ICM — What the Independent Chip Model Actually Computes
ICM stands for Independent Chip Model. It answers one question: if the tournament stopped right now, what is each remaining player's stack actually worth in prize money? The answer is almost never the stack's share of the chips, and the gap is larger than most people expect — a player holding half the chips three-handed is usually worth well under half the pool. That single fact is why deals get made, why short stacks are less desperate than they feel, and why a chip leader who calls off for their tournament life is often making a losing play with the best hand.
Stacks of 5,000, 3,000 and 2,000 out of 10,000. The chip-proportional column is what a straight chip chop would pay. The ICM column is what each seat is really worth, and the two disagree by more than ten percent of the whole prize pool.
Player
Chip leader
Chips
5,000 (50%)
Chip chop pays
$500.00
ICM value
$383.93
Difference
−$116.07
Player
Middle stack
Chips
3,000 (30%)
Chip chop pays
$300.00
ICM value
$327.50
Difference
+$27.50
Player
Short stack
Chips
2,000 (20%)
Chip chop pays
$200.00
ICM value
$288.57
Difference
+$88.57
Player
Total
Chips
10,000
Chip chop pays
$1,000.00
ICM value
$1,000.00
Difference
—
Player
Chips
Chip chop pays
ICM value
Difference
Chip leader
5,000 (50%)
$500.00
$383.93
−$116.07
Middle stack
3,000 (30%)
$300.00
$327.50
+$27.50
Short stack
2,000 (20%)
$200.00
$288.57
+$88.57
Total
10,000
$1,000.00
$1,000.00
—
Where those numbers come from
ICM assumes the chance of finishing first equals your share of the chips, then re-runs the same assumption on whoever is left to get second, and so on. These are the finish probabilities behind the table above.
Player
Chip leader (5,000)
Finishes 1st
50.0%
Finishes 2nd
33.9%
Finishes 3rd
16.1%
Player
Middle stack (3,000)
Finishes 1st
30.0%
Finishes 2nd
37.5%
Finishes 3rd
32.5%
Player
Short stack (2,000)
Finishes 1st
20.0%
Finishes 2nd
28.6%
Finishes 3rd
51.4%
Player
Finishes 1st
Finishes 2nd
Finishes 3rd
Chip leader (5,000)
50.0%
33.9%
16.1%
Middle stack (3,000)
30.0%
37.5%
32.5%
Short stack (2,000)
20.0%
28.6%
51.4%
Players
6-8 seats
Setup
15 minutes
After game
Share results
What the model says
ICM converts a chip stack into an expected share of the prize pool. It does it with one assumption applied repeatedly: your probability of winning outright is your share of the chips in play. Once you have that, the probability of finishing second is the sum, over every other player, of the chance that they win multiplied by your share of the chips that remain after their stack is removed. Third place works the same way one level down. Multiply each finish probability by what that finish pays, add them up, and you have the stack's cash value.
Working it through, three-handed
Stacks are 5,000, 3,000 and 2,000, and the pool is $1,000 paid 50/30/20. The leader wins outright 50% of the time. For second place, either the middle stack wins first — 30% of the time — and the leader then holds 5,000 of the remaining 7,000, or the short stack wins first at 20% and the leader holds 5,000 of 8,000. That comes to 33.9%. Whatever is left, 16.1%, is third. So the leader is worth 0.500 × $500 plus 0.339 × $300 plus 0.161 × $200, which is $383.93 — not the $500 that half the chips would suggest.
Why the chip leader is worth less than their chips
Because first prize is not proportional to the chips you need to win it. Going from 20% of the chips to 50% roughly doubles and a half your equity in chips, but first place only pays two and a half times what third does while being far harder to reach. Every chip you win is worth less than the one before it, and every chip you lose costs more than the last one did. That asymmetry is the whole of ICM, and it is why a large stack should decline marginal all-ins that a cash-game player would snap off.
Why the short stack gains
The short stack in the table is worth $288.57 against the $200 a chip chop would hand them, a 44% premium, because they are already guaranteed a paid finish. Reaching the money is the expensive part, and they have done it. Everything above the minimum payout is what they have left to play for, and their chips only have to buy the difference between third and second. This is why short stacks at a final table are rarely as close to worthless as the chip counts look, and why they can reasonably refuse a chip-proportional deal.
The four assumptions, and when each breaks
ICM assumes skill is equal, position does not exist, blinds never go up, and no player ever makes a different decision because of the model. All four are false. A stronger player is worth more than their chips; the big blind is worth less than the same stack on the button because they are about to pay; with 20 big blinds left the next level matters more than any of this; and everybody at a final table is adjusting to ICM pressure, which changes the finish probabilities the model assumed. The number is a useful reference point, not a settlement.
ICM pressure, in practice
The practical consequence is that calls get tighter as the pay jumps get bigger, and they get tighter for the players who have most to lose. On a bubble with one spot left, the big stack can raise almost anything and the medium stacks have to fold hands that are comfortably ahead, because busting costs them a payout while the big stack only loses chips. Nobody is calculating this at the table; they are applying a rule of thumb — do not go broke while somebody else is about to — that ICM explains.
Using it for a deal, or not
An ICM deal divides the remaining prize pool by these equities instead of by chip count. It is the more correct division and it is also opaque: nobody at a kitchen table can check the arithmetic, and a deal nobody can check is a deal somebody resents at breakfast. The chop calculator on this site does a chip chop with a save, which gets close enough for a home game and can be followed by everyone in the room. Use ICM if your group already knows what it is.
Why it barely matters in a cash game
In a cash game a chip is worth its face value, always, because you can stand up and take it to the window. Doubling your stack doubles your money, so the model has nothing to correct and ICM does not apply. It only exists because tournament chips cannot be cashed out and their value comes entirely from the payout structure they might eventually reach. Flat payouts make the effect small; top-heavy payouts make it large; winner-take-all removes it completely.
Keeping the numbers straight at a home game
All of this assumes everyone agrees on the stacks and the pool, which at one in the morning is not a given. PokerChip.live records every buy-in, rebuy and elimination as it happens, so the chip counts and the prize pool are not being reconstructed from memory when a deal comes up. Settle the arithmetic before the argument, not during it.
FAQ
Questions about icm poker
01
What is ICM in poker?
The Independent Chip Model. It converts a tournament chip stack into an expected share of the prize pool, by working out how often that stack finishes in each paid position and multiplying by what each position pays.
02
What does ICM mean?
It stands for Independent Chip Model. The name comes from the assumption it makes: that each chip is independent and equally likely to end up anywhere, so your chance of winning is simply your share of the chips in play.
03
How is ICM calculated?
Your chance of finishing first is your share of the chips. Your chance of second is the sum over every opponent of the chance they finish first times your share of the chips left without them. Repeat for each paid place, multiply by the payouts, and add.
04
Why is the chip leader worth less than their chip share?
Because first prize does not scale with the chips needed to win it. Each chip gained is worth less than the last and each chip lost costs more than the last, so half the chips buys well under half the pool whenever the payouts are not winner-take-all.
05
Is ICM used in cash games?
No. A cash-game chip is worth its face value because you can cash it out at any time, so there is nothing for the model to correct. ICM exists only because tournament chips get their value from a payout structure rather than from a cage.
06
Is an ICM deal better than a chip chop?
It is more accurate, because it prices chips against the actual payout structure instead of at face value. It is also much harder to explain, which is why home games usually run a chip chop with a save and leave ICM to groups that already use it.
07
What is ICM pressure?
The effect of pay jumps on how wide players can call. When busting costs a guaranteed payout, medium stacks have to fold hands that are ahead of the raising range, and the big stack can attack with almost anything because it only risks chips.
08
What does ICM not account for?
Skill differences, table position, the blind structure, and the fact that opponents are adjusting to ICM themselves. It is a reference point for how much a stack is worth, not a substitute for reading the specific table you are sitting at.
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