How much is each stack worth with 5 players left?
The stacks are one short stack: one player holds 5,000 chips, a third of each of the others at 15,000. That makes 65,000 chips in play, and two places paid, 65 and 35 percent. The table gives each seat's share of the prize pool next to its share of the chips.
| Seat | Chips | Share of chips | ICM equity | ICM minus chips |
|---|---|---|---|---|
| Seat 1 | 15,000 | 23.08% | 22.94% | -0.13 points |
| Seat 2 | 15,000 | 23.08% | 22.94% | -0.13 points |
| Seat 3 | 15,000 | 23.08% | 22.94% | -0.13 points |
| Seat 4 | 15,000 | 23.08% | 22.94% | -0.13 points |
| Seat 5 | 5,000 | 7.69% | 8.23% | +0.54 points |
The chips overstate the big stacks and understate the small ones. Seat 4 is worth 0.13 points less than its chip share, while Seat 5 is worth 0.54 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 5 stack (5,000 chips) is paid 16.9% of the time, and the Seat 1 stack (15,000 chips) is paid 45.8% of the time.
| Seat | First | Second | Third | Fourth | Fifth | Paid |
|---|---|---|---|---|---|---|
| Seat 1 | 23.08% | 22.69% | 22.03% | 20.55% | 11.65% | 45.77% |
| Seat 2 | 23.08% | 22.69% | 22.03% | 20.55% | 11.65% | 45.77% |
| Seat 3 | 23.08% | 22.69% | 22.03% | 20.55% | 11.65% | 45.77% |
| Seat 4 | 23.08% | 22.69% | 22.03% | 20.55% | 11.65% | 45.77% |
| Seat 5 | 7.69% | 9.23% | 11.87% | 17.80% | 53.41% | 16.92% |
| Seat | From first | From second | Total |
|---|---|---|---|
| Seat 1 | 15.00 | 7.94 | 22.94% |
| Seat 2 | 15.00 | 7.94 | 22.94% |
| Seat 3 | 15.00 | 7.94 | 22.94% |
| Seat 4 | 15.00 | 7.94 | 22.94% |
| Seat 5 | 5.00 | 3.23 | 8.23% |
What is the bubble factor for each seat with 5 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 1.27 with Seat 1 facing Seat 2; the smallest is 1.05 with Seat 1 facing Seat 5.
| Seat | vs Seat 1 | vs Seat 2 | vs Seat 3 | vs Seat 4 | vs Seat 5 |
|---|---|---|---|---|---|
| Seat 1 | none | 1.27 | 1.27 | 1.27 | 1.05 |
| Seat 2 | 1.27 | none | 1.27 | 1.27 | 1.05 |
| Seat 3 | 1.27 | 1.27 | none | 1.27 | 1.05 |
| Seat 4 | 1.27 | 1.27 | 1.27 | none | 1.05 |
| Seat 5 | 1.08 | 1.08 | 1.08 | 1.08 | none |
How much equity does a call need?
When the smallest stack (Seat 5) calls an all-in from the biggest (Seat 1), the bubble factor is 1.08. A call that needs 50% in chips needs 52.0% once prize money counts, which is 2.0 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.05 and needs 51.3%, 1.3 points over the chip figure. The smaller stack is the one that pays the larger ICM premium, because losing the all-in costs it 8.23% of the prize pool and winning adds 7.59%.
| 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 | 1.0838 | 50.0% | 52.0% | 8.23% | 15.83% | 0.00% |
| Biggest stack calls smallest | 5,000 | 1.0544 | 50.0% | 51.3% | 22.94% | 29.69% | 15.83% |
Where can I compare other stack patterns?
Each payout structure and player count has the same stack patterns, so you can see which of them moves the numbers most. The ICM calculator takes your own stacks and payouts.
How was this ICM table computed?
Each player finishes first with a chance equal to their share of the chips, and every later place is drawn the same way from the players left. Prize equity is the payout of each place times the chance of finishing there. The bubble factor divides the equity lost by losing an all-in by the equity gained by winning it, with the other stacks unchanged, and a player who reaches 0 chips 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 5 players left?
- Seat 1 holds 15,000 chips, 23.1% of the chips in play, and is worth 22.9% of the prize pool when 2 places pay 65/35 percent. That is -0.13 points against its chip share.
- What equity does the smallest stack need to call the biggest stack's all-in?
- 52.0%. In chips alone the call breaks even at 50%, but the bubble factor of 1.08 raises the requirement because losing costs the smallest stack 8.23% 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 22.9% of the prize pool for 23.1% of the chips.