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Humans Can Still Out-Bluff Machines
Pcol writes "The New York Times reports that in a poker game this week between man and machine, a program called Polaris fought a close match, but lost to two well-known professional poker players. Designing a poker playing algorithm is a different and more difficult challenge for software designers than chess and checkers because of uncertainties introduced by the hidden cards held by each player and difficult-to-quantify risk-taking behaviors such as bluffing. The game-tree approach doesn't work in poker because in many situations there is no one best move and a top-notch player adapts his play over time, exploiting his opponent's behavior. Polaris build a series of "bots" that have differing personalities or styles of play, ranging from aggressive to passive. Researchers monitored the performance of three bots and then moved them in and out of the lineup like football players."
The implication here is that there is no (known) equilibrium mixed strategy for bluffs (because if there were then Polaris could be coded to use it).
Is that really true?! It seems very counterintuitive.
Certainly there's nothing special in general about games involving bluff. One of Von Neumann's first game theory case studies involved a simplified version of poker precisely to demonstrate how to automate bluffing.
There were ten "bots"; which bot was in use was controlled by a "coach" program. They actually ran three different programs over the course of the tournament, and that setup actually lost to the humans. The coach / agent approach is an interesting one for a variety of reasons, and it is most definitely a valid strategy.
Because there's more to a situation than your cards. There's your chip stack, your blinds, the action behind you, your opponents chip stacks, the payment structure, and your position. Pushing on 8-3 unsuited is a poor move, but there's at least two situations where it's called for- if you're far from a money boundary in the payment structure, have a small number of chips in compared to the blinds (say an M of 3-5), and all players before you folded. In this case, by pushing in you're likely to win the blinds. Especially if none of your remaining opponents have a big stack. The risk can be worth it, since it makes absolutely no difference what hand you go out on unless you reach a new money boundary, and you'll have to win at least 1 hand to do so. And with 83, you're likely to have 2 live cards if called by a high ace (AK, AQ, AJ, AT). Note that you'd only want to do this if first into the pot- someone who called the blind is too likely to call you for only an additional 2-4 big blinds.
The other situation to try it in is a squeeze play- if you have a raise and a call behind you, you have a very tight table image, and you think they don't have good hands. A raise, especially an all in raise, is signaling an extremely good hand. From a tight player, this must be respected. You can get both players to fold here if they don't have premium hands (AK, QQ-AA). This is a high risk move though, and you must have been playing extremely tight, versus people capable of laying down a good hand, to try it.
I still have more fans than freaks. WTF is wrong with you people?
Keep in mind these bots play Limit hold'em, where the size of the bets is fixed. No-limit hold'em, the kind you typically see on tv is a much more complex problem - size of bets add more potentially misleading information and more choices to make. (that's why its more exciting to watch than limit)
Look at the first entry (bottom of page) on the Polaris team's blog for the second day. The day that the humans started winning:
e /Live/Day2Session1/
http://www.cs.ualberta.ca/~games/poker/man-machin
The U of A team gave the humans the logs of the first two games!
Perhaps after the entire match they could have reviewed the game logs, however this give the humans an unfair advantage during the second day. I can't believe that this isn't getting more attention -- they bascially gave the human team a huge insight into the inner workings, strategy, and tendencies of their opponent. Something that Polaris definitely did not have.
In my opinion this sours the competition and completely invalidates the final two matches. The human likely found a weakness (or two or three) and exploited it, and we can't know for sure that they would have found the weakness without those logs.
That was a huge mistake by the U of A team, and they have apparently got away with it without anyone noticing.
"I'd venture to say that pot-limit omaha high is a *far* more psychological game."
You'd be wrong. I made my living for two years playing PLO almost exclusively, at a high level (fuck you UIGEA and everyone who voted for you). The general consensus among students of the game is that PLO is one of the least psychological games played. The lack of bluffing being the major reason. Bluffing occurs, but the very same reason you cite as making it more psychological is why you're wrong the number of hands played. Playing such a large number of hand (50% is insane, and I challenge you to show me some poker tracker stats of someone who wins playing 50% of their hands long term). In fact, if a computer were to win consistently, I think PLO is a game that it would play.
"I don't think there's a difference between statistical knowledge and psychology."
Then let me learn you up. Let's use PLO. I have A-A-10-J double suited. I raise pot preflop. A VERY tight player reraises, and I call. Flop come K-K-K. Against an aggro player, I can reasonably infer that my 2nd nuts is good. Against Mr. Tighty, who I have seen reraise only with large suited pairs (KKJQ, QQJ10) or rundown hands (9-10-J-Q, 10-J-Q-K) I know within a certain range what he's holding, with some certainty. I am first to act, I check, he bets, I raise, and Mr. Tighty RERAISES. Based on my assessment of his likely behavior (psychology) I can reasonably infer that he has the K. Statistically, you NEVER lay down K's full of A's, but when your read (psychology) is good and the opponent is uncreative and direct (psychology) you lay it down.
Statistically the correct play is to put it all in if you can, but by understanding the other players decision making process (psychology) you can find a fold.
You're wrong again
I only go to buffets for the unlimited soft serve.