AI for Poker

::: {style="MARGIN-TOP: 0in; MARGIN-LEFT: 0in; WIDTH: 2.445in; DIRECTION: ltr"} AI for Poker :::

::: {style="MARGIN-TOP: 0.049in; MARGIN-LEFT: 0in; WIDTH: 1.486in; DIRECTION: ltr"} Sunday, May 28, 2006

9:28 PM :::

Daniel Crenna, one of the finalists in the "Made in Express" contest, felt I went too far in dismissing the entrants when I said their projects were unrealistically ambitious.[  ]{style="mso-spacerun: yes"}One of his co-finalists is a professor of robotics, Daniel is confident of his approach, etc. Okay. Why someone capable of writing, in a month or two, a realtime 3-D vision system in C# from scratch is looking to win a \$10,000 prize is beyond me, but bully for them for doing it.

[Crenna is developing a domain-specific (visual) language for poker robots. He says that he doesn't intend to "]{style="FONT-SIZE: 11pt"}[advance the state of the art (not in this competition, anyway), but I will do my best to make what is currently available more accessible," with a drag-and-drop interface. This is a worthy goal and not in the same realm of ambition that the 3-D vision system is. I think that it still lies in the realm of "if you can do this, you shouldn't be giving it up for a \$10K prize," but that's his business, not mine. ]{style="FONT-SIZE: 12pt"}

Modeling poker is a fascinating problem. I have just subscribed to Crenna's blog and look forward to reading on his progress: I hope he'll forgive me kibbutzing.

The thing about Poker, and Texas Hold-Em in particular, and Tournament Texas Hold-Em in double-particular, is that it brings the forefront the problem of modeling intentionality. First-order intentionality is when you look at your cards and say "I believe I have a strong hand," (and therefore, I will play). That's easy. The great thing about Texas Hold-Em is that while there's variability in what cards will come up, the variability in what cards you have is very small and the importance of first-order intentionality is minimal.

A "poker intelligence" based on first-order intentionality would have a table of starting hands that are "likely to win" and bet on, say, A-7 or better, fold anything else. After that, it would be driven by pot odds. It would ignore other players betting patterns and would be very easy to beat.

Second-order intentionality is (he played and, therefore,) "I think he has a strong hand," and would be necessary for any non-trivial poker intelligence. So, for instance, if the other player opened, the poker intelligence might "put him" on an A-7 or better and compare the pot odds against various predictions of what the other player might do. Obviously, people play differently, but you should get some results if you had a parameterized model ("Aggressive player," "Passive player," etc.).

Poker betting signals third-order intentionality: (I bet aggressively out of position so) "I think he thinks I have a strong hand." And even the lamest poker player understands bluffing "I think (if I bluff) he will think that I think I have a strong hand." To call a bluff requires a decision about fourth-order intentionality: "He thinks I think he thinks I have a good hand," and, just to take things to what is generally considered the human limit, [tournament ]{style="FONT-STYLE: italic"}texas hold 'em happens so fast that you have to model your opponent's model for dealing with bluffing: fifth-order intentionality.

By the time you get to fifth-order intentionality, you're verging on comic territory -- "Only a fool would put poison in the cup in front of him!" I don't think that fifth-order intentionality is necessary for a non-trivial poker intelligence, but I do assert that third-order intentionality [is]{style="FONT-WEIGHT: bold"} necessary, since that's the level at which bluffing takes place.

Another possibility is to collapse the model into statistics: model your opponent as "10% of the time, he's betting over his card's true odds (aka bluffing)," but putting such a parameter to an opponent's play is very difficult since it is difficult to get enough data about your opponent's real situation versus the evolving pot odds. Again, especially in tournament hold 'em.

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