[Aisthesis]

Hmmmm... that's sort of what I'm trying to do, but in a sense less ambitious. Let's say we're sitting at a table with 9 players. Each has a PSF given. Now, given the PSFs of everyone else, you could certainly come up with a set of optimal PSFs for you (there will no doubt be a lot of co-optimal solutions).

So, I guess that will be part of the result... "in principle." The way the model is set up, you can actually calculate the value of your PSF given the other PSFs even before any cards are dealt. Actually defining the set of co-optimal PSFs would presumably be simply impossible given the variety of ways in which the game can go. It will be possible, though, to define the set of co-optimal PSFs at a given card-situation d later on in the hand--i.e., when there's just not as much to figure.

As to the set of axioms, I agree that I don't like having so many, but my real goal here is completeness. I want to provide an accurate description of the whole thing. As a result, a lot of the "axioms" are kind of trivialities corresponding to rules of the game. For example, there's a relationship "Next" between card-situations (this is the relationship which makes the set D of card-situations partially ordered).

A few sample axioms:

If Next (d1, d2), then tau(d1) = tau(d2) where the function tau returns the number of players at the table.

If Next(d1, d2), then beta(i, d1) <= beta(i, d2) for 0 < i < tau(d1) + 1 and where the beta function returns the total amount of money put into the pot by the player in the i-th position in card-situation d.

Anyhow, there are lots of functions and relationships necessary to give a complete picture of all the relevant aspects, and my goal here, for the moment, is completeness.

Also, with this view, one can at least CONSIDER various criteria for "optimal"--e.g., positive but sub-optimal value but lower swings for a given PSF (standard deviation).

Anyhow, your point is well-taken regarding the complexity. It will be too complicated to solve in the general sense. But I think it will allow for some theorems--just not THE optimal PSF given other PSFs. It will be more along the lines that "this PSF is better than another PSF given the other PSFs at the table."

One thing I will say, though: At least the way I'm doing it, I don't think NL is much more complicated than limit. Perhaps in some way easier. The NL aspect is essentially captured in another axiom (there are probably a few, but I'd have to check):

For all d and for all i with 1 <= i <= tau(d), then beta(i, d) <= sigma(i, d) where sigma returns the initial stack-size of the player in the i-th position.

At least on the basis of the model I'm using, I think it would require more axioms to define allowable bets in a limit game. Also the unlimited number of re-raises allowed makes it easier (at least in terms of axioms) rather than more difficult.

So, anyhow, while I think simplifications can definitely lead to greater ease of analysis of quite a lot of situations (where the more complex model can make it very difficult to get anywhere), I guess all I'm really claiming is that a complete model seems to allow proving SOME things and should have SOME value as a tool for analysis--how far it actually gets us is completely unclear to me, though.