How much is the biggest stack worth in ICM with 4 players left?

Seat 1 holds 15,000 chips, 37.5% of the chips in play, and is worth 36.0% of the prize pool when 2 places pay 65/35 percent. That is -1.50 points against its chip share.

What equity does the smallest stack need to call the biggest stack's all-in?

54.5%. In chips alone the call breaks even at 50%, but the bubble factor of 1.20 raises the requirement because losing costs the smallest stack 14.00% 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 36.0% of the prize pool for 37.5% of the chips.

ICM: Two big stacks, 4 Players, 2 Paid

With 4 players left and 2 paid (65/35 percent), the biggest stack of 15,000 chips holds 37.5% of the chips but is worth 36.0% of the prize pool. The smallest, 5,000 chips, holds 12.5% and is worth 14.0%.

How much is each stack worth with 4 players left?

Here the stacks follow the two big stacks pattern, where two players hold 15,000 chips each and the rest hold 5,000 each. Together they hold 40,000 chips, and two places paid, 65 and 35 percent. Read each seat's prize equity against its chip share in the table.

Chips and prize equity with 4 players left, payouts 65/35 percent
Seat	Chips	Share of chips	ICM equity	ICM minus chips
Seat 1	15,000	37.50%	36.00%	-1.50 points
Seat 2	15,000	37.50%	36.00%	-1.50 points
Seat 3	5,000	12.50%	14.00%	+1.50 points
Seat 4	5,000	12.50%	14.00%	+1.50 points

Share of the chips against share of the prize pool

Seat 1Chips 37.5%Prize 36.0%
Seat 2Chips 37.5%Prize 36.0%
Seat 3Chips 12.5%Prize 14.0%
Seat 4Chips 12.5%Prize 14.0%

Chips and prize money do not trade one for one. The biggest loss against chip share is 1.50 points for Seat 2, and the biggest gain is 1.50 points for Seat 3.

How often does each seat finish in the money?

Equity comes from the places a stack can finish in. With 2 paid, Seat 1 (15,000 chips) is in the money 70.7% of the time and Seat 4 (5,000 chips) 29.3%.

Chance of finishing in each place
Seat	First	Second	Third	Fourth	Paid
Seat 1	37.50%	33.21%	21.07%	8.21%	70.71%
Seat 2	37.50%	33.21%	21.07%	8.21%	70.71%
Seat 3	12.50%	16.79%	28.93%	41.79%	29.29%
Seat 4	12.50%	16.79%	28.93%	41.79%	29.29%

Where each seat's prize equity comes from, in points of the prize pool
Seat	From first	From second	Total
Seat 1	24.38	11.63	36.00%
Seat 2	24.38	11.63	36.00%
Seat 3	8.13	5.87	14.00%
Seat 4	8.13	5.87	14.00%

What is the bubble factor for each seat with 4 players left?

Bubble factor compares what a lost all-in costs with what a won one gains, both in prize equity. In this spot it runs from 1.09 (Seat 1 calling Seat 3) up to 1.78 (Seat 1 calling Seat 2). A figure of 1 would mean chips and prize money agree.

Bubble factor when the row seat calls an all-in from the column seat
Seat	vs Seat 1	vs Seat 2	vs Seat 3	vs Seat 4
Seat 1	none	1.78	1.09	1.09
Seat 2	1.78	none	1.09	1.09
Seat 3	1.20	1.20	none	1.10
Seat 4	1.20	1.20	1.10	none

How much equity does a call need?

When the smallest stack (Seat 4) calls an all-in from the biggest (Seat 1), the bubble factor is 1.20. A call that needs 50% in chips needs 54.5% once prize money counts, which is 4.5 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.09 and needs 52.1%, 2.1 points over the chip figure. The smaller stack is the one that pays the larger ICM premium, because losing the all-in costs it 14.00% of the prize pool and winning adds 11.67%.

Break-even equity for two all-in calls, risking and winning the same chips
Call	All-in (chips)	Bubble factor	Chip break-even	ICM break-even	Equity now	Equity if win	Equity if lose
Smallest stack calls biggest	5,000	1.2000	50.0%	54.5%	14.00%	25.67%	0.00%
Biggest stack calls smallest	5,000	1.0877	50.0%	52.1%	36.00%	45.50%	25.67%

Where can I compare other stack patterns?

Compare this pattern with its siblings, with the other payout structure, and with one player more or fewer. The ICM calculator takes your own stacks, and the push or fold calculator prices a shove with the same model.

How was this ICM table 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

How much is the biggest stack worth in ICM with 4 players left?: Seat 1 holds 15,000 chips, 37.5% of the chips in play, and is worth 36.0% of the prize pool when 2 places pay 65/35 percent. That is -1.50 points against its chip share.
What equity does the smallest stack need to call the biggest stack's all-in?: 54.5%. In chips alone the call breaks even at 50%, but the bubble factor of 1.20 raises the requirement because losing costs the smallest stack 14.00% 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 36.0% of the prize pool for 37.5% of the chips.