How much is each stack worth with 6 players left?
Here the stacks follow the one chip leader pattern, where one player holds 20,000 chips, twice each of the others at 10,000. Together they hold 70,000 chips, and two places paid, 65 and 35 percent. Read each seat's prize equity against its chip share in the table.
| Seat | Chips | Share of chips | ICM equity | ICM minus chips |
|---|---|---|---|---|
| Seat 1 | 20,000 | 28.57% | 26.90% | -1.67 points |
| Seat 2 | 10,000 | 14.29% | 14.62% | +0.33 points |
| Seat 3 | 10,000 | 14.29% | 14.62% | +0.33 points |
| Seat 4 | 10,000 | 14.29% | 14.62% | +0.33 points |
| Seat 5 | 10,000 | 14.29% | 14.62% | +0.33 points |
| Seat 6 | 10,000 | 14.29% | 14.62% | +0.33 points |
The chips overstate the big stacks and understate the small ones. Seat 1 is worth 1.67 points less than its chip share, while Seat 2 is worth 0.33 points more.
How often does each seat finish in the money?
ICM gets each equity from the chance of finishing in every place. The Seat 6 stack (10,000 chips) is paid 29.5% of the time, and the Seat 1 stack (20,000 chips) is paid 52.4% of the time.
| Seat | First | Second | Third | Fourth | Fifth | Sixth | Paid |
|---|---|---|---|---|---|---|---|
| Seat 1 | 28.57% | 23.81% | 19.05% | 14.29% | 9.52% | 4.76% | 52.38% |
| Seat 2 | 14.29% | 15.24% | 16.19% | 17.14% | 18.10% | 19.05% | 29.52% |
| Seat 3 | 14.29% | 15.24% | 16.19% | 17.14% | 18.10% | 19.05% | 29.52% |
| Seat 4 | 14.29% | 15.24% | 16.19% | 17.14% | 18.10% | 19.05% | 29.52% |
| Seat 5 | 14.29% | 15.24% | 16.19% | 17.14% | 18.10% | 19.05% | 29.52% |
| Seat 6 | 14.29% | 15.24% | 16.19% | 17.14% | 18.10% | 19.05% | 29.52% |
| Seat | From first | From second | Total |
|---|---|---|---|
| Seat 1 | 18.57 | 8.33 | 26.90% |
| Seat 2 | 9.29 | 5.33 | 14.62% |
| Seat 3 | 9.29 | 5.33 | 14.62% |
| Seat 4 | 9.29 | 5.33 | 14.62% |
| Seat 5 | 9.29 | 5.33 | 14.62% |
| Seat 6 | 9.29 | 5.33 | 14.62% |
What is the bubble factor for each seat with 6 players left?
Every call has a bubble factor, the equity lost on a loss over the equity gained on a win. The largest at this table is 1.19 with Seat 2 facing Seat 1; the smallest is 1.12 with Seat 1 facing Seat 2.
| Seat | vs Seat 1 | vs Seat 2 | vs Seat 3 | vs Seat 4 | vs Seat 5 | vs Seat 6 |
|---|---|---|---|---|---|---|
| Seat 1 | none | 1.12 | 1.12 | 1.12 | 1.12 | 1.12 |
| Seat 2 | 1.19 | none | 1.13 | 1.13 | 1.13 | 1.13 |
| Seat 3 | 1.19 | 1.13 | none | 1.13 | 1.13 | 1.13 |
| Seat 4 | 1.19 | 1.13 | 1.13 | none | 1.13 | 1.13 |
| Seat 5 | 1.19 | 1.13 | 1.13 | 1.13 | none | 1.13 |
| Seat 6 | 1.19 | 1.13 | 1.13 | 1.13 | 1.13 | none |
How much equity does a call need?
When the smallest stack (Seat 6) calls an all-in from the biggest (Seat 1), the bubble factor is 1.19. A call that needs 50% in chips needs 54.3% once prize money counts, which is 4.3 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.12 and needs 52.9%, 2.9 points over the chip figure. The smaller stack is the one that pays the larger ICM premium, because losing the all-in costs it 14.62% of the prize pool and winning adds 12.29%.
| Call | All-in (chips) | Bubble factor | Chip break-even | ICM break-even | Equity now | Equity if win | Equity if lose |
|---|---|---|---|---|---|---|---|
| Smallest stack calls biggest | 10,000 | 1.1899 | 50.0% | 54.3% | 14.62% | 26.90% | 0.00% |
| Biggest stack calls smallest | 10,000 | 1.1217 | 50.0% | 52.9% | 26.90% | 37.86% | 14.62% |
Where can I compare other stack patterns?
Compare this pattern with its siblings, with the other payout structure, and with one player more or fewer. The ICM calculator takes your own stacks, and the push or fold calculator prices a shove with the same model.
How was this ICM table computed?
A player finishes first with chance equal to their share of the chips; each next place goes to the players left in proportion to their stacks. Equity is the payout of each place times the chance of finishing there. The bubble factor is prize equity lost by losing the all-in divided by prize equity gained by winning it, with the other stacks unchanged; a player whose stack reaches 0 busts and takes the lowest place.
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
- How much is the biggest stack worth in ICM with 6 players left?
- Seat 1 holds 20,000 chips, 28.6% of the chips in play, and is worth 26.9% of the prize pool when 2 places pay 65/35 percent. That is -1.67 points against its chip share.
- What equity does the smallest stack need to call the biggest stack's all-in?
- 54.3%. In chips alone the call breaks even at 50%, but the bubble factor of 1.19 raises the requirement because losing costs the smallest stack 14.62% of the prize pool.
- Why is ICM equity different from chip share?
- Because the prize pool is paid by place, not by chips. Doubling a stack does not double its payout, so each extra chip is worth less than the one before it. Here the biggest stack is worth 26.9% of the prize pool for 28.6% of the chips.