How is ICM calculated?
ICM, the Independent Chip Model, takes every player's chance of finishing first as their share of the chips. Given who finished first, the next place is awarded among the rest in proportion to their chips, and so on down the places. A player's prize equity is each place's payout times the chance of finishing there, added up.
Take three players holding 5,000, 3,000, 2,000 chips with payouts of 50/30/20 percent. The first player finishes first with chance 5,000 / 10,000, which is 50.0%. For second place, add up the chance that each other player won and this player took second among the rest.
| Player | Chips | Chance of first | Chance of second | Chance of third | ICM equity |
|---|---|---|---|---|---|
| Player 1 | 5,000 | 50.00% | 33.93% | 16.07% | 38.3929% |
| Player 2 | 3,000 | 30.00% | 37.50% | 32.50% | 32.7500% |
| Player 3 | 2,000 | 20.00% | 28.57% | 51.43% | 28.8571% |
Player 1 is worth 0.50 x 50 + 0.3393 x 30 + 0.1607 x 20 = 38.3929 percent of the prize pool, against 50% of the chips. The three equities add to 100 percent.
What is the bubble factor?
The bubble factor measures how much more a lost all-in costs than a won all-in gains, in prize equity. It is equity lost by losing divided by equity gained by winning. Chip EV break-even for a call risking R to win G is R / (R + G); the ICM break-even is BF x R / (BF x R + G), so a bubble factor of 1.5 on an even-money call lifts the requirement from 50 percent to 60 percent.
Which ICM example matches my tournament?
Pick the number of players left and the number of paid places. Each of the eight structure pages compares the stack patterns side by side, and each of the 38 pattern pages gives the full seat-by-seat table and bubble factor matrix.
| Structure | Payouts | Stack patterns |
|---|---|---|
| 3 players left, 2 paid | 65/35 percent | 4 |
| 3 players left, 3 paid | 50/30/20 percent | 4 |
| 4 players left, 2 paid | 65/35 percent | 5 |
| 4 players left, 3 paid | 50/30/20 percent | 5 |
| 5 players left, 2 paid | 65/35 percent | 5 |
| 5 players left, 3 paid | 50/30/20 percent | 5 |
| 6 players left, 2 paid | 65/35 percent | 5 |
| 6 players left, 3 paid | 50/30/20 percent | 5 |
What does ICM leave out?
ICM looks only at chip counts and payouts. It does not know about blinds and antes still to come, position, or how well each player plays, and it assumes the chance of winning is proportional to chips. It is a standard approximation, and the examples here use it exactly as defined, so you can compare your own spot against them.
How were the examples computed?
Under the Malmuth-Harville model a stack wins first place in proportion to its chips, then the next place is awarded among the rest in the same proportion, and so on. Equity adds up the payout of each place weighted by those chances. For the bubble factor, a player whose stack falls to 0 busts into the lowest place and the other stacks stay put.
Source: Malmuth-Harville ICM, computed by GeorgeLiPoker's own library. The model follows D. A. Harville, 'Assigning Probabilities to the Outcomes of Multi-Entry Competitions', Journal of the American Statistical Association, 1973.
Questions
- What does ICM stand for in poker?
- ICM stands for Independent Chip Model. It converts the chips each player holds in a tournament into a share of the prize pool, using the payouts and the chance of finishing in each place.
- What is the ICM formula?
- A player finishes first with chance equal to their share of the chips, and each next place goes to the players left in proportion to their chips. Equity is the payout of each place times the chance of finishing there, summed over places. For stacks 5,000, 3,000, 2,000 and payouts 50/30/20 percent, that gives 38.39%, 32.75%, 28.86%.
- Why do short stacks call tighter in a tournament?
- Losing the last chips ends the tournament and costs the whole prize equity, while winning the same chips adds less. That is the bubble factor. In all 38 examples here the bubble factor is above 1, the lowest being 1.03, so the equity needed to call is higher than the chip figure.