[hansarnic]

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Position doesn't matter. Nor do blinds or skill levels. But it would validate (or disprove) ICM, which would be useful in itself.

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I have some doubts about that. It raises an interesting question though: can a game of players who all play the same generate different equities for the same stack distribution, by the manner in which they all play? It seems there should be an easy logical proof or an easy counterexample, but neither came to me in the 10 seconds it took me to write this post.

eastbay

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Ok, I thought of one. Consider HU match. Strategy A is to push when you have half or more of the chips, and fold if you have less than half. Clearly equity distribution is a step function for two players both playing this strategy.

Strategy B is push everything, call everything. We know that equity distribution is basically linear for this strategy.

So the answer is yes: the equity function of a game of players all playing the same strategy does depend on the strategy employed. And this is why I am not too fond of your "validation" of ICM for all pushes. It may generate a reasonable distribution, but it also may not, and I don't think it will close the case either way.

eastbay

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Don't think I understand Eastbay.

Strategy A leads to the player with the most chips at the start of the HU match winning virtually 100% of the time, no?

So that player has more skill (or rather the lower stacked player has no skill as he just folds every hand giving the game to his opponent).

Strategy B takes skill entierly out of the equation.

And yes, there are a couple of proofs of $EV = Chip count in HU in TPFAP, one of which is calculated on the basis of both players going all-in every hand.