Mathematical models

[Aisthesis]

Hey, thx! I'll check those out and see if there's anything similar.

Actually, I'd also be more than happy to post the model, but it's already 35 pages single-spaced in a Word file including LOTS of functions--and, in working on it, I just found another bug.

The short version is simply this: I define a certain partially ordered set D, which represents what I call card-situations. These are conjunctions of cards and betting actions and tells. The set is partially ordered because from one situation, there are various possible successors to it in terms of the rules of the game. So, I set up a bunch of axioms (I have 32 of them) according to which the set must "behave" in terms of various functions--which return values for the rake, for holdings, for the flop, etc., etc.

Anyhow, (and here's the trick to it) I then introduce these functions, which I call psychological state functions or PSFs, which give the probabilities that a player takes a certain course of action in card-situation d. You could also call them "strategies," and they are to some extent, but I feel like the PSF idea is a little more general and suggests also any kinds of uncertainty (as well as randomized strategies), feelings of confidence, feelings of fear, etc. into the probabilities of taking various actions. So, a PSF, while it gives a probability function specifying probabilities for all allowable actions at d, has a lot of different factors going into it.

The first actual substantive result (no idea what becomes "provable" on the basis of this model--maybe only trivialities, maybe some interesting stuff) would then be a general definition of value for all possible card-situations and all possible PSFs. Obviously, a PSF in conjunction with a card-situation only has value relative to the other players' PSFs.

Anyhow, that's the basic idea, but it's not at all easy getting to an explicit (recursive) definition of value, which begins, so to speak, at the end, namely when the pot is distributed either by default (all but one fold) or at showdown.

You might want to check out the University of Alberta games group.

[Aisthesis]

Yeah, that's what kept coming up on that link the first guy gave. It looks like they're the closest, although they're doing it more from an AI standpoint--which has lots of overlaps with what I'm trying, but not entirely the same. But there are definitely some interesting articles along similar lines.
Without having a website of my own, do you know of any place I could get it out on the web once I have gotten at least all of the bugs that I myself see out of it?

I'd like to get some good critique, but the "interest group" is definitely going to be restricted to people who have had at least something like a solid formal logic course in college and are willing to wade through a lot of formalisms for the sake of poker analysis. Keeping the latter under control is really the biggest problem (I think I'm doing moderately well at it, but wish I could simplify some more)...

[Leonardo]

To start with, try to build a program that just plays the river well. To do so, you would simply need a set of hands that the other player can have, and a set of actions that the player will take with each hand. Work out the optimal play. Dont worry about past betting. You can add a funcionality later that takes into consideration past betting and updates possible holdings. Leave that till last. Once you have the optimal play for the river you can move backwards to preflop quite easily. Then you have the problem or working out a) What the player has and b) what they will do with each holding. This is terribly difficult. A way of doing that would be to define 10 or 15 profiles and then try to fit each player to a profile from his play. For making the profiles you can either go through and define every play (stupid way and very long and difficult) or you could work out the optimal play that your opponent should make in theory and then slant the play towards certain tendencies, such as being too aggressive or dumb or whatever.