[Aisthesis]

I'm guessing the complete coinflips won't influence the results much anyway. What's interesting also, after all this, is that really it can be calculated completely independently of any ranking list!!! A stack-size will be the result.

If one wanted to get really picky, it would also be worth noting that it can actually be rational to call even outside of the blinds as slight underdog at times: for example, if you're only a 49-51 underdog but you only have to call $1,000 for a shot at a pot of $2,000. But I don't think it's going to make much difference there.

Anyhow, I'm probably going to be away from my computer for a couple of days (so don't think that my lack of posts means that I have lost any interest in this idea).

I think we both have a pretty good idea as to what hands are underdogs to any given hand, so that won't even require pokerstove in all but a few cases. Only the superior hands are really relevant, and stack-size is going to depend a lot on how big a dog one actually is. Pairs will also be fairly easy down to a certain point.

Anyhow, a preliminary consideration before wrapping this up for the next few days: With 9 players, blinds at 100/200 and antes at 25, there is 525 in the pot before anyone has bet. In my experience, the most relevant stack-sizes for thinking about this problem are when you're in the range of 1,200-2,400--that is, 2.5 to 5 times the current pot. Below that, you're getting extremely desparate (also useful to figure out, but the A9s question has already given some pointers in this direction). Above that, you're in a position to actually play the hand, and, at least for me, I wouldn't be inclined to go all-in at that point with a stack any larger than 2,400 (actually even at 2,400, I'd be awfully inclined to try a limp even with a big hand and then proceed from there). The stack of 1,200 also has waited awfully long to make a move, but I do have something like that happen once in a great while if the cards are running in some bad ways. But I think a stack of 2.5 times the pot really is the low end of the spectrum.

With blinds at 100/200 and no antes, the pot is only 300 prior to all betting, and I think that tends to raise the maximum value of interest. With as much as 1,800 (possibly even more), I think the all-in is well worth considering, as it's awfully hard even to limp at that point. That's a stack of 6 times the pot, and I think the math of the all-in move might be worth investigating up to stacks as big as 7 times the pot.

In practice, I'm still a bit undecided as to when you've actually reached the "all-in or fold" point, but I think this problem should have a lot of interest for stacks from 2.5 times pot up to 7 times pot. That at least narrows down the range of hands for which one will need to go through all the necessary calculations. (a complete table matching a hand with a stack-size depending on number of players is also possible for any given hand, but I think it's really mainly worth the effort on hands where the result is in that range).