How much is the biggest stack worth in ICM with 5 players left?

Seat 1 holds 20,000 chips, 33.3% of the chips in play, and is worth 28.7% of the prize pool when 3 places pay 50/30/20 percent. That is -4.67 points against its chip share.

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

62.2%. In chips alone the call breaks even at 50%, but the bubble factor of 1.65 raises the requirement because losing costs the smallest stack 17.83% 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 28.7% of the prize pool for 33.3% of the chips.

ICM: One chip leader, 5 Players, 3 Paid

In ICM, 20,000 chips out of 5 players is 33.3% of the chips and 28.7% of the prize money when 3 places pay 50/30/20 percent. The 10,000-chip stack holds 16.7% of the chips and is worth 17.8%.

How much is each stack worth with 5 players left?

60,000 chips are in play in the one chip leader pattern, where one player holds 20,000 chips, twice each of the others at 10,000. 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 5 players left, payouts 50/30/20 percent
Seat	Chips	Share of chips	ICM equity	ICM minus chips
Seat 1	20,000	33.33%	28.67%	-4.67 points
Seat 2	10,000	16.67%	17.83%	+1.17 points
Seat 3	10,000	16.67%	17.83%	+1.17 points
Seat 4	10,000	16.67%	17.83%	+1.17 points
Seat 5	10,000	16.67%	17.83%	+1.17 points

Share of the chips against share of the prize pool

Seat 1Chips 33.3%Prize 28.7%
Seat 2Chips 16.7%Prize 17.8%
Seat 3Chips 16.7%Prize 17.8%
Seat 4Chips 16.7%Prize 17.8%
Seat 5Chips 16.7%Prize 17.8%

Prize money flattens the stacks. Seat 1 gives up 4.67 points of equity compared with its share of the chips, and Seat 2 gains 1.17 points.

How often does each seat finish in the money?

Equity comes from the places a stack can finish in. With 3 paid, Seat 1 (20,000 chips) is in the money 80.0% of the time and Seat 5 (10,000 chips) 55.0%.

Chance of finishing in each place
Seat	First	Second	Third	Fourth	Fifth	Paid
Seat 1	33.33%	26.67%	20.00%	13.33%	6.67%	80.00%
Seat 2	16.67%	18.33%	20.00%	21.67%	23.33%	55.00%
Seat 3	16.67%	18.33%	20.00%	21.67%	23.33%	55.00%
Seat 4	16.67%	18.33%	20.00%	21.67%	23.33%	55.00%
Seat 5	16.67%	18.33%	20.00%	21.67%	23.33%	55.00%

Where each seat's prize equity comes from, in points of the prize pool
Seat	From first	From second	From third	Total
Seat 1	16.67	8.00	4.00	28.67%
Seat 2	8.33	5.50	4.00	17.83%
Seat 3	8.33	5.50	4.00	17.83%
Seat 4	8.33	5.50	4.00	17.83%
Seat 5	8.33	5.50	4.00	17.83%

What is the bubble factor for each seat with 5 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 1.30 (Seat 1 calling Seat 2) up to 1.65 (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	vs Seat 4	vs Seat 5
Seat 1	none	1.30	1.30	1.30	1.30
Seat 2	1.65	none	1.43	1.43	1.43
Seat 3	1.65	1.43	none	1.43	1.43
Seat 4	1.65	1.43	1.43	none	1.43
Seat 5	1.65	1.43	1.43	1.43	none

How much equity does a call need?

When the smallest stack (Seat 5) calls an all-in from the biggest (Seat 1), the bubble factor is 1.65. A call that needs 50% in chips needs 62.2% once prize money counts, which is 12.2 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.30 and needs 56.5%, 6.5 points over the chip figure. The smaller stack is the one that pays the larger ICM premium, because losing the all-in costs it 17.83% of the prize pool and winning adds 10.83%.

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	10,000	1.6462	50.0%	62.2%	17.83%	28.67%	0.00%
Biggest stack calls smallest	10,000	1.3000	50.0%	56.5%	28.67%	37.00%	17.83%

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?

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 5 players left?: Seat 1 holds 20,000 chips, 33.3% of the chips in play, and is worth 28.7% of the prize pool when 3 places pay 50/30/20 percent. That is -4.67 points against its chip share.
What equity does the smallest stack need to call the biggest stack's all-in?: 62.2%. In chips alone the call breaks even at 50%, but the bubble factor of 1.65 raises the requirement because losing costs the smallest stack 17.83% 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 28.7% of the prize pool for 33.3% of the chips.