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

Seat 1 holds 20,000 chips, 40.0% of the chips in play, and is worth 37.1% of the prize pool when 2 places pay 65/35 percent. That is -2.94 points against its chip share.

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

54.0%. In chips alone the call breaks even at 50%, but the bubble factor of 1.17 raises the requirement because losing costs the smallest stack 11.21% 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 37.1% of the prize pool for 40.0% of the chips.

ICM: Stack ladder, 4 Players, 2 Paid

4 players are left, 2 get paid (65/35 percent), and the stacks are set out as stack ladder. ICM values the biggest stack at 37.1% of the prize pool for 40.0% of the chips, and the smallest at 11.2% for 10.0%.

How much is each stack worth with 4 players left?

The stacks are stack ladder: stacks of 5,000, 10,000, 15,000 and so on: the biggest is as many times 5,000 as there are players. That makes 50,000 chips in play, and two places paid, 65 and 35 percent. The table gives each seat's share of the prize pool next to its share of the chips.

Chips and prize equity with 4 players left, payouts 65/35 percent
Seat	Chips	Share of chips	ICM equity	ICM minus chips
Seat 1	20,000	40.00%	37.06%	-2.94 points
Seat 2	15,000	30.00%	30.29%	+0.29 points
Seat 3	10,000	20.00%	21.44%	+1.44 points
Seat 4	5,000	10.00%	11.21%	+1.21 points

Share of the chips against share of the prize pool

Seat 1Chips 40.0%Prize 37.1%
Seat 2Chips 30.0%Prize 30.3%
Seat 3Chips 20.0%Prize 21.4%
Seat 4Chips 10.0%Prize 11.2%

The chips overstate the big stacks and understate the small ones. Seat 1 is worth 2.94 points less than its chip share, while Seat 3 is worth 1.44 points more.

How often does each seat finish in the money?

Equity comes from the places a stack can finish in. With 2 paid, Seat 1 (20,000 chips) is in the money 71.6% of the time and Seat 4 (5,000 chips) 23.5%.

Chance of finishing in each place
Seat	First	Second	Third	Fourth	Paid
Seat 1	40.00%	31.59%	20.63%	7.78%	71.59%
Seat 2	30.00%	30.83%	26.19%	12.98%	60.83%
Seat 3	20.00%	24.13%	31.75%	24.13%	44.13%
Seat 4	10.00%	13.45%	21.43%	55.12%	23.45%

Where each seat's prize equity comes from, in points of the prize pool
Seat	From first	From second	Total
Seat 1	26.00	11.06	37.06%
Seat 2	19.50	10.79	30.29%
Seat 3	13.00	8.44	21.44%
Seat 4	6.50	4.71	11.21%

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

Every call has a bubble factor, the equity lost on a loss over the equity gained on a win. The largest at this table is 1.63 with Seat 2 facing Seat 1; the smallest is 1.07 with Seat 1 facing 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	1.39	1.18	1.07
Seat 2	1.63	none	1.18	1.07
Seat 3	1.37	1.26	none	1.07
Seat 4	1.17	1.13	1.09	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 1.17. A call that needs 50% in chips needs 54.0% once prize money counts, which is 4.0 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 51.6%, 1.6 points over the chip figure. The smaller stack is the one that pays the larger ICM premium, because losing the all-in costs it 11.21% of the prize pool and winning adds 9.54%.

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	1.1747	50.0%	54.0%	11.21%	20.75%	0.00%
Biggest stack calls smallest	5,000	1.0664	50.0%	51.6%	37.06%	44.38%	29.25%

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?

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 20,000 chips, 40.0% of the chips in play, and is worth 37.1% of the prize pool when 2 places pay 65/35 percent. That is -2.94 points against its chip share.
What equity does the smallest stack need to call the biggest stack's all-in?: 54.0%. In chips alone the call breaks even at 50%, but the bubble factor of 1.17 raises the requirement because losing costs the smallest stack 11.21% 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 37.1% of the prize pool for 40.0% of the chips.