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

Seat 1 holds 15,000 chips, 50.0% of the chips in play, and is worth 38.5% of the prize pool when 3 places pay 50/30/20 percent. That is -11.50 points against its chip share.

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

56.3%. In chips alone the call breaks even at 50%, but the bubble factor of 1.29 raises the requirement because losing costs the smallest stack 7.50% 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 38.5% of the prize pool for 50.0% of the chips.

ICM: Stack ladder, 3 Players, 3 Paid

With 3 players left and 3 paid (50/30/20 percent), the biggest stack of 15,000 chips holds 50.0% of the chips but is worth 38.5% of the prize pool. The smallest, 5,000 chips, holds 16.7% and is worth 27.5%.

How much is each stack worth with 3 players left?

30,000 chips are in play in the stack ladder pattern, where stacks of 5,000, 10,000, 15,000 and so on: the biggest is as many times 5,000 as there are players. The prize pool pays three places paid, 50, 30 and 20 percent, and the table converts each seat's chips into prize equity.

Chips and prize equity with 3 players left, payouts 50/30/20 percent
Seat	Chips	Share of chips	ICM equity	ICM minus chips
Seat 1	15,000	50.00%	38.50%	-11.50 points
Seat 2	10,000	33.33%	34.00%	+0.67 points
Seat 3	5,000	16.67%	27.50%	+10.83 points

Share of the chips against share of the prize pool

Seat 1Chips 50.0%Prize 38.5%
Seat 2Chips 33.3%Prize 34.0%
Seat 3Chips 16.7%Prize 27.5%

Chips and prize money do not trade one for one. The biggest loss against chip share is 11.50 points for Seat 1, and the biggest gain is 10.83 points for Seat 3.

How often does each seat finish in the money?

ICM gets each equity from the chance of finishing in every place. The Seat 3 stack (5,000 chips) is paid 100.0% of the time, and the Seat 1 stack (15,000 chips) is paid 100.0% of the time.

Chance of finishing in each place
Seat	First	Second	Third	Paid
Seat 1	50.00%	35.00%	15.00%	100.00%
Seat 2	33.33%	40.00%	26.67%	100.00%
Seat 3	16.67%	25.00%	58.33%	100.00%

Where each seat's prize equity comes from, in points of the prize pool
Seat	From first	From second	From third	Total
Seat 1	25.00	10.50	3.00	38.50%
Seat 2	16.67	12.00	5.33	34.00%
Seat 3	8.33	7.50	11.67	27.50%

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 1.07 (Seat 1 calling Seat 3) up to 1.62 (Seat 2 calling Seat 1). 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	1.20	1.07
Seat 2	1.62	none	1.08
Seat 3	1.29	1.15	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 1.29. A call that needs 50% in chips needs 56.3% once prize money counts, which is 6.3 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 51.7%, 1.7 points over the chip figure. The smaller stack is the one that pays the larger ICM premium, because losing the all-in costs it 7.50% of the prize pool and winning adds 5.83%.

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	1.2857	50.0%	56.3%	27.50%	33.33%	20.00%
Biggest stack calls smallest	5,000	1.0690	50.0%	51.7%	38.50%	43.33%	33.33%

Where can I compare other stack patterns?

Each payout structure and player count has the same stack patterns, so you can see which of them moves the numbers most. The ICM calculator takes your own stacks and payouts.

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 3 players left?: Seat 1 holds 15,000 chips, 50.0% of the chips in play, and is worth 38.5% of the prize pool when 3 places pay 50/30/20 percent. That is -11.50 points against its chip share.
What equity does the smallest stack need to call the biggest stack's all-in?: 56.3%. In chips alone the call breaks even at 50%, but the bubble factor of 1.29 raises the requirement because losing costs the smallest stack 7.50% 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 38.5% of the prize pool for 50.0% of the chips.