as fun player, too tight, too loose, etc), then try to predict their hands based on their moves. Otherwise I guess they would be losing money: poker is zero sum by its nature, and the casino's cut on top of that makes it negative sum!