ICM with 6 players left and 3 places paid

With 6 players left and 3 places paid (50/30/20 percent), ICM moves a stack's prize equity by up to 3.33 points away from its chip share across the 5 stack patterns. The highest bubble factor in any of them is 2.05.

  • 6Players left
  • 50/30/20Places paid
  • 5Stack patterns

How do the payouts shape ICM with 6 players left?

3 of the 6 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. That leaves 3 players short of the money.

How do the stack patterns compare with 6 players left?

Each pattern below is one way 6 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.

Biggest and smallest stack by pattern
PatternBiggest: share of chipsBiggest: prize equitySmallest: share of chipsSmallest: prize equityHighest bubble factor
Even stacks16.7%16.7%16.7%16.7%1.39
One chip leader28.6%25.2%14.3%15.0%1.45
One short stack18.8%18.6%6.3%7.0%1.47
Two big stacks30.0%26.9%10.0%11.5%2.05
Stack ladder28.6%25.8%4.8%5.6%1.82
Prize equity of every seat, biggest stack first, in percent of the prize pool
PatternSeat 1Seat 2Seat 3Seat 4Seat 5Seat 6
Even stacks16.6716.6716.6716.6716.6716.67
One chip leader25.2414.9514.9514.9514.9514.95
One short stack18.6018.6018.6018.6018.607.02
Two big stacks26.9026.9011.5511.5511.5511.55
Stack ladder25.8222.9019.4615.4210.785.62
Chance of finishing in the money
PatternBiggest stackSmallest stack
Even stacks50.0%50.0%
One chip leader71.4%45.7%
One short stack55.6%22.1%
Two big stacks76.4%36.8%
Stack ladder73.8%18.1%

What does each pattern show with 6 players left?

Even stacks: 16.67% of the chips is worth 16.67% at the top of the table (+0.00 points), and 16.67% is worth 16.67% at the bottom (+0.00 points).

One chip leader: the biggest stack holds 28.57% of the chips and is worth 25.24%, which is -3.33 points. The smallest holds 14.29% and is worth 14.95%, +0.67 points.

One short stack: 18.75% of the chips is worth 18.60% at the top of the table (-0.15 points), and 6.25% is worth 7.02% at the bottom (+0.77 points).

Two big stacks: the biggest stack holds 30.00% of the chips and is worth 26.90%, which is -3.10 points. The smallest holds 10.00% and is worth 11.55%, +1.55 points.

Stack ladder. Seat 1 turns 28.57% of the chips into 25.82% of the prize pool (-2.75 points), while Seat 6 turns 4.76% into 5.62% (+0.86 points).

What does a call cost with 6 players left?

Break-even equity when the smallest stack calls the biggest
PatternAll-in (chips)Bubble factorChip break-evenICM break-even
Even stacks10,0001.388950.0%58.1%
One chip leader10,0001.453750.0%59.2%
One short stack5,0001.148050.0%53.4%
Two big stacks5,0001.362450.0%57.7%
Stack ladder5,0001.148350.0%53.5%

The costliest call for a short stack is in the "one chip leader" pattern, where it needs 59.2% 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?

Under the Malmuth-Harville model a stack wins first place in proportion to its chips, then the next place is awarded among the rest in the same proportion, and so on. Equity adds up the payout of each place weighted by those chances. For the bubble factor, a player whose stack falls to 0 busts into the lowest place and the other stacks stay put.

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 6 players left and 3 paid?
Each seat is worth 16.67% 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 1.39.
How far can ICM move a stack from its chip share with 6 players left?
Up to 3.33 points in the one chip leader 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.