ICM with 5 players left and 3 places paid

The payouts of 50/30/20 percent with 5 players left pull stacks up to 4.67 points away from their chip shares, depending on the pattern. The highest bubble factor in any of the 5 stack patterns is 2.35.

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

How do the payouts shape ICM with 5 players left?

3 of the 5 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 2 players short of the money.

How do the stack patterns compare with 5 players left?

Each pattern below is one way 5 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 stacks20.0%20.0%20.0%20.0%1.54
One chip leader33.3%28.7%16.7%17.8%1.65
One short stack23.1%22.8%7.7%9.0%1.71
Two big stacks33.3%29.6%11.1%13.6%2.35
Stack ladder33.3%29.3%6.7%8.2%2.11
Prize equity of every seat, biggest stack first, in percent of the prize pool
PatternSeat 1Seat 2Seat 3Seat 4Seat 5
Even stacks20.0020.0020.0020.0020.00
One chip leader28.6717.8317.8317.8317.83
One short stack22.7522.7522.7522.758.99
Two big stacks29.6329.6313.5813.5813.58
Stack ladder29.3125.7921.3015.398.21
Chance of finishing in the money
PatternBiggest stackSmallest stack
Even stacks60.0%60.0%
One chip leader80.0%55.0%
One short stack67.8%28.8%
Two big stacks83.6%44.3%
Stack ladder82.6%26.8%

What does each pattern show with 5 players left?

Even stacks. Seat 1 turns 20.00% of the chips into 20.00% of the prize pool (+0.00 points), while Seat 5 turns 20.00% into 20.00% (+0.00 points).

One chip leader: the biggest stack holds 33.33% of the chips and is worth 28.67%, which is -4.67 points. The smallest holds 16.67% and is worth 17.83%, +1.17 points.

One short stack: the biggest stack holds 23.08% of the chips and is worth 22.75%, which is -0.32 points. The smallest holds 7.69% and is worth 8.99%, +1.30 points.

Two big stacks: the biggest stack holds 33.33% of the chips and is worth 29.63%, which is -3.70 points. The smallest holds 11.11% and is worth 13.58%, +2.47 points.

Stack ladder: the biggest stack holds 33.33% of the chips and is worth 29.31%, which is -4.02 points. The smallest holds 6.67% and is worth 8.21%, +1.54 points.

What does a call cost with 5 players left?

Break-even equity when the smallest stack calls the biggest
PatternAll-in (chips)Bubble factorChip break-evenICM break-even
Even stacks10,0001.538550.0%60.6%
One chip leader10,0001.646250.0%62.2%
One short stack5,0001.216150.0%54.9%
Two big stacks5,0001.507550.0%60.1%
Stack ladder5,0001.256650.0%55.7%

The costliest call for a short stack is in the "one chip leader" pattern, where it needs 62.2% 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?

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

What is the ICM value of an even stack with 5 players left and 3 paid?
Each seat is worth 20.00% 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 1.54.
How far can ICM move a stack from its chip share with 5 players left?
Up to 4.67 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.