How much is the biggest stack worth in ICM with 3 players left?

Seat 1 holds 15,000 chips, 42.9% of the chips in play, and is worth 41.6% of the prize pool when 2 places pay 65/35 percent. That is -1.25 points against its chip share.

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

55.8%. In chips alone the call breaks even at 50%, but the bubble factor of 1.26 raises the requirement because losing costs the smallest stack 16.79% 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 41.6% of the prize pool for 42.9% of the chips.

ICM: One short stack, 3 Players, 2 Paid

Take 3 players, 2 paid places (65/35 percent) and one short stack: the largest stack converts 42.9% of the chips into 41.6% of the prize pool, and the smallest turns 14.3% into 16.8%.

How much is each stack worth with 3 players left?

Here the stacks follow the one short stack pattern, where one player holds 5,000 chips, a third of each of the others at 15,000. Together they hold 35,000 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 3 players left, payouts 65/35 percent
Seat	Chips	Share of chips	ICM equity	ICM minus chips
Seat 1	15,000	42.86%	41.61%	-1.25 points
Seat 2	15,000	42.86%	41.61%	-1.25 points
Seat 3	5,000	14.29%	16.79%	+2.50 points

Share of the chips against share of the prize pool

Seat 1Chips 42.9%Prize 41.6%
Seat 2Chips 42.9%Prize 41.6%
Seat 3Chips 14.3%Prize 16.8%

ICM pays less than chip share to the stacks at the top and more to the stacks at the bottom: Seat 2 falls 1.25 points short, and Seat 3 comes out 2.50 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 82.1% of the time, the smallest 35.7%, with 2 places paid.

Chance of finishing in each place
Seat	First	Second	Third	Paid
Seat 1	42.86%	39.29%	17.86%	82.14%
Seat 2	42.86%	39.29%	17.86%	82.14%
Seat 3	14.29%	21.43%	64.29%	35.71%

Where each seat's prize equity comes from, in points of the prize pool
Seat	From first	From second	Total
Seat 1	27.86	13.75	41.61%
Seat 2	27.86	13.75	41.61%
Seat 3	9.29	7.50	16.79%

What is the bubble factor for each seat with 3 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 2.18 (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
Seat 1	none	2.18	1.09
Seat 2	2.18	none	1.09
Seat 3	1.26	1.26	none

How much equity does a call need?

When the smallest stack (Seat 3) calls an all-in from the biggest (Seat 1), the bubble factor is 1.26. A call that needs 50% in chips needs 55.8% once prize money counts, which is 5.8 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 52.3%, 2.3 points over the chip figure. The smaller stack is the one that pays the larger ICM premium, because losing the all-in costs it 16.79% of the prize pool and winning adds 13.29%.

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	1.2634	50.0%	55.8%	16.79%	30.07%	0.00%
Biggest stack calls smallest	5,000	1.0949	50.0%	52.3%	41.61%	52.14%	30.07%

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?

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

How much is the biggest stack worth in ICM with 3 players left?: Seat 1 holds 15,000 chips, 42.9% of the chips in play, and is worth 41.6% of the prize pool when 2 places pay 65/35 percent. That is -1.25 points against its chip share.
What equity does the smallest stack need to call the biggest stack's all-in?: 55.8%. In chips alone the call breaks even at 50%, but the bubble factor of 1.26 raises the requirement because losing costs the smallest stack 16.79% 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 41.6% of the prize pool for 42.9% of the chips.