ICM with 6 players left: even stacks, 2 paid

Take 6 players, 2 paid places (65/35 percent) and even stacks: the largest stack converts 16.7% of the chips into 16.7% of the prize pool, and the smallest turns 16.7% into 16.7%.

  • 6Players left
  • 65/35Places paid
  • 16.7%Biggest stack worth
  • 16.7%Smallest stack worth

How much is each stack worth with 6 players left?

60,000 chips are in play in the even stacks pattern, where every player holds 10,000 chips. The prize pool pays two places paid, 65 and 35 percent, and the table converts each seat's chips into prize equity.

Chips and prize equity with 6 players left, payouts 65/35 percent
SeatChipsShare of chipsICM equityICM minus chips
Seat 110,00016.67%16.67%+0.00 points
Seat 210,00016.67%16.67%+0.00 points
Seat 310,00016.67%16.67%+0.00 points
Seat 410,00016.67%16.67%+0.00 points
Seat 510,00016.67%16.67%+0.00 points
Seat 610,00016.67%16.67%+0.00 points
Share of the chips against share of the prize pool
  • Seat 1Chips 16.7%Prize 16.7%
  • Seat 2Chips 16.7%Prize 16.7%
  • Seat 3Chips 16.7%Prize 16.7%
  • Seat 4Chips 16.7%Prize 16.7%
  • Seat 5Chips 16.7%Prize 16.7%
  • Seat 6Chips 16.7%Prize 16.7%

ICM pays less than chip share to the stacks at the top and more to the stacks at the bottom: Seat 6 falls 0.00 points short, and Seat 1 comes out 0.00 points ahead.

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 33.3% of the time, the smallest 33.3%, with 2 places paid.

Chance of finishing in each place
SeatFirstSecondThirdFourthFifthSixthPaid
Seat 116.67%16.67%16.67%16.67%16.67%16.67%33.33%
Seat 216.67%16.67%16.67%16.67%16.67%16.67%33.33%
Seat 316.67%16.67%16.67%16.67%16.67%16.67%33.33%
Seat 416.67%16.67%16.67%16.67%16.67%16.67%33.33%
Seat 516.67%16.67%16.67%16.67%16.67%16.67%33.33%
Seat 616.67%16.67%16.67%16.67%16.67%16.67%33.33%
Where each seat's prize equity comes from, in points of the prize pool
SeatFrom firstFrom secondTotal
Seat 110.835.8316.67%
Seat 210.835.8316.67%
Seat 310.835.8316.67%
Seat 410.835.8316.67%
Seat 510.835.8316.67%
Seat 610.835.8316.67%

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 1.16, for Seat 1 calling Seat 2, and the lowest is 1.16, for Seat 1 calling Seat 2.

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 1none1.161.161.161.161.16
Seat 21.16none1.161.161.161.16
Seat 31.161.16none1.161.161.16
Seat 41.161.161.16none1.161.16
Seat 51.161.161.161.16none1.16
Seat 61.161.161.161.161.16none

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 1.16. A call that needs 50% in chips needs 53.8% once prize money counts, which is 3.8 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.16 and needs 53.8%, 3.8 points over the chip figure. Here the bigger stack pays the larger premium: losing costs it 16.67% of the prize pool and winning adds 14.33%.

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 biggest10,0001.162850.0%53.8%16.67%31.00%0.00%
Biggest stack calls smallest10,0001.162850.0%53.8%16.67%31.00%0.00%

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 10,000 chips, 16.7% of the chips in play, and is worth 16.7% of the prize pool when 2 places pay 65/35 percent. That is +0.00 points against its chip share.
What equity does the smallest stack need to call the biggest stack's all-in?
53.8%. In chips alone the call breaks even at 50%, but the bubble factor of 1.16 raises the requirement because losing costs the smallest stack 16.67% 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 16.7% of the prize pool for 16.7% of the chips.