Surely nobody is surprised? Perfect knowledge of probabilities, no emotion and immune to bluffing.
There's no such thing.
An algorithm playing straight hand value based on probabilities is more susceptible to bluffing, not less. And this is no limit, where a single hand can swing all the chips.
Any poker AI that isn't a loser is going to have some pretty sophisticated modeling of the opponent.
It makes much more sense for the strategy space to be the set of probability distributions over game moves (i.e. mixed strategies).
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.
It'd be far too easy to recognize when they have a good hand and fold and to push them off all their marginal hands.
> 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?
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!
Find the right balance, and your opponent can't exploit you. With no-limit hold'em this is extremely complicated, and until recently the best humans have always beaten the best bots.