[Aisthesis]

Quite a difference, huh?!! That value is actually somewhat too high, since Sklansky is figuring stack-size as a ratio to BB rather than total pot, so you can knock off 1/3 right there, and more if there are antes. Also there's a small boost due to the fact that the SB part of it is "pre-paid." But still, the difference is HUGE!

I'm going to try and calculate it through for 5 hands (just rather tedious running so many hands through pokerstove) and see what I come up with.

Part of the problem with A9s is that it's such a big dog to lots of the hands that beat it--all of the aces with better kickers. It only holds up reasonably well against the pairs 66-88, which are still rated as superior hands in K-S. So, the "how big of an underdog" aspect definitely is going to play a big role on this type of problem.

Another consideration: With the formula, it's also easy to run this through for the hand that has, say, a 70% (or pick any %) chance of being the best among n hands. So, for the question of when it is plus EV to go all-in from a tournament shortstack, a higher probability might be desirable--certainly is from EP, but I'll be interested in the results at 50% for 5 players as a starting point.

Actually, an "equation" for all this would involve 2 variables (given the number of players), it seems to me, in order to solve for stack-size: "f" as the percent favorite the aggregate of all superior hands is over the given hand; and "p" the percentile ranking of the given hand--p would determine how often the whole table would fold with inferior hands, hence increasing the probability of winning the pot uncontested. For example, if your hand is in the top 30%, the assumption would be that you win the pot uncontested 70% of the time...

The interesting thing is that both f and p are determined in the list for each given hand. So, it's possible (easy if you could devise a program to calculate f--with pokerstove it requires a lot of legwork) for every position to determine the maximum stacksize with which it is plus EV to move in with any given hand.

So, that's another interesting thing to try: Figure out the maximum stack-sizes for 9 players on all hands superior to A9s. I think I could actually do that by hand (although I think I'd start at the top of the list and work my way down, perhaps avoiding some of the marginal ones close to A9s in rank; anyhow, the further down on the list, the more tedious the calculation becomes).