Re: ICM problems
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One way of ruling out some levels of complexity is to work out examples exactly. Some of the denominators are huge, so any simplification would still have to be able to produce huge denominators, too.
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Would I be right to say that if you want to input integer stack sizes, and output exact rational numbers for the probability of player i getting position j in this ICM model, then in terms of encoding input and output as binary strings, the output length is exponential in the input length?
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It could be worse than that, as a factorial is involved, but I think that is a poor measure of complexity. n! and (2n choose n) would also seem very complicated that way.
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