// ICM calculator · 3 left · 3 paid

Three-handed, equal stacks, top three paid

Seat 1 shoves and Seat 2 has to decide. In chips the call needs 48.5% equity; under ICM it needs 55.9%, a risk premium of 7.4%.

Everyone is already in the money and the stacks are level. There is no bubble left, but there is still a pay jump on every place, and the player who busts takes third while the one who doubles is not yet guaranteed first. ICM charges the caller a premium even here.

Seat	Chips	Share	P(1st)	P(2nd)	P(3rd)	ICM value	Chip-EV value
Seat 1shoves	5,000	33.3%	33.3%	33.3%	33.3%	33.33	33.33
Seat 2calls?	5,000	33.3%	33.3%	33.3%	33.3%	33.33	33.33
Seat 3	5,000	33.3%	33.3%	33.3%	33.3%	33.33	33.33

Seat 2 facing Seat 1’s shove

Equity needed, ICM55.9%

Equity needed, chip EV48.5%

Risk premium+7.4%

Bubble factor1.35

If Seat 2…	Seat 2 chips	Seat 1 chips	Seat 2 ICM value	Change vs folding
Fold	5,000	5,300	33.12	·
Call and win	10,300	busted	43.46	+10.34
Call and lose	busted	10,300	20.00	-13.12

The working

What is at risk. The smaller stack decides it: Seat 2 risks 5,000 chips to win 5,000 plus the 300 already in the middle.
Chip EV. Calling breaks even in chips when equity × 10,300 = 5,000, so the call needs 5,000 ÷ 10,300 = 48.54%.
ICM. Calling with equity q is worth q × 43.46 + (1 − q) × 20.00; folding is worth 33.12. They are equal at q = (33.12 − 20.00) ÷ (43.46 − 20.00) = 55.93%.
Bubble factor. Prize equity lost per chip lost, over prize equity won per chip won: (13.12 ÷ 5,000) ÷ (10.34 ÷ 5,300) = 1.35. 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, 48.54%, is free in chips but costs 1.73 in prize equity against folding.

Which hands can call

Against a shover holding the top 50% of hands (91 hand classes, 670 combos, ranked as on /hands), each starting hand’s all-in equity compared with the two prices above.

Shover’s range, top

AAAKsAQsAJsATsA9sA8sA7s56%A6s54%A5s54%A4s53%A3s53%A2s52%AKoKKKQsKJsKTs55%K9s53%K8s50%K7s49%K6sK5sK4sK3sK2sAQoKQoQQQJs51%QTs50%Q9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJo54%QJo49%JJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKTo53%QToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9o50%Q9oJ9oT9o9998s97s96s95s94s93s92sA8o55%K8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7o53%K7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6o52%K6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5o52%K5oQ5oJ5oT5o95o85o75o65o5554%54s53s52sA4o50%K4oQ4oJ4oT4o94o84o74o64o54o4452%43s42sA3o50%K3oQ3oJ3oT3o93o83o73o63o53o43o3350%32sA2o49%K2oQ2oJ2oT2o92o82o72o62o52o42o32o22

calls under ICM calls at chip EV only (equity shown) folds either way

ICM calls with 23 hand classes (11.9% of hands). Chip EV would call with 49 (26.8%). Folds under ICM that chip EV calls: KTs, A7s, KJo, 55, QJs, K9s, A5s, A6s, A8o, KTo, QTs, A4s and 14 more.

The working, for Seat 2

First place. The model gives each player the tournament with probability equal to their share of the chips: 5,000 ÷ 15,000 = 33.33%.
Second place. Someone else wins, then Seat 2 takes first among the players left, again in proportion to chips. Summed over who won: (5,000/15,000)·(5,000/10,000) + (5,000/15,000)·(5,000/10,000) = 33.33%.
Every later place works the same way, over every order in which the places above can be filled. That is 3! = 6 finishing orders in all, summed exactly (no sampling).
ICM value. Each place's probability times its prize: 33.33% × 50.00 + 33.33% × 30.00 + 33.33% × 20.00 = 33.33. If prizes were paid in proportion to chips the same stack would be worth 33.33.

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%
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%