How much is each stack worth with 6 players left?
105,000 chips are in play in the stack ladder pattern, where stacks of 5,000, 10,000, 15,000 and so on: the biggest is as many times 5,000 as there are players. The prize pool pays three places paid, 50, 30 and 20 percent, and the table converts each seat's chips into prize equity.
| Seat | Chips | Share of chips | ICM equity | ICM minus chips |
|---|---|---|---|---|
| Seat 1 | 30,000 | 28.57% | 25.82% | -2.75 points |
| Seat 2 | 25,000 | 23.81% | 22.90% | -0.91 points |
| Seat 3 | 20,000 | 19.05% | 19.46% | +0.42 points |
| Seat 4 | 15,000 | 14.29% | 15.42% | +1.13 points |
| Seat 5 | 10,000 | 9.52% | 10.78% | +1.26 points |
| Seat 6 | 5,000 | 4.76% | 5.62% | +0.86 points |
The chips overstate the big stacks and understate the small ones. Seat 1 is worth 2.75 points less than its chip share, while Seat 5 is worth 1.26 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 (5,000 chips) is paid 18.1% of the time, and the Seat 1 stack (30,000 chips) is paid 73.8% of the time.
| Seat | First | Second | Third | Fourth | Fifth | Sixth | Paid |
|---|---|---|---|---|---|---|---|
| Seat 1 | 28.57% | 24.85% | 20.38% | 14.96% | 8.60% | 2.64% | 73.80% |
| Seat 2 | 23.81% | 22.79% | 20.77% | 17.19% | 11.36% | 4.08% | 67.38% |
| Seat 3 | 19.05% | 19.70% | 20.14% | 19.29% | 15.19% | 6.62% | 58.89% |
| Seat 4 | 14.29% | 15.76% | 17.73% | 20.34% | 20.35% | 11.53% | 47.78% |
| Seat 5 | 9.52% | 11.09% | 13.47% | 17.57% | 26.03% | 22.31% | 34.08% |
| Seat 6 | 4.76% | 5.81% | 7.49% | 10.65% | 18.46% | 52.82% | 18.06% |
| Seat | From first | From second | From third | Total |
|---|---|---|---|---|
| Seat 1 | 14.29 | 7.45 | 4.08 | 25.82% |
| Seat 2 | 11.90 | 6.84 | 4.15 | 22.90% |
| Seat 3 | 9.52 | 5.91 | 4.03 | 19.46% |
| Seat 4 | 7.14 | 4.73 | 3.55 | 15.42% |
| Seat 5 | 4.76 | 3.33 | 2.69 | 10.78% |
| Seat 6 | 2.38 | 1.74 | 1.50 | 5.62% |
What is the bubble factor for each seat with 6 players left?
Bubble factor compares what a lost all-in costs with what a won one gains, both in prize equity. In this spot it runs from 1.06 (Seat 1 calling Seat 6) up to 1.82 (Seat 2 calling Seat 1). A figure of 1 would mean chips and prize money agree.
| Seat | vs Seat 1 | vs Seat 2 | vs Seat 3 | vs Seat 4 | vs Seat 5 | vs Seat 6 |
|---|---|---|---|---|---|---|
| Seat 1 | none | 1.64 | 1.42 | 1.26 | 1.15 | 1.06 |
| Seat 2 | 1.82 | none | 1.47 | 1.29 | 1.16 | 1.07 |
| Seat 3 | 1.66 | 1.59 | none | 1.31 | 1.17 | 1.07 |
| Seat 4 | 1.48 | 1.43 | 1.38 | none | 1.18 | 1.07 |
| Seat 5 | 1.31 | 1.28 | 1.24 | 1.21 | none | 1.08 |
| Seat 6 | 1.15 | 1.13 | 1.12 | 1.10 | 1.09 | 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 1.15. A call that needs 50% in chips needs 53.5% once prize money counts, which is 3.5 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.06 and needs 51.5%, 1.5 points over the chip figure. The smaller stack is the one that pays the larger ICM premium, because losing the all-in costs it 5.62% of the prize pool and winning adds 4.90%.
| Call | All-in (chips) | Bubble factor | Chip break-even | ICM break-even | Equity now | Equity if win | Equity if lose |
|---|---|---|---|---|---|---|---|
| Smallest stack calls biggest | 5,000 | 1.1483 | 50.0% | 53.5% | 5.62% | 10.52% | 0.00% |
| Biggest stack calls smallest | 5,000 | 1.0638 | 50.0% | 51.5% | 25.82% | 28.99% | 22.44% |
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 30,000 chips, 28.6% of the chips in play, and is worth 25.8% of the prize pool when 3 places pay 50/30/20 percent. That is -2.75 points against its chip share.
- What equity does the smallest stack need to call the biggest stack's all-in?
- 53.5%. In chips alone the call breaks even at 50%, but the bubble factor of 1.15 raises the requirement because losing costs the smallest stack 5.62% 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 25.8% of the prize pool for 28.6% of the chips.