Exploring how marginal chip value changes with stack size

[pzhon]

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It appears that solving the ICM in its general form becomes intractable with increasing numbers of prizes and increasing numbers of players remaining active.

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This is an interesting point, and I'd like to know how much this has been discussed before.

In the course of other consultation, I recommended the use of the ICM as a settlement for stopped tournaments to a major poker server. They seemed interested until I mentioned that the exact calculation is complicated, and they may need to use an approximation if there are hundreds of players. Does anyone have a good approximation? I found one which is computable, but which does not preserve the property that the matrix of finishing probabilities has the property that each row and column sum to 1.

Another tractable problem related to the ICM is showing that you always lose E$ when you take an EChip-neutral gamble. As I recall, no one posted a proof on a past thread where this was conjectured. Maybe it would be good to gamble to knock out the short stack on the bubble when you have the second or third stack, but the ICM doesn't seem to say this.