Poker ICM: how chips turn into money
What is ICM in poker?
ICM (the Independent Chip Model) converts tournament chips into real money. In a cash game a chip is worth its face value. In a tournament it isn’t: prizes are paid by finishing place, and the winner never gets the whole prize pool, however many chips they hold. So every extra chip you win is worth less than the last one, and losing your stack costs more than doubling it gains.
An ICM calculator takes the stacks and the payout structure and returns each stack’s $EV — what it is worth in prize money right now, assuming everyone plays equally well from here. Those numbers drive call-or-fold decisions on the bubble and at the final table, final table deals and post-session hand reviews.
The Malmuth–Harville model, with a 3-player example
Mason Malmuth brought to poker a model that statistician David Harville proposed for horse racing in 1973. It has a single rule: your chance to win equals your share of the chips. For 2nd place, assume someone else has already finished 1st, remove their chips and divide your stack by the chips that remain. Repeat for every place and every possible finishing order.
P(i = 1) = sᵢ / S
P(i = 2) = Σⱼ≠ᵢ P(j = 1) · sᵢ / (S − sⱼ)
$EVᵢ = Σₖ P(i = k) · payoutₖThe calculator is exact, with no simulation: it iterates over every subset of players (1,024 states for ten players instead of 3.6 million finishing orders), so the answer is instant and matches a full brute force.
Example: three players left with A on 5,000, B on 3,000 and C on 2,000 chips; $100 is paid 50/30/20. For player A:
- 1st place: 5,000 / 10,000 = 50.0%.
- 2nd place: if B finishes first (30%), A takes 2nd with 5,000 / 7,000 = 71.4%; if C does (20%), with 5,000 / 8,000 = 62.5%. Total 0.3 × 0.714 + 0.2 × 0.625 = 33.9%.
- 3rd place: 100% − 50.0% − 33.9% = 16.1%.
- $EV = 0.500 × $50 + 0.339 × $30 + 0.161 × $20 = $38.39.
| Player | Chips | Share | 1st | 2nd | 3rd | ICM $EV | Chip chop |
|---|---|---|---|---|---|---|---|
| A | 5,000 | 50% | 50.0% | 33.9% | 16.1% | $38.39 | $40.00 |
| B | 3,000 | 30% | 30.0% | 37.5% | 32.5% | $32.75 | $32.00 |
| C | 2,000 | 20% | 20.0% | 28.6% | 51.4% | $28.86 | $28.00 |
| Total | 10,000 | 100% | 100% | 100% | 100% | $100.00 | $100.00 |
A holds half the chips but only 38.4% of the money under ICM. Short stack C, with 20% of the chips, is worth 28.9% of the pool: at worst C still collects $20 for 3rd. That is the core idea of ICM — a big stack’s chips are cheaper, a short stack’s chips are dearer.
When ICM matters — and when it doesn’t
- The money bubble. Busting one step before the money is the most expensive mistake: medium stacks should avoid clashing with each other while the big stack pressures them with shoves.
- The final table. Pay jumps grow with every bust, especially in MTTs where 1st pays 5–10 times as much as 9th. Every all-in decision here is worth checking under ICM.
- Satellites. All seats are equal, so chips beyond what locks up a seat are worth almost nothing. It’s the most ICM-heavy format: near the bubble, folding even very strong hands can be correct.
- When ICM barely matters. Early in a tournament, far from the money, ICM is close to chip EV. Heads-up it is exactly chip EV: equity is linear in chips and there is no risk premium. ICM doesn’t apply to cash games.
Final table deals: ICM chop, chip chop and leaving money for 1st
When a few players are left at a final table, they can agree to split the prize money instead of playing it out (or play on for only part of it). There are three common ways to do a deal, and the calculator shows all of them.
- Chip chop. Everyone gets the last remaining payout and the rest is split by chip share. In our example: A $40.00, B $32.00, C $28.00. Simple, but the leader gets more than their equity.
- ICM chop. Everyone gets their ICM $EV: A $38.39, B $32.75, C $28.86. The chip chop overpays A by $1.61 at B’s and C’s expense. The bigger the stack gaps, the further chip chop and ICM drift apart.
- Leave money for 1st. Players set aside part of first prize to play for and split the rest by ICM. Leaving $10: A takes $33.39 now, B $29.75, C $26.86 ($90.00 in total), and the winner gets the $10. On average A wins $5.00 of it, which brings A exactly back to the ICM $EV — the deal is neutral for everyone.
The calculator rounds the amounts to cents so they add up to the prize pool exactly. Check the site’s rules before dealing — not every room or club allows deals — and remember that ICM ignores skill: a stronger player may ask for more than their equity.
Risk premium and bubble factor
In chip EV, calling an all-in is profitable when your equity beats the pot odds. Under ICM that isn’t enough: losing your stack costs more money than winning the same number of chips gains. The risk premium is the gap between the equity ICM demands and the pot odds. The bubble factor tells you how many times more a lost chip costs than a won chip.
Example — an SNG bubble: four players, payouts $500/$300/$200, stacks 3,500/2,500/2,500/1,500, blinds 100/200. The chip leader shoves from the small blind; you’re in the big blind with 2,500. By chips you’d need 46.0% equity, but ICM demands 65.8%: a risk premium of 19.8 pp and a bubble factor of 2.26. Folding keeps $245.32, doubling up gets you $372.80, losing gets $0. Even against a wide shoving range only the very top of your range can call. This spot is the calculator’s default — change the stacks and watch the threshold move.
Limitations of ICM
- Ignores skill. The model treats every player as equal. In reality a strong player’s chips are worth more and a weak player’s less.
- Ignores position and blinds. A short stack about to post the big blind is worth less than the same stack on the button, but ICM can’t see that. It also ignores the blind level: 10 BB and 100 BB with the same chip share look identical to the model.
- No future hands. ICM values the stacks as they are right now. Models such as FGS (Future Game Simulation) play a few hands ahead, which is solver territory.
- Slightly overrates short stacks. In practice short stacks finish high a little less often than Harville predicts, and big stacks a little more often.
- No bounties. In knockout tournaments part of the chips’ value is in bounties; for GGPoker’s Ocean KO there’s a dedicated Ocean KO calculator.