[Slim Pickens]

You are getting farther, not closer. This needs to be clarified: ICM does not include anythihng about "hand ranges." The Independent Chip Model is just a way of taking chip stacks in a tournament, where the chips are entirely worthless $-wise until the tournament is over, and estimating how much these now-worthless chips might represent in terms of $ at the conclusion of the tournament. All this business about hand ranges and stuff is an extension to the analysis whereby we can take the ICM results for several different sets of chips stacks, usually related by a scenario where you either win or lose a hand, and compare the different outcomes in terms of $ instead of chips.

ICM's only basis is a clever recursion that represents a common sense approach to valuing tournament chips. My chance of winning first prize is equal to my fraction of the chips in play. My chance of finishing second is equal to my fraction of the chips in play if you assume each other player wins, based on his fraction of the chips in play, and so on.