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Thanks for explaining your argument. Let's suppose you're right - that playing by the numbers is sufficient. In this case you would not have to keep track of p

by gizmo 18y ago

Thanks for explaining your argument. Let's suppose you're right - that playing by the numbers is sufficient. In this case you would not have to keep track of player histories, as you consider every hand without context. But this can only result in one thing: your play style will be constant. You will always take the best action with probability P and (semi)bluff with probability 1 - P. The human notices this and starts playing very aggressively. As a result the PC will fold winning hands and lose many blinds. What the PC should do is change tactics. Get aggressive or start laying traps (e.g. slowplay a great hand so it looks weak, to lure the aggressive human player into bluffing a lot of money). If the computer always plays optimally from hand to hand it cannot deduce changes in playing style and will therefore always lose. From this I can only conclude that psychological aspects can never be ignored in poker.

aggieben 18y ago
I never really meant that the calculations should be without context. One could keep a "running distribution" to update P (probably a bunch of Ps, actually) as you play. Maybe we're now just looking at the same thing from different angles. You say "use psychology" and I say "use numbers", but in the end, maybe it's the same thing and it's harder than I'm giving it credit for. Thanks for the poker lesson, by the way. Next time I see a game I'll be more interested.
- gizmo 18y ago
  Ah-hah. But that's the problem. So you need some kind of distribution for each of the different tactics the player plays. And then you need some heuristics to predict which tactic is going to follow which tactic. It's a slippery slope, I guess. I don't know where to draw the line myself. It can be argued that as soon as something is modeled by a computer it ceases to be psychology and becomes mundane math. But I do still believe that most tactics people use to trick others with need to show up in the code in some way. I won't use the "Clearly you've never done x" line again. It was cheap and uncalled for. Thanks for calling me out on that.
- mattmaroon 18y ago
  So psychology and math in poker are sort of two sides of the same coin. Generally, psychology means narrowing your opponent's range of possible holdings as much as possible, while preventing him from doing the same to you. You do this to enable yourself to make better math-based decisions, and cause him to make worse ones. If you can accurately pinpoint your opponent's range, and predict how he'd react with the hands in that range on future rounds, the game becomes a rather trivial math problem for a computer. It can simply enumerate all of the possibilities and determine the correct course of action. Unfortunately narrowing a person's range and predicting how they'd play in future rounds is very hard to do for a human, and presumably even harder for a computer.
dejb 18y ago
Actually this is not correct. The perfect unbeatable game theoretical model actually doesn't take into consideration the history of the other player. There's maths and stuff by John Nash to prove this. The game theory perfect model will always play as if it is playing a perfect opponent. In way you could say that the mathematically perfect player is so on guard against tricks by an opponent that even after 20 consecutive raises by an opponent it still doesn't alter its strategy. Of course the strategy will not lose just because a player raises once and consequently it also won't lose to a player who raises all the time. However by doing this the algorithm will miss out on substantial chances to exploit an imperfect opponent's weaknesses (in this case being way too aggressive). As a poker pro there is a (small) chance this 'perfect' player wouldn't even beat the rake against fish. However it would not lose (on average) to the best player in the world (and would probably win). This might all seem to go against your intuition and experience as someone who is probably a really good poker player but it has been mathematically proven as part of game theory. Of course finding/creating this 'perfect' playing strategy is probably more complicated than 'solving' chess which most people believe to be impossible.
- gizmo 18y ago
  You're right. History doesn't matter and cannot possibly matter in a perfect game. After all, by using the same strategy for more than few hands the player gives information away unnecessarily. So in a perfect game people will switch tactics at any moment, which removes the history element altogether. So the reason why changing tactics every hand is ineffective in the real world is because people believe that the way you played hands before gives information about your play in the future: your table image. But you only work on your table image in the first place so you can exploit it later. When playing against a perfect opponent you won't sacrifice opportunity to maintain an image, because the opponent will always play in the same way (the opponent knows you can change tactics at any moment). However! The perfect strategy is still absolutely useless in a tournament and most other games. Because exploiting weakness and amassing chips is the objective for the first hours, and the perfect model is bad for that. Still, it's all fascinating. Appreciate your explanation.

by gizmo 18y ago

aggieben 18y ago

I never really meant that the calculations should be without context. One could keep a "running distribution" to update P (probably a bunch of Ps, actually) as you play. Maybe we're now just looking at the same thing from different angles. You say "use psychology" and I say "use numbers", but in the end, maybe it's the same thing and it's harder than I'm giving it credit for. Thanks for the poker lesson, by the way. Next time I see a game I'll be more interested.

gizmo 18y ago
Ah-hah. But that's the problem. So you need some kind of distribution for each of the different tactics the player plays. And then you need some heuristics to predict which tactic is going to follow which tactic. It's a slippery slope, I guess. I don't know where to draw the line myself. It can be argued that as soon as something is modeled by a computer it ceases to be psychology and becomes mundane math. But I do still believe that most tactics people use to trick others with need to show up in the code in some way. I won't use the "Clearly you've never done x" line again. It was cheap and uncalled for. Thanks for calling me out on that.
mattmaroon 18y ago
So psychology and math in poker are sort of two sides of the same coin. Generally, psychology means narrowing your opponent's range of possible holdings as much as possible, while preventing him from doing the same to you. You do this to enable yourself to make better math-based decisions, and cause him to make worse ones. If you can accurately pinpoint your opponent's range, and predict how he'd react with the hands in that range on future rounds, the game becomes a rather trivial math problem for a computer. It can simply enumerate all of the possibilities and determine the correct course of action. Unfortunately narrowing a person's range and predicting how they'd play in future rounds is very hard to do for a human, and presumably even harder for a computer.

dejb 18y ago

Actually this is not correct. The perfect unbeatable game theoretical model actually doesn't take into consideration the history of the other player. There's maths and stuff by John Nash to prove this. The game theory perfect model will always play as if it is playing a perfect opponent. In way you could say that the mathematically perfect player is so on guard against tricks by an opponent that even after 20 consecutive raises by an opponent it still doesn't alter its strategy. Of course the strategy will not lose just because a player raises once and consequently it also won't lose to a player who raises all the time. However by doing this the algorithm will miss out on substantial chances to exploit an imperfect opponent's weaknesses (in this case being way too aggressive). As a poker pro there is a (small) chance this 'perfect' player wouldn't even beat the rake against fish. However it would not lose (on average) to the best player in the world (and would probably win). This might all seem to go against your intuition and experience as someone who is probably a really good poker player but it has been mathematically proven as part of game theory. Of course finding/creating this 'perfect' playing strategy is probably more complicated than 'solving' chess which most people believe to be impossible.

gizmo 18y ago
You're right. History doesn't matter and cannot possibly matter in a perfect game. After all, by using the same strategy for more than few hands the player gives information away unnecessarily. So in a perfect game people will switch tactics at any moment, which removes the history element altogether. So the reason why changing tactics every hand is ineffective in the real world is because people believe that the way you played hands before gives information about your play in the future: your table image. But you only work on your table image in the first place so you can exploit it later. When playing against a perfect opponent you won't sacrifice opportunity to maintain an image, because the opponent will always play in the same way (the opponent knows you can change tactics at any moment). However! The perfect strategy is still absolutely useless in a tournament and most other games. Because exploiting weakness and amassing chips is the objective for the first hours, and the perfect model is bad for that. Still, it's all fascinating. Appreciate your explanation.