// ICM calculator · 9 left · 9 paid
Nine-handed final table: calling the short stack
Seat 9 shoves and Seat 2 has to decide. In chips the call needs 41.7% equity; under ICM it needs 43.7%, a risk premium of 2.0%.
A full final table with a pay jump on every place. The shortest stack shoves and the second stack, who covers them comfortably, has to decide. Most of the risk is a small dent in a big stack, and a win knocks out a player and moves everyone up the ladder, so the premium is modest.
| Seat | Chips | Share | P(1st) | P(2nd) | P(3rd) | P(4th) | P(5th) | P(6th) | P(7th) | P(8th) | P(9th) | ICM value | Chip-EV value | ICM − chips |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Seat 1 | 40,000 | 22.3% | 22.3% | 19.8% | 17.1% | 14.2% | 11.1% | 7.9% | 4.8% | 2.2% | 0.6% | 16.21 | 22.35 | -6.14 |
| Seat 2calls? | 32,000 | 17.9% | 17.9% | 17.1% | 16.0% | 14.5% | 12.5% | 10.0% | 7.0% | 3.8% | 1.1% | 14.64 | 17.88 | -3.23 |
| Seat 3 | 27,000 | 15.1% | 15.1% | 15.0% | 14.8% | 14.2% | 13.2% | 11.5% | 8.9% | 5.4% | 1.9% | 13.52 | 15.08 | -1.57 |
| Seat 4 | 22,000 | 12.3% | 12.3% | 12.7% | 13.1% | 13.4% | 13.4% | 12.8% | 11.2% | 7.9% | 3.2% | 12.24 | 12.29 | -0.05 |
| Seat 5 | 18,000 | 10.1% | 10.1% | 10.7% | 11.4% | 12.2% | 13.0% | 13.5% | 13.2% | 10.7% | 5.3% | 11.08 | 10.06 | +1.02 |
| Seat 6 | 15,000 | 8.4% | 8.4% | 9.1% | 9.9% | 10.9% | 12.2% | 13.6% | 14.6% | 13.5% | 7.8% | 10.10 | 8.38 | +1.72 |
| Seat 7 | 12,000 | 6.7% | 6.7% | 7.4% | 8.2% | 9.4% | 10.8% | 12.8% | 15.5% | 17.0% | 12.1% | 9.01 | 6.70 | +2.31 |
| Seat 8 | 8,000 | 4.5% | 4.5% | 5.0% | 5.8% | 6.8% | 8.2% | 10.4% | 14.1% | 21.4% | 23.8% | 7.34 | 4.47 | +2.87 |
| Seat 9shoves | 5,000 | 2.8% | 2.8% | 3.2% | 3.7% | 4.5% | 5.6% | 7.4% | 10.6% | 18.1% | 44.1% | 5.86 | 2.79 | +3.07 |
Seat 2 facing Seat 9’s shove
Equity needed, ICM43.7%
Equity needed, chip EV41.7%
Risk premium+2.0%
Bubble factor1.09
| If Seat 2… | Seat 2 chips | Seat 9 chips | Seat 2 ICM value | Change vs folding |
|---|---|---|---|---|
| Fold | 32,000 | 7,000 | 14.53 | · |
| Call and win | 39,000 | busted | 16.11 | +1.58 |
| Call and lose | 27,000 | 12,000 | 13.30 | -1.23 |
The working
- What is at risk. The smaller stack decides it: Seat 2 risks 5,000 chips to win 5,000 plus the 2,000 already in the middle.
- Chip EV. Calling breaks even in chips when equity × 12,000 = 5,000, so the call needs 5,000 ÷ 12,000 = 41.67%.
- ICM. Calling with equity q is worth q × 16.11 + (1 − q) × 13.30; folding is worth 14.53. They are equal at q = (14.53 − 13.30) ÷ (16.11 − 13.30) = 43.70%.
- Bubble factor. Prize equity lost per chip lost, over prize equity won per chip won: (1.23 ÷ 5,000) ÷ (1.58 ÷ 7,000) = 1.09. 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, 41.67%, is free in chips but costs 0.06 in prize equity against folding.
Which hands can call
Against a shover holding the top 40% of hands (74 hand classes, 536 combos, ranked as on /hands), each starting hand’s all-in equity compared with the two prices above.
Shover’s range, top
AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5s43%K4s42%K3sK2sAQoKQoQQQJsQTsQ9s44%Q8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQTo44%JToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8o44%Q8oJ8oT8o98o8887s86s85s84s83s82sA7oK7o42%Q7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
calls under ICM calls at chip EV only (equity shown) folds either way
ICM calls with 52 hand classes (27.9% of hands). Chip EV would call with 58 (31.5%). Folds under ICM that chip EV calls: Q9s, QTo, K8o, K5s, K7o, K4s.
The working, for Seat 2
- First place. The model gives each player the tournament with probability equal to their share of the chips: 32,000 ÷ 179,000 = 17.88%.
- Second place. Someone else wins, then Seat 2 takes first among the players left, again in proportion to chips. Summed over who won: (40,000/179,000)·(32,000/139,000) + (27,000/179,000)·(32,000/152,000) + (22,000/179,000)·(32,000/157,000) + (18,000/179,000)·(32,000/161,000) + (15,000/179,000)·(32,000/164,000) + (12,000/179,000)·(32,000/167,000) + (8,000/179,000)·(32,000/171,000) + (5,000/179,000)·(32,000/174,000) = 17.09%.
- Every later place works the same way, over every order in which the places above can be filled. That is 9! = 362,880 finishing orders in all, summed exactly (no sampling).
- ICM value. Each place's probability times its prize: 17.88% × 30.00 + 17.09% × 20.00 + 15.99% × 14.00 + 14.50% × 10.00 + 12.54% × 8.00 + 10.04% × 6.50 + 7.03% × 5.00 + 3.79% × 3.50 + 1.14% × 3.00 = 14.64. If prizes were paid in proportion to chips the same stack would be worth 17.88.
// settle the thread
The link carries every stack and prize. Anyone who opens it gets the same numbers, computed again in their own browser.
Move a stack, add a prize, change who shoves: open this spot in the calculator and every number is computed again in your browser.
Change the stacks →// what is computed, and what is assumed
- 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.
More ICM spots
| 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% |
| Middle stack calls the chip leader | 9 | 63.1% | 47.4% |