How do the payouts shape ICM with 3 players left?
3 of the 3 players still in get paid, at 50/30/20 percent. The steps are 20 points from first to second, 10 from second to third and 20 from third to nothing. No one is on the bubble.
How do the stack patterns compare with 3 players left?
Each pattern below is one way 3 players might split their chips. The table puts the biggest and smallest stack of each next to their chip share, with the highest bubble factor in the pattern. Open a pattern for the full table of every seat.
| Pattern | Biggest: share of chips | Biggest: prize equity | Smallest: share of chips | Smallest: prize equity | Highest bubble factor |
|---|---|---|---|---|---|
| Even stacks | 33.3% | 33.3% | 33.3% | 33.3% | 1.33 |
| One chip leader | 50.0% | 38.3% | 25.0% | 30.8% | 1.44 |
| One short stack | 42.9% | 36.8% | 14.3% | 26.4% | 1.62 |
| Stack ladder | 50.0% | 38.5% | 16.7% | 27.5% | 1.62 |
| Pattern | Seat 1 | Seat 2 | Seat 3 |
|---|---|---|---|
| Even stacks | 33.33 | 33.33 | 33.33 |
| One chip leader | 38.33 | 30.83 | 30.83 |
| One short stack | 36.79 | 36.79 | 26.43 |
| Stack ladder | 38.50 | 34.00 | 27.50 |
| Pattern | Biggest stack | Smallest stack |
|---|---|---|
| Even stacks | 100.0% | 100.0% |
| One chip leader | 100.0% | 100.0% |
| One short stack | 100.0% | 100.0% |
| Stack ladder | 100.0% | 100.0% |
What does each pattern show with 3 players left?
Even stacks: the biggest stack holds 33.33% of the chips and is worth 33.33%, which is +0.00 points. The smallest holds 33.33% and is worth 33.33%, +0.00 points.
One chip leader. Seat 1 turns 50.00% of the chips into 38.33% of the prize pool (-11.67 points), while Seat 3 turns 25.00% into 30.83% (+5.83 points).
One short stack: the biggest stack holds 42.86% of the chips and is worth 36.79%, which is -6.07 points. The smallest holds 14.29% and is worth 26.43%, +12.14 points.
Stack ladder. Seat 1 turns 50.00% of the chips into 38.50% of the prize pool (-11.50 points), while Seat 3 turns 16.67% into 27.50% (+10.83 points).
What does a call cost with 3 players left?
| Pattern | All-in (chips) | Bubble factor | Chip break-even | ICM break-even |
|---|---|---|---|---|
| Even stacks | 10,000 | 1.3333 | 50.0% | 57.1% |
| One chip leader | 10,000 | 1.4444 | 50.0% | 59.1% |
| One short stack | 5,000 | 1.1842 | 50.0% | 54.2% |
| Stack ladder | 5,000 | 1.2857 | 50.0% | 56.3% |
The costliest call for a short stack is in the "one chip leader" pattern, where it needs 59.1% equity rather than 50%. Put that number against the equity of the hand you hold before you call off a stack.
Where can I look at a different payout or player count?
The other seven structure pages cover three to six players left with two or three places paid. The ICM calculator takes any stacks and payouts of your own, up to ten players.
How were these ICM tables 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
- What is the ICM value of an even stack with 3 players left and 3 paid?
- Each seat is worth 33.33% of the prize pool, the same as its share of the chips, because equal stacks are equal in ICM. The bubble factor between any two seats is 1.33.
- How far can ICM move a stack from its chip share with 3 players left?
- Up to 12.14 points in the one short stack pattern with 3 places paid at 50/30/20 percent. The biggest stack gives equity up and the smallest takes it.
- Do these examples include the effect of blinds or antes?
- No. ICM values stacks by chips alone, so blinds, antes, position and the skill of the players do not enter. Use the push or fold calculator to price a shove with blinds and a prize pool together.