Calculate Independent Chip Model equity for each player based on chip stacks and prizes.
The Independent Chip Model (ICM) converts tournament chip stacks into real dollar equity based on the prize pool structure. Unlike cash games where every chip has the same value, tournament chips have diminishing marginal value — doubling your stack doesn't double your equity because you can still only win first place.
ICM is crucial for making correct decisions at final tables and on the bubble. A short stack might have less chips than the big stack, but proportionally their chips are worth more per unit because of survival equity. This is why you see big stacks attack and short stacks tighten up near pay jumps — it's the mathematically correct strategy.
The Malmuth-Harville model calculates the probability of each player finishing in each position based on chip stacks. Each player's probability of finishing 1st equals their chip share. Probability of 2nd is calculated by removing each possible 1st-place finisher and recalculating. This continues recursively for all prize positions.
ICM assumes all players are equally skilled and doesn't account for position, blinds, or future play. It's a snapshot model. In practice, skilled players have higher equity than ICM suggests, and stack sizes relative to blinds matter. Still, ICM is the standard framework for tournament decision-making.