How Is ICM Calculated in Poker?

ICM is calculated by working out each player’s probability of finishing in every paid position, multiplying those probabilities by the prize for each spot, and adding them up. The starting point is simple: your chance of finishing first equals your stack divided by the total chips in play. From there the model branches through second, third, and so on.

The core formula

The model rests on one assumption: each chip is equally likely to be the last one standing, so your odds of winning equal your share of all chips. Formally:

P(finish 1st) = your stack ÷ total chips

For the next places, you “remove” the winner and repeat the same logic on the remaining stacks. P(you finish 2nd) is the sum, over every opponent who could finish first, of the chance they win times your chance of being top of the leftovers. Your ICM value is then:

Equity = P(1st)×Prize₁ + P(2nd)×Prize₂ + P(3rd)×Prize₃ + …

Worked example: three players left

Three players remain. The prize pool pays $50 / $30 / $20 for 1st / 2nd / 3rd. Stacks:

Player	Chips	Chip %
A	5,000	50%
B	3,000	30%
C	2,000	20%

Total = 10,000 chips. Let’s calculate Player A’s equity step by step.

Step 1 — first place. A’s stack is 50% of all chips, so:

P(A 1st) = 5,000 ÷ 10,000 = 0.50

Step 2 — second place. A finishes 2nd only if B or C finishes 1st and then A is the larger of the two survivors.

• If B wins (P = 3,000/10,000 = 0.30): remaining are A 5,000 and C 2,000 (total 7,000). A is 2nd with probability 5,000/7,000 ≈ 0.714. Contribution: 0.30 × 0.714 = 0.214.
• If C wins (P = 2,000/10,000 = 0.20): remaining are A 5,000 and B 3,000 (total 8,000). A is 2nd with probability 5,000/8,000 = 0.625. Contribution: 0.20 × 0.625 = 0.125.

P(A 2nd) = 0.214 + 0.125 = 0.339

Step 3 — third place. Probabilities must sum to 1, so:

P(A 3rd) = 1 − 0.50 − 0.339 = 0.161

Step 4 — multiply by prizes:

Equity = 0.50×$50 + 0.339×$30 + 0.161×$20 = $25.00 + $10.17 + $3.22 = $38.39

The full table

Run the same process for B and C and you get every player’s real-money value:

Player	Chips	Chip %	ICM equity	Equity %
A	5,000	50%	$38.39	38.4%
B	3,000	30%	$32.75	32.8%
C	2,000	20%	$28.86	28.9%
Total	10,000	100%	$100.00	100%

The headline result: Player A owns 50% of the chips but only 38% of the money. The big stack’s chips are “overvalued” by raw count, while the short stack (20% of chips, 29% of the money) is “undervalued.” That’s diminishing chip value made concrete — and it’s exactly why a chip leader can’t bully recklessly and a short stack isn’t as doomed as the chip count suggests.

Doing it for real

The branches multiply fast — four players means twenty-four orderings, and full tables are impractical by hand. In practice you:

• Estimate at the table. First-place equity (chips ÷ total) plus a feel for the pay jumps is usually enough for a decision.
• Verify with a calculator. ICM calculators and trainers crunch the exact numbers; many also show the equity swing of a specific all-in, which is what you actually care about.
• Learn the swings, not the digits. What matters is “how much equity do I gain vs. risk,” not the third decimal place.

If the probability-times-payout logic feels familiar, it’s the same expected-value thinking behind poker odds and math. For where these numbers change real decisions, see what ICM is and ICM deal making, or return to the ICM hub.