How much is each stack worth with 4 players left?
50,000 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 | 20,000 | 40.00% | 33.60% | -6.40 points |
| Seat 2 | 15,000 | 30.00% | 29.49% | -0.51 points |
| Seat 3 | 10,000 | 20.00% | 23.59% | +3.59 points |
| Seat 4 | 5,000 | 10.00% | 13.32% | +3.32 points |
ICM pays less than chip share to the stacks at the top and more to the stacks at the bottom: Seat 1 falls 6.40 points short, and Seat 3 comes out 3.59 points ahead.
How often does each seat finish in the money?
ICM gets each equity from the chance of finishing in every place. The Seat 4 stack (5,000 chips) is paid 44.9% of the time, and the Seat 1 stack (20,000 chips) is paid 92.2% of the time.
| Seat | First | Second | Third | Fourth | Paid |
|---|---|---|---|---|---|
| Seat 1 | 40.00% | 31.59% | 20.63% | 7.78% | 92.22% |
| Seat 2 | 30.00% | 30.83% | 26.19% | 12.98% | 87.02% |
| Seat 3 | 20.00% | 24.13% | 31.75% | 24.13% | 75.87% |
| Seat 4 | 10.00% | 13.45% | 21.43% | 55.12% | 44.88% |
| Seat | From first | From second | From third | Total |
|---|---|---|---|---|
| Seat 1 | 20.00 | 9.48 | 4.13 | 33.60% |
| Seat 2 | 15.00 | 9.25 | 5.24 | 29.49% |
| Seat 3 | 10.00 | 7.24 | 6.35 | 23.59% |
| Seat 4 | 5.00 | 4.04 | 4.29 | 13.32% |
What is the bubble factor for each seat with 4 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 1.13 (Seat 1 calling Seat 4) up to 2.69 (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 |
|---|---|---|---|---|
| Seat 1 | none | 1.71 | 1.31 | 1.13 |
| Seat 2 | 2.69 | none | 1.48 | 1.16 |
| Seat 3 | 2.35 | 2.17 | none | 1.18 |
| Seat 4 | 1.57 | 1.48 | 1.30 | none |
How much equity does a call need?
When the smallest stack (Seat 4) calls an all-in from the biggest (Seat 1), the bubble factor is 1.57. A call that needs 50% in chips needs 61.1% once prize money counts, which is 11.1 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.13 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 13.32% of the prize pool and winning adds 8.46%.
| 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 | 1.5738 | 50.0% | 61.1% | 13.32% | 21.79% | 0.00% |
| Biggest stack calls smallest | 5,000 | 1.1251 | 50.0% | 52.9% | 33.60% | 38.39% | 28.21% |
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 4 players left?
- Seat 1 holds 20,000 chips, 40.0% of the chips in play, and is worth 33.6% of the prize pool when 3 places pay 50/30/20 percent. That is -6.40 points against its chip share.
- What equity does the smallest stack need to call the biggest stack's all-in?
- 61.1%. In chips alone the call breaks even at 50%, but the bubble factor of 1.57 raises the requirement because losing costs the smallest stack 13.32% 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 33.6% of the prize pool for 40.0% of the chips.