KEY TAKEAWAYS
CONTENTS
A poker ICM calculator converts chip stacks into prize-money equity, using the tournament’s payout structure. In the example worked below, a player with 6,000 of 10,000 chips holds 60% of the chips but has an ICM value of only 41.24% of the prize pool, while the player with 1,000 chips (10% of the chips) is worth 24.93%. The gap exists because prizes are paid by finishing place, not by chips, so each extra chip is worth less than the one before it.
This article explains what the Independent Chip Model is, what a calculator needs and returns, how the figures are calculated step by step, and how to read the output. Every ICM number shown is calculated in the article from the stated stacks and payouts. The example is hypothetical, and the focus is on understanding the output, not on telling anyone what to do with it.
What Is ICM in Poker?
ICM stands for Independent Chip Model. It is a method for estimating how much prize money each remaining player in a tournament can expect, given every stack and every payout. The result is an expected prize value for each player, which can be shown in currency or as a share of the prize pool.
It differs from the figure produced by a hand-equity calculator. A hand-equity calculator reports the chance that a hand wins a single deal. ICM reports prize equity across the whole tournament, so the two numbers answer different questions and are not interchangeable.
A common version of the model rests on one assumption: the chance that a player finishes first equals that player’s share of all the chips. To find who finishes second, the winner is removed and the same rule is applied to the remaining stacks, and so on down the paid places. Because that is the only input to the chances, the model ignores skill, position and future blinds, a limit discussed later.
What a Poker ICM Calculator Takes In and Returns
A calculator needs two sets of inputs. The first is every remaining player’s chip stack, entered in the same units. The second is the payout for each paid place, in currency or in percentages of the prize pool. If more players remain than places are paid, the lowest places simply carry a payout of zero.
The output is, at minimum, each player’s ICM value. Some calculators also return the probability of each finishing place, and some display the value as a percentage of the prize pool. Conventions differ between tools: some show the result in currency, some as a percentage, and some also show the chip-chop value for comparison. A reader should check which form a given tool uses before comparing figures.
The calculation behind the output is short enough to do by hand for three players, which is what the next section shows.
How ICM Is Calculated, Step by Step
Step 1: Chances of finishing first
Divide each stack by the total number of chips. With stacks of 6,000, 3,000 and 1,000, the total is 10,000, so the chances are 60%, 30% and 10%.
Step 2: Chances of finishing second
For each possible winner, remove that player and apply the same rule to the others. If the 6,000 stack wins, the 3,000 stack is second with probability 3,000 ÷ 4,000 = 0.75 and the 1,000 stack with 0.25. Weight each case by the chance that winner finishes first, and add the cases for each player.
Step 3: Chances of finishing third
With three players, the third-place chance is whatever remains: 1 minus the first-place chance minus the second-place chance.
Step 4: Multiply by the payouts
Each finishing probability is multiplied by that place’s payout, and the products are added. ICM value = P(1st) × first prize + P(2nd) × second prize + P(3rd) × third prize.
Worked Example: Three Players, Payouts of 50, 30 and 20
Suppose three players remain with stacks of 6,000 (player A), 3,000 (player B) and 1,000 (player C), and the payouts are 50, 30 and 20 from a prize pool of 100. This is a hypothetical example. For second place, if A wins (probability 0.6), B is second with 0.75 and C with 0.25. If B wins (0.3), A is second with 6,000 ÷ 7,000 = 6/7 and C with 1/7. If C wins (0.1), A is second with 6,000 ÷ 9,000 = 2/3 and B with 1/3.
Player A’s second-place chance is therefore 0.3 × 6/7 + 0.1 × 2/3 = 34/105, about 32.4%. Player B’s is 0.6 × 0.75 + 0.1 × 1/3 = 29/60, about 48.3%. Player C’s is 0.6 × 0.25 + 0.3 × 1/7 = 27/140, about 19.3%. The remainders give third place: A 8/105 (7.6%), B 13/60 (21.7%) and C 99/140 (70.7%).
| Player (stack) | 1st | 2nd | 3rd | ICM value | Chip-chop value |
|---|---|---|---|---|---|
| A (6,000) | 60.0% | 32.4% | 7.6% | 41.24 | 60.00 |
| B (3,000) | 30.0% | 48.3% | 21.7% | 33.83 | 30.00 |
| C (1,000) | 10.0% | 19.3% | 70.7% | 24.93 | 10.00 |
Applying the payouts to player A gives 0.6 × 50 + 0.3238 × 30 + 0.0762 × 20 = 30.00 + 9.71 + 1.52, which is 41.24 when computed from the unrounded probabilities. For B the sum is 15.00 + 14.50 + 4.33 = 33.83, and for C it is 5.00 + 5.79 + 14.14 = 24.93. The three values add up to 100, the whole prize pool, which is the check that the calculation is consistent.
Reading the Output: Chips Are Not Linear Money
The last two columns of the table show the main lesson. The chip-chop value splits the prize pool in proportion to chips, giving 60, 30 and 10. ICM compresses the spread: the chip leader is worth 18.76 less than the chip-chop figure and the short stack 14.93 more. Prizes are fixed by place, so extra chips raise a player’s chances of a better place at a decreasing rate.
The same effect shows up when chips move between players. The table below applies the same method to two new stack sets, in which player B wins 1,000 chips from player A or loses 1,000 chips to player A, with player C unchanged at 1,000.
| Stacks (A / B / C) | A’s value | B’s value | C’s value |
|---|---|---|---|
| 6,000 / 3,000 / 1,000 (start) | 41.24 | 33.83 | 24.93 |
| 5,000 / 4,000 / 1,000 (B wins 1,000) | 38.89 | 36.44 | 24.67 |
| 7,000 / 2,000 / 1,000 (B loses 1,000) | 43.53 | 30.89 | 25.58 |
Winning 1,000 chips raises B’s value by 36.44 − 33.83 = 2.61. Losing the same 1,000 chips lowers it by 33.83 − 30.89 = 2.94. Equal chip changes produce unequal value changes, which is why ICM figures cannot be read as a straight conversion rate between chips and money.
Common Mistakes With ICM Figures
The first mistake is reading ICM value as a forecast of winnings. The 41.24 for player A is an average over many repetitions of the same situation. In any single tournament, A finishes first, second or third and is paid exactly one of the prizes.
A second mistake is entering incomplete inputs. Leaving out one remaining stack or one paid place changes every figure, because every probability depends on the total number of chips and every value depends on the payouts.
Third, confusing ICM value with hand equity. Hand equity is the chance of winning one deal, while ICM value is prize money across the whole tournament, so a player who is an 80% favorite in one all-in has not won 80% of the prize pool.
The fourth mistake is comparing a percentage-of-pool figure from one tool with a currency figure from another. Both can be correct and still look different, so check the units first. Finally, treating the model’s assumptions as facts leads to overconfidence, as the next section explains.
What ICM Can and Cannot Tell You
ICM answers one narrow question: what is each stack worth in prize money, if finishing chances follow stack share? It does not model skill, position, blind levels or later bounties, so a real player’s expected result can differ from the ICM value. The figures here describe the model, not the quality of any decision.
The payout structure matters as much as the stacks. A flatter or steeper structure changes every value, even with identical chip counts. Everything on this page describes averages over many repetitions. Poker involves real financial risk, short-term results depend heavily on luck, and the legal age and legality of real-money poker vary by state and venue.
The Next Step After ICM
Charts used in tournaments rest on assumptions about stacks and payouts, and the grid format they use is explained in how to read a preflop poker chart. Knowing which assumptions sit behind a number is what separates reading a tool’s output from just accepting it.
