Chips are not dollars: ICM
In a tournament, a chip you win is worth less than a chip you lose. Here is the model that says how much.
7 minute read
In a cash game a chip is a dollar, and doubling your stack doubles your money. In a tournament, prize money is paid by finishing position, and the last chip in the room is worth nothing to the person holding it because they already have first place. Chips and dollars come apart.
Independent Chip Model
P(you finish 1st) = your chips ÷ all chips
P(2nd) sums over every possible winner: P(they win) × your share of the chips that remain. Equity = Σ P(place) × prize.
Four left, three paid ($500 / $300 / $200). Prize pool $1,000.
| Player | Chips | Chip share | Chip-share value | ICM equity |
|---|---|---|---|---|
| P1 | 12,000 | 40.0% | $400 | $336.03 |
| P2 | 9,000 | 30.0% | $300 | $294.88 |
| P3 | 6,000 | 20.0% | $200 | $235.87 |
| P4 | 3,000 | 10.0% | $100 | $133.21 |
Big stacks are worth less than their chip share, short stacks more: a chip you win is worth less than a chip you lose.
Stacks and prizes
4 left · 3 paid| Player | Chips | Chip share | Prize equity | Prize share |
|---|---|---|---|---|
| You | 40.0% | $336.03 | 33.6% | |
| P2 | 30.0% | $294.88 | 29.5% | |
| P3 | 20.0% | $235.87 | 23.6% | |
| P4 | 10.0% | $133.21 | 13.3% |
Payouts
Malmuth–Harville ICM: your chance of first is your chip share; later places follow from the remaining chips. It ignores blinds, position and skill — a model, not a prophecy.
A model with known blind spots
ICM ignores blinds, position, who acts next and who plays better. It is the standard starting point, not the final word, and this site labels it as a model everywhere it appears.
Quick check
Four players, equal stacks, prizes $500 / $300 / $200. What is each player's ICM equity?
Show answer
$250 each — a quarter of the $1,000 pool. Symmetry needs no calculation.