[Aisthesis]

I think I could give an exact definition of perfect play--but it's also not clear to me whether it provides a better or worse approximation of practical situations, and it also clearly makes the simulation completely impossible by hand.

But why not use essentially the same definition the you did on the SB case?

The definition would then be this (?): You turn your cards face up, and any opponent calls if he has +EV given the size of the pot coming to him. I would further assume that all opponents have you covered, but no further betting is allowed (a lot like Sklanksy's recent "unusual hypothetical situation"). Further, you are always UTG, but we simply run the question for tables with 10 all the way down to just 3 players.

But in addition to the unusual situation resulting on the 22 hand, there are also going to be complications from the simulation standpoint: If you move in UTG and flip over your cards, say UTG+1 has a good hand giving pot odds for a call. The calling criteria are now going to go way down for all subsequent players.

As I say, I really have no clue how one puts together the kind of code you run to get results on something like that, but it would definitely have to get data off of a lot of unusual situations, many of which have quite low probabilities.

That problem looks to me like it is well-defined, anyway. And if you are willing to write code to get clean results on that problem, the results would be EXTREMELY interesting imo. I'd be particularly interested in how those results match up with the ones I've gotten by hand.

I also have some somewhat vague ideas as to how one might define a game-theoretical situation without the "open cards" assumption. That approach would imo be better in principle, as it also would incorporate the "gap concept," but I still can't quite figure out how to make the calling criteria truly well-defined given the variables involved--specifically, stack-size, since the smaller your stack, the larger your range of hands is going to be for the initial all-in. That type of solution would imo be the "perfect" game-theoretical model for practice, but, even if one could define a precise range of hands for "hero" given his stack-size (hence giving the opponents at least a well-defined decision), the solution to that problem would create a lot of complications of its own, I would think.