[Paragon]

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Where does this come from? It hasn't been proved beyond doubt that your probability of winning is exactly equal to your stack size as a proportion of the chips in play, has it? That's been used as a reasonable assumption for various models, such as ICM, but I see no reason to take it as fact.

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There is some mathematical basis to assume your chance of winning is exactly proportional to your stack and the total number of chips in the tournament (especially for a single table).

Take a specific example with 10 or fewer players at a table all with various stacks sizes. Now have every player go allin every hand regardless of cards until someone wins. The chance you win is precisely that proportion in this example. Extending this method you can also find the exact odds of finishing 2nd-10th as well. The algorithm for ICM merely does this, then checks the percentage of the prize pool awarded for each place, and then gives you the value of your stack in terms of real dollars. I actually wrote a program that simulated this (everyone allin) and everything all converges nicely to ICM results. In any case, although I would hesitate to say anything is a fact when theorizing about poker, this proportion everyone constantly refers to is more than a wild guess at least.

Anyway, this would help explain Che's example with the two table scenario. Suppose you have Table A where everyone has stack size X, and Table B where one person has stack size X and all others have less than X. If you freeze the tournament at this point and everyone starts repeatedly allining, my intuition thinks the one player on Table B would have the greatest +$EV, assuming you get the table balancing algorithms identical to PartyPoker or whoever. I never tested anything like this.

In my opinion, the greatest shortcoming to ICM is that it does not factor in fold equity of future hands. I'm not sure how you could analytically describe that though.