ICM with 6 players left: two big stacks, 2 paid

In ICM, 15,000 chips out of 6 players is 30.0% of the chips and 28.7% of the prize money when 2 places pay 65/35 percent. The 5,000-chip stack holds 10.0% of the chips and is worth 10.7%.

  • 6Players left
  • 65/35Places paid
  • 28.7%Biggest stack worth
  • 10.7%Smallest stack worth

How much is each stack worth with 6 players left?

The stacks are two big stacks: two players hold 15,000 chips each and the rest hold 5,000 each. That makes 50,000 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.

Chips and prize equity with 6 players left, payouts 65/35 percent
SeatChipsShare of chipsICM equityICM minus chips
Seat 115,00030.00%28.67%-1.33 points
Seat 215,00030.00%28.67%-1.33 points
Seat 35,00010.00%10.67%+0.67 points
Seat 45,00010.00%10.67%+0.67 points
Seat 55,00010.00%10.67%+0.67 points
Seat 65,00010.00%10.67%+0.67 points
Share of the chips against share of the prize pool
  • Seat 1Chips 30.0%Prize 28.7%
  • Seat 2Chips 30.0%Prize 28.7%
  • Seat 3Chips 10.0%Prize 10.7%
  • Seat 4Chips 10.0%Prize 10.7%
  • Seat 5Chips 10.0%Prize 10.7%
  • Seat 6Chips 10.0%Prize 10.7%

Prize money flattens the stacks. Seat 2 gives up 1.33 points of equity compared with its share of the chips, and Seat 3 gains 0.67 points.

How often does each seat finish in the money?

Before payouts are applied, each stack has a chance of every finishing place. The biggest stack cashes 56.2% of the time, the smallest 21.9%, with 2 places paid.

Chance of finishing in each place
SeatFirstSecondThirdFourthFifthSixthPaid
Seat 130.00%26.19%20.24%13.57%7.38%2.62%56.19%
Seat 230.00%26.19%20.24%13.57%7.38%2.62%56.19%
Seat 310.00%11.90%14.88%18.21%21.31%23.69%21.90%
Seat 410.00%11.90%14.88%18.21%21.31%23.69%21.90%
Seat 510.00%11.90%14.88%18.21%21.31%23.69%21.90%
Seat 610.00%11.90%14.88%18.21%21.31%23.69%21.90%
Where each seat's prize equity comes from, in points of the prize pool
SeatFrom firstFrom secondTotal
Seat 119.509.1728.67%
Seat 219.509.1728.67%
Seat 36.504.1710.67%
Seat 46.504.1710.67%
Seat 56.504.1710.67%
Seat 66.504.1710.67%

What is the bubble factor for each seat with 6 players left?

The bubble factor is the prize equity a player loses by losing an all-in divided by the equity gained by winning it. The highest figure here is 1.46, for Seat 1 calling Seat 2, and the lowest is 1.07, for Seat 1 calling Seat 3.

Bubble factor when the row seat calls an all-in from the column seat
Seatvs Seat 1vs Seat 2vs Seat 3vs Seat 4vs Seat 5vs Seat 6
Seat 1none1.461.071.071.071.07
Seat 21.46none1.071.071.071.07
Seat 31.131.13none1.081.081.08
Seat 41.131.131.08none1.081.08
Seat 51.131.131.081.08none1.08
Seat 61.131.131.081.081.08none

How much equity does a call need?

When the smallest stack (Seat 6) calls an all-in from the biggest (Seat 1), the bubble factor is 1.13. A call that needs 50% in chips needs 53.1% once prize money counts, which is 3.1 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.07 and needs 51.8%, 1.8 points over the chip figure. The smaller stack is the one that pays the larger ICM premium, because losing the all-in costs it 10.67% of the prize pool and winning adds 9.42%.

Break-even equity for two all-in calls, risking and winning the same chips
CallAll-in (chips)Bubble factorChip break-evenICM break-evenEquity nowEquity if winEquity if lose
Smallest stack calls biggest5,0001.132750.0%53.1%10.67%20.08%0.00%
Biggest stack calls smallest5,0001.072950.0%51.8%28.67%36.67%20.08%

Where can I compare other stack patterns?

Open a sibling to see how the same payouts value a different split of the chips. For your own stacks and payouts, use the ICM calculator.

How was this ICM table 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

How much is the biggest stack worth in ICM with 6 players left?
Seat 1 holds 15,000 chips, 30.0% of the chips in play, and is worth 28.7% of the prize pool when 2 places pay 65/35 percent. That is -1.33 points against its chip share.
What equity does the smallest stack need to call the biggest stack's all-in?
53.1%. In chips alone the call breaks even at 50%, but the bubble factor of 1.13 raises the requirement because losing costs the smallest stack 10.67% 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 28.7% of the prize pool for 30.0% of the chips.