Common
Independent Chip Model
Mathematical model in poker
Independent Chip Model
In poker, the Independent Chip Model (ICM), also known as the Malmuth–Harville method, is a mathematical model that approximates a player's overall equity in an incomplete tournament. David Harville first developed the model in a 1973 paper on horse racing; in 1987, Mason Malmuth independently rediscovered it for poker. In the ICM, all players have equal skill, so current stack sizes entirely determine the probability distribution for each player's final ranking. The model then approximates this probability distribution and computes expected prize money. Poker players use ICM to estimate their tournament equity, negotiate final-table deals, and evaluate strategic decisions. Poker solvers use ICM as a utility function to optimize strategies in terms of expected prize money. ICM calculations require the chip stacks of all remaining players and the payout structure. However, enumerating every possible finishing order becomes computationally intractable as the number of players increases...
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