Testing ICM -- some questions for discussion

[John Paul]

Hello,
I have been following this thread over the past few days. If I understand everything, Marv has showen that if both players push every turn, then their % equity =% chips. Shadow has pointed out that a the meaning of being a "better" player than your oppenent is that your %equity > %chips.

Taken together - It might be worth thinking about how betterness occurs. If the short stack is small enough - their blind will put them all in. At this point, for both players %equity = %chips. So neither can play better here.

Even if the blinds do not put the short stack all in, it sems to be the 2+2 dogma that you can have a stack so short that you have to push any 2 cards, and the big stack should always call. In this case neither player can play better, just worse than pushing. Can this stack size be determined analytically in terms of stack sizes and blind sizes?

So, if you are going to be better than someone HU, that is have your $Equity>Chip Equity, you must have to do it when the stacks are more equal in size. That is, there has to be some fixed chip level where pushing/calling pushes is not the best possible play. But I wonder if you could devise an optimum strategy based on the equity of individual hands vs. random hands. I don't think that you could necessarily come up with an analytical solution for every situation, but I suspect that you could narrow down the possiblities.

What do folks think?

John Paul