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Having a poker AI that plays deterministic strategies is an obviously terrible idea, for the precise reason you mention. It makes much more sense for the strat

Having a poker AI that plays deterministic strategies is an obviously terrible idea, for the precise reason you mention. 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.

hnkain 10y ago
It would be surprising to me if a completely deterministic strategy wasn't within some very close margin of an optimal strategy. For example, if you think you should raise with JJ 1/3 of the time and call the rest of the time in some spot, then you can raise JcJd and JhJs and call with the other jacks. This can give your opponent slightly more information about your range in some cases (for example, if they hold a J themselves), and of course you can only approximate correct frequencies, but it's highly unlikely (in my opinion at least) that such a deterministic strategy would be terrible.
- xapata 10y ago
  Conversely, I'd be very surprised if any deterministic strategy were remotely good. I've played against people with reasonable tight-aggressive strategies who were a bit too deterministic. They get crushed. 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.
  - DCF 10y ago
    Which really shows how the game has gotten so much harder. Ten years ago someone playing a fundamentally solid deterministic strategy could print money online. And in many low stakes casino games that is probably still true.
jasonwatkinspdx 10y ago
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!

hnkain 10y ago

It would be surprising to me if a completely deterministic strategy wasn't within some very close margin of an optimal strategy. For example, if you think you should raise with JJ 1/3 of the time and call the rest of the time in some spot, then you can raise JcJd and JhJs and call with the other jacks. This can give your opponent slightly more information about your range in some cases (for example, if they hold a J themselves), and of course you can only approximate correct frequencies, but it's highly unlikely (in my opinion at least) that such a deterministic strategy would be terrible.

xapata 10y ago
Conversely, I'd be very surprised if any deterministic strategy were remotely good. I've played against people with reasonable tight-aggressive strategies who were a bit too deterministic. They get crushed. 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.
- DCF 10y ago
  Which really shows how the game has gotten so much harder. Ten years ago someone playing a fundamentally solid deterministic strategy could print money online. And in many low stakes casino games that is probably still true.

jasonwatkinspdx 10y ago

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!