ICM calculator
Stacks and payouts in; every player’s chance of every place and what their stack is worth in prize money out, summed over every finishing order. Then the question that matters at the table: how much equity does this call need once chips stop being money?
This is the worked example SNG bubble: the chip leader shoves on the second stack; change any stack or prize above.
| Seat | Chips | Share | P(1st) | P(2nd) | P(3rd) | ICM value | Chip-EV value | ICM − chips |
|---|---|---|---|---|---|---|---|---|
| Seat 1shoves | 6,000 | 44.4% | 44.4% | 31.2% | 18.0% | 35.18 | 44.44 | -9.26 |
| Seat 2calls? | 3,500 | 25.9% | 25.9% | 29.9% | 27.7% | 27.46 | 25.93 | +1.53 |
| Seat 3 | 2,500 | 18.5% | 18.5% | 23.6% | 30.8% | 22.50 | 18.52 | +3.98 |
| Seat 4 | 1,500 | 11.1% | 11.1% | 15.3% | 23.6% | 14.86 | 11.11 | +3.75 |
Seat 2 facing Seat 1’s shove
| If Seat 2… | Seat 2 chips | Seat 1 chips | Seat 2 ICM value | Change vs folding |
|---|---|---|---|---|
| Fold | 3,500 | 6,300 | 27.27 | · |
| Call and win | 7,300 | 2,500 | 38.11 | +10.84 |
| Call and lose | busted | 9,800 | 0.00 | -27.27 |
The working
- What is at risk. The smaller stack decides it: Seat 2 risks 3,500 chips to win 3,500 plus the 300 already in the middle.
- Chip EV. Calling breaks even in chips when equity × 7,300 = 3,500, so the call needs 3,500 ÷ 7,300 = 47.95%.
- ICM. Calling with equity q is worth q × 38.11 + (1 − q) × 0.00; folding is worth 27.27. They are equal at q = (27.27 − 0.00) ÷ (38.11 − 0.00) = 71.56%.
- Bubble factor. Prize equity lost per chip lost, over prize equity won per chip won: (27.27 ÷ 3,500) ÷ (10.84 ÷ 3,800) = 2.73. Above one, a chip lost costs more than a chip won is worth.
- What chip EV gets wrong. A call with exactly the chip-EV break-even equity, 47.95%, is free in chips but costs 9.00 in prize equity against folding.
Which hands can call
Against a shover holding the top 20% of hands (40 hand classes, 276 combos, ranked as on /hands), each starting hand’s all-in equity compared with the two prices above.
ICM calls with 2 hand classes (0.9% of hands). Chip EV would call with 19 (9.5%). Folds under ICM that chip EV calls: QQ, JJ, TT, 99, 88, AKs, 77, AQs, AJs, AKo, ATs, AQo and 5 more.
The working, for Seat 2
- First place. The model gives each player the tournament with probability equal to their share of the chips: 3,500 ÷ 13,500 = 25.93%.
- Second place. Someone else wins, then Seat 2 takes first among the players left, again in proportion to chips. Summed over who won: (6,000/13,500)·(3,500/7,500) + (2,500/13,500)·(3,500/11,000) + (1,500/13,500)·(3,500/12,000) = 29.87%.
- Every later place works the same way, over every order in which the places above can be filled. That is 4! = 24 finishing orders in all, summed exactly (no sampling).
- ICM value. Each place's probability times its prize: 25.93% × 50.00 + 29.87% × 30.00 + 27.65% × 20.00 = 27.46. If prizes were paid in proportion to chips the same stack would be worth 25.93.
The link carries every stack and prize. Anyone who opens it gets the same numbers, computed again in their own browser.
- Computed exactly: every seat’s probability of every place, summed over every finishing order, then each prize times its probability. No sampling.
- Assumed: the Independent Chip Model. Your chance of finishing first is your share of the chips, and each later place goes the same way among the players left (Malmuth-Harville). It knows nothing about skill, position, the size of the blinds, or who is about to be in the big blind. Where the model is wrong, so are these numbers, and it is a model, not a solve.
- Assumed: the hand ends the decision. The call price compares this hand only: fold now, or get the chips in and see a showdown. It does not value the spots a bigger stack will get later, which is what future-game simulations try to add.
- Splits count as half a win, as equity always does. Under ICM a split pot leaves stacks almost unchanged, which is worth very nearly the same.
- Which hands call uses the engine’s preflop all-in equity matrix (200,000 sampled run-outs per hand pair, card removal applied), so a hand within a few tenths of a point of the price could fall either side. The shove range is the top X% by equity against a random hand: an assumption about the shover, not a read. For shove and call ranges that are solved rather than assumed, at equal stacks, see the ICM push/fold charts.
- Input: stacks in chips, and the prizes still to be decided, largest first, in any unit: percent, dollars, or seats. Prizes already banked do not change any decision, so leave them out. The pot is any chips already in the middle (blinds and antes), not counted in anyone’s stack.
Worked examples
9 spots, each with its own page: the full ICM table, the three ways the all-in can end, the price of the call, and which hands clear it.
| Spot | Players | Needs (ICM) | Needs (chip EV) |
|---|---|---|---|
| Second stack calls the chip leader | 4 | 71.6% | 47.9% |
| Third stack calls the second stack | 4 | 64.9% | 47.2% |
| Chip leader calls the short stack | 4 | 48.7% | 45.5% |
| Second stack facing a shove, four equal seats | 5 | 90.1% | 50.0% |
| Equal stacks, button shoves into the big blind | 3 | 55.9% | 48.5% |
| Two left: ICM changes nothing | 2 | 48.2% | 48.2% |
| Only first place paid | 3 | 48.5% | 48.5% |
| Second stack calls the shortest stack | 9 | 43.7% | 41.7% |
| Middle stack calls the chip leader | 9 | 63.1% | 47.4% |
Why a chip you win is worth less than a chip you lose
In a cash game a chip is a chip. In a tournament the money is paid by finishing place, and a stack can only ever win first place once. Doubling up does not double what a stack is worth; busting takes all of it. So prize equity bends: every extra chip adds a little less than the one before, and a call that is break-even in chips loses money. On the four-handed bubble above, the second stack needs 71.6% equity to call the chip leader, against 47.9% in chips. The gap is the risk premium; the ratio of what a lost chip costs to what a won chip earns is the bubble factor, here 2.73.
When ICM does not matter
Two cases make prize equity exactly linear in chips, and the calculator shows both: heads-up play, where second place is already locked in, and a winner-take-all prize. Compare the winner-take-all page with the same stacks paying three places: identical chips, identical shove, a different price. The extreme is the satellite bubble, where every seat pays the same and the call needs 90.1% equity: more than aces have against any two cards.
What this means for the push/fold charts
The push/fold charts on this site are solved in chip EV, which is right for heads-up play and for cash games, and too loose near a bubble or a big pay jump. Calling ranges shrink most: a shover also collects the blinds whenever everyone folds, while a caller only ever gets the showdown. How far each range should move depends on every stack at the table, which is why we print the chip-EV solution and this calculator side by side rather than a single “ICM chart” that would only fit one table.
ICM tells you what the call needs. Whether your hand has it is an equity question: the spot check prices any hand against a stated range, with the working.
Check a spot →