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

Seat 1 holds 15,000 chips, 30.0% of the chips in play, and is worth 29.7% of the prize pool when 2 places pay 65/35 percent. That is -0.33 points against its chip share.

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

53.0%. 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 11.00% 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 29.7% of the prize pool for 30.0% of the chips.

ICM: One short stack, 4 Players, 2 Paid

In ICM, 15,000 chips out of 4 players is 30.0% of the chips and 29.7% 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 11.0%.

How much is each stack worth with 4 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 50,000 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	30.00%	29.67%	-0.33 points
Seat 2	15,000	30.00%	29.67%	-0.33 points
Seat 3	15,000	30.00%	29.67%	-0.33 points
Seat 4	5,000	10.00%	11.00%	+1.00 points

Share of the chips against share of the prize pool

Seat 1Chips 30.0%Prize 29.7%
Seat 2Chips 30.0%Prize 29.7%
Seat 3Chips 30.0%Prize 29.7%
Seat 4Chips 10.0%Prize 11.0%

Prize money flattens the stacks. Seat 3 gives up 0.33 points of equity compared with its share of the chips, and Seat 4 gains 1.00 points.

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 59.0% of the time and Seat 4 (5,000 chips) 22.9%.

Chance of finishing in each place
Seat	First	Second	Third	Fourth	Paid
Seat 1	30.00%	29.05%	26.90%	14.05%	59.05%
Seat 2	30.00%	29.05%	26.90%	14.05%	59.05%
Seat 3	30.00%	29.05%	26.90%	14.05%	59.05%
Seat 4	10.00%	12.86%	19.29%	57.86%	22.86%

Where each seat's prize equity comes from, in points of the prize pool
Seat	From first	From second	Total
Seat 1	19.50	10.17	29.67%
Seat 2	19.50	10.17	29.67%
Seat 3	19.50	10.17	29.67%
Seat 4	6.50	4.50	11.00%

What is the bubble factor for each seat with 4 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 1.44, for Seat 1 calling Seat 2, and the lowest is 1.07, for Seat 1 calling Seat 4.

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	1.44	1.44	1.07
Seat 2	1.44	none	1.44	1.07
Seat 3	1.44	1.44	none	1.07
Seat 4	1.13	1.13	1.13	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 1.13. A call that needs 50% in chips needs 53.0% once prize money counts, which is 3.0 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 11.00% of the prize pool and winning adds 9.75%.

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	1.1282	50.0%	53.0%	11.00%	20.75%	0.00%
Biggest stack calls smallest	5,000	1.0700	50.0%	51.7%	29.67%	38.00%	20.75%

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 4 players left?: Seat 1 holds 15,000 chips, 30.0% of the chips in play, and is worth 29.7% of the prize pool when 2 places pay 65/35 percent. That is -0.33 points against its chip share.
What equity does the smallest stack need to call the biggest stack's all-in?: 53.0%. 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 11.00% 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 29.7% of the prize pool for 30.0% of the chips.