ICM calculator

Enter the chip counts of the players left and the prizes still to be paid. The calculator works out what each stack is worth under the Independent Chip Model, exactly, and compares it with a chip chop.

3 players, 10,000 chips, 1,000.00 to be paid.

Player	Chips	Chip share	ICM value	ICM share	Chip chop	P(1st)	P(2nd)	P(3rd)
Player 1	5,000	50.0%	383.93	38.4%	400.00	50.0%	33.9%	16.1%
Player 2	3,000	30.0%	327.50	32.8%	320.00	30.0%	37.5%	32.5%
Player 3	2,000	20.0%	288.57	28.9%	280.00	20.0%	28.6%	51.4%

How to use it

List the players still in the tournament with their current chips, and the prizes that are still to be won, largest first. Leave out players who have already been paid. If six players remain but only three places pay, enter all six stacks and three prizes: the model accounts for the chance of finishing out of the money.

The prizes can be anything that is split by finishing position: cash at a home game, a trophy fund, or league points. ICM does not care about the unit.

The method: Malmuth-Harville

The Independent Chip Model assigns each player a chance of winning equal to their share of the chips: a player with 5,000 of 10,000 chips wins half the time. It then applies the same rule again to decide second place among those left, and so on. This finishing-order rule is the Harville formula, published by David Harville in 1973 for horse-race betting, and was applied to poker tournaments by Mason Malmuth, which is why the combination is usually called Malmuth-Harville.

For players i, j, k with stacks s and total S, the probability that i wins, j comes second and k third is:

(sᵢ / S) × (sⱼ / (S − sᵢ)) × (sₖ / (S − sᵢ − sⱼ))

A player's ICM value is the sum, over every finishing order, of that probability times the prize they would receive. Rather than listing every order, which grows factorially, this calculator works through every set of players who have already finished, of which there are 2ⁿ. That is exact, with no simulation, for up to 16 players.

Worked example

Three players have 5,000, 3,000 and 2,000 chips, with 500, 300 and 200 still to pay. Player 1 wins 5,000 / 10,000 = 50% of the time. Player 1 finishes second if player 2 wins and then player 1 beats player 3 (0.3 × 5,000/7,000 = 21.4%), or player 3 wins and player 1 beats player 2 (0.2 × 5,000/8,000 = 12.5%): 33.9% in total. That leaves 16.1% for third. The value is 0.5 × 500 + 0.339 × 300 + 0.161 × 200 = 383.93.

Player 1 holds 50% of the chips but only 38.4% of the prize value. Player 3 holds 20% of the chips but 28.9% of the value, because 200 is guaranteed to somebody and it most often goes to the short stack. A chip chop, which gives everyone third-place money and splits the remaining 400 by chips, lands in between at 400, 320 and 280.

Where ICM is weak

It ignores skill and position. A strong player with the big blind coming around is treated exactly like anyone else with the same stack.
It ignores the blinds. A short stack that is about to be forced all-in is worth less than ICM says; a short stack with plenty of time is closer to its ICM value.
It is often criticised for overvaluing very short stacks and undervaluing big ones, mostly for the blind-pressure reason above. Other models exist, such as Malmuth-Weitzman, which models who is eliminated next instead of who wins, and simulation-based "future game" models. They give different numbers from the same stacks; no single one is correct.
It assumes nothing changes before the next bust. Early in a tournament, with dozens of places to go, the model is too crude to be useful.

ICM is best used as a neutral reference: for understanding why a call that is correct in chips can be wrong in prize value, and as a fair starting point when the players at a home-game final table agree to split the remaining prizes.

Common questions

What does ICM stand for?

Independent Chip Model. It converts tournament chip stacks into shares of the prize pool by estimating how likely each player is to finish in each paid place, using only the stack sizes. It is called independent because it assumes each player's chance of winning depends only on their chips, not on skill, position or the blinds.

Why is the chip leader's ICM value less than their share of the chips?

Because a tournament pays out in steps. Doubling your chips does not double your prize: you can only win first place once. The big stack's extra chips are worth less in prize terms than the short stack's last chips, which are what stand between it and the next payout. ICM shifts value from big stacks towards small ones for that reason.

Is ICM a fair way to split a prize pool?

It is the most widely used objective method, and it is fairer to short stacks than a pure chip chop. It is still a model: it ignores skill, who has position, and how big the blinds are relative to the stacks. Many final tables use the ICM figures as a starting point and adjust them by agreement, often leaving some amount to play for.

How many players can it handle?

Up to 16. The exact calculation works through every possible set of finishers, which doubles in size with each extra player. Sixteen players is about a million subsets, still instant in a browser; much beyond that, simulations are used instead.

Can I use percentages instead of amounts for the payouts?

Yes. ICM is linear in the payouts, so entering 50, 30, 20 gives each player's share in percent. The chip-chop column works the same way.