[Jerrod Ankenman]

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Thanks Jerrod, you're right. In the above description I erroneously extended the functional expression for the EV in the jam-or-fold game to the full game.

However, when limited to situations in which the strategic choices are limited to jam-or-fold, the same argument can still be used, and leads to the conclusion (I'll try to be more careful in formulating this statement...!):

1) in a situation where the opponent could raise a call, a jam-or-fold strategy is suboptimal for a stack larger than 12 times the opponent's 2/3rd stake in the pot,

and/or:

2) in a situation where a call would end the pre-flop betting, a jam-or-fold strategy is suboptimal for a stack larger than 6 times the opponent's 2/3rd stake in the pot.

[Do you agree with this? I don't think your last remark (and the comparison with Roshambo) is relevant: I am not comparing two different strategies against a presumed suboptimal strategy of the opponent. Rather, I am comparing two strategies for the same player (the SB): 'jam-or-fold' versus 'always-minraise'.]

From our discussion so far, I presume you would conclude that 2) is likely correct, but that 1) does not hold true...?

I don't think I can argue against that conclusion.

So, if theory isn't going to settle the question up to which stack size jam-or-fold from the SB is near-optimal, one could look for empirical data. Indeed, it would be interesting to have statistics on heads-up EV for the SB as function of stack size. The big question is whether the EV observed in practice indeed drops negative for stacks deeper than 8 BB.

Anyone who has such statistics available?

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Well let's be clear; I don't know what *OPTIMAL* is, and so it's entirely possible that at like 10 or 11, optimal is not jam-or-fold. However, my claim is that the difference in nemesis equity between the best jam-or-fold strategy and the optimal strategy (which might include limping or raising to a smaller amount and postflop play) is small enough that we don't care that much, particularly because the optimal strategy is basically intractable while the jam-or-fold problem is tractable.

My Roshambo remark was just to clarify about that you can't make comparative goodness comparisons between strategies with an eye toward claiming they are or are not close to optimal. It wasn't a very good example. It seems that the rest of my post was better. [img]/images/graemlins/smile.gif[/img]

Anyway, the question of up to what stack size jof is near-optimal basically depends on what you want to call near-optimal. I mean, it seems in your original post you used "same side of zero" as a qualitative measure of near-optimal, which is probably okay for the actual case. But I mean, if the first stack where you do something besides JoF is 8.5, then at 9, JoF is still going to be "near-optimal" by my definition. The structure of the problem just isn't such that there will be big cliffs of equity where a strategy with limping is a big quantitative leap forward. This happens in other games, but I'm pretty sure it doesn't happen here - JoF is very smooth and the second guy still has the option of putting his money in preflop if he wants.