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

Seat 1 holds 15,000 chips, 33.3% of the chips in play, and is worth 29.6% of the prize pool when 3 places pay 50/30/20 percent. That is -3.70 points against its chip share.

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

60.1%. In chips alone the call breaks even at 50%, but the bubble factor of 1.51 raises the requirement because losing costs the smallest stack 13.58% 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 29.6% of the prize pool for 33.3% of the chips.

ICM: Two big stacks, 5 Players, 3 Paid

5 players are left, 3 get paid (50/30/20 percent), and the stacks are set out as two big stacks. ICM values the biggest stack at 29.6% of the prize pool for 33.3% of the chips, and the smallest at 13.6% for 11.1%.

How much is each stack worth with 5 players left?

45,000 chips are in play in the two big stacks pattern, where two players hold 15,000 chips each and the rest hold 5,000 each. 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	15,000	33.33%	29.63%	-3.70 points
Seat 2	15,000	33.33%	29.63%	-3.70 points
Seat 3	5,000	11.11%	13.58%	+2.47 points
Seat 4	5,000	11.11%	13.58%	+2.47 points
Seat 5	5,000	11.11%	13.58%	+2.47 points

Share of the chips against share of the prize pool

Seat 1Chips 33.3%Prize 29.6%
Seat 2Chips 33.3%Prize 29.6%
Seat 3Chips 11.1%Prize 13.6%
Seat 4Chips 11.1%Prize 13.6%
Seat 5Chips 11.1%Prize 13.6%

The chips overstate the big stacks and understate the small ones. Seat 2 is worth 3.70 points less than its chip share, while Seat 3 is worth 2.47 points more.

How often does each seat finish in the money?

Equity comes from the places a stack can finish in. With 3 paid, Seat 1 (15,000 chips) is in the money 83.6% of the time and Seat 5 (5,000 chips) 44.3%.

Chance of finishing in each place
Seat	First	Second	Third	Fourth	Fifth	Paid
Seat 1	33.33%	29.17%	21.07%	12.02%	4.40%	83.57%
Seat 2	33.33%	29.17%	21.07%	12.02%	4.40%	83.57%
Seat 3	11.11%	13.89%	19.29%	25.32%	30.40%	44.29%
Seat 4	11.11%	13.89%	19.29%	25.32%	30.40%	44.29%
Seat 5	11.11%	13.89%	19.29%	25.32%	30.40%	44.29%

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	8.75	4.21	29.63%
Seat 2	16.67	8.75	4.21	29.63%
Seat 3	5.56	4.17	3.86	13.58%
Seat 4	5.56	4.17	3.86	13.58%
Seat 5	5.56	4.17	3.86	13.58%

What is the bubble factor for each seat with 5 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 2.35 with Seat 1 facing Seat 2; the smallest is 1.17 with Seat 1 facing Seat 3.

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	2.35	1.17	1.17	1.17
Seat 2	2.35	none	1.17	1.17	1.17
Seat 3	1.51	1.51	none	1.23	1.23
Seat 4	1.51	1.51	1.23	none	1.23
Seat 5	1.51	1.51	1.23	1.23	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 1.51. A call that needs 50% in chips needs 60.1% once prize money counts, which is 10.1 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.17 and needs 53.9%, 3.9 points over the chip figure. The smaller stack is the one that pays the larger ICM premium, because losing the all-in costs it 13.58% of the prize pool and winning adds 9.01%.

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	1.5075	50.0%	60.1%	13.58%	22.59%	0.00%
Biggest stack calls smallest	5,000	1.1701	50.0%	53.9%	29.63%	35.65%	22.59%

Where can I compare other stack patterns?

Compare this pattern with its siblings, with the other payout structure, and with one player more or fewer. The ICM calculator takes your own stacks, and the push or fold calculator prices a shove with the same model.

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 5 players left?: Seat 1 holds 15,000 chips, 33.3% of the chips in play, and is worth 29.6% of the prize pool when 3 places pay 50/30/20 percent. That is -3.70 points against its chip share.
What equity does the smallest stack need to call the biggest stack's all-in?: 60.1%. In chips alone the call breaks even at 50%, but the bubble factor of 1.51 raises the requirement because losing costs the smallest stack 13.58% 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 29.6% of the prize pool for 33.3% of the chips.