How much is the biggest stack worth in ICM with 6 players left?

Seat 1 holds 30,000 chips, 28.6% of the chips in play, and is worth 27.3% of the prize pool when 2 places pay 65/35 percent. That is -1.30 points against its chip share.

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

51.5%. In chips alone the call breaks even at 50%, but the bubble factor of 1.06 raises the requirement because losing costs the smallest stack 5.13% 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 27.3% of the prize pool for 28.6% of the chips.

ICM: Stack ladder, 6 Players, 2 Paid

Take 6 players, 2 paid places (65/35 percent) and stack ladder: the largest stack converts 28.6% of the chips into 27.3% of the prize pool, and the smallest turns 4.8% into 5.1%.

How much is each stack worth with 6 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 105,000 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 6 players left, payouts 65/35 percent
Seat	Chips	Share of chips	ICM equity	ICM minus chips
Seat 1	30,000	28.57%	27.27%	-1.30 points
Seat 2	25,000	23.81%	23.45%	-0.36 points
Seat 3	20,000	19.05%	19.28%	+0.23 points
Seat 4	15,000	14.29%	14.80%	+0.52 points
Seat 5	10,000	9.52%	10.07%	+0.55 points
Seat 6	5,000	4.76%	5.13%	+0.37 points

Share of the chips against share of the prize pool

Seat 1Chips 28.6%Prize 27.3%
Seat 2Chips 23.8%Prize 23.5%
Seat 3Chips 19.0%Prize 19.3%
Seat 4Chips 14.3%Prize 14.8%
Seat 5Chips 9.5%Prize 10.1%
Seat 6Chips 4.8%Prize 5.1%

ICM pays less than chip share to the stacks at the top and more to the stacks at the bottom: Seat 1 falls 1.30 points short, and Seat 5 comes out 0.55 points ahead.

How often does each seat finish in the money?

ICM gets each equity from the chance of finishing in every place. The Seat 6 stack (5,000 chips) is paid 10.6% of the time, and the Seat 1 stack (30,000 chips) is paid 53.4% of the time.

Chance of finishing in each place
Seat	First	Second	Third	Fourth	Fifth	Sixth	Paid
Seat 1	28.57%	24.85%	20.38%	14.96%	8.60%	2.64%	53.42%
Seat 2	23.81%	22.79%	20.77%	17.19%	11.36%	4.08%	46.60%
Seat 3	19.05%	19.70%	20.14%	19.29%	15.19%	6.62%	38.75%
Seat 4	14.29%	15.76%	17.73%	20.34%	20.35%	11.53%	30.04%
Seat 5	9.52%	11.09%	13.47%	17.57%	26.03%	22.31%	20.61%
Seat 6	4.76%	5.81%	7.49%	10.65%	18.46%	52.82%	10.57%

Where each seat's prize equity comes from, in points of the prize pool
Seat	From first	From second	Total
Seat 1	18.57	8.70	27.27%
Seat 2	15.48	7.98	23.45%
Seat 3	12.38	6.90	19.28%
Seat 4	9.29	5.52	14.80%
Seat 5	6.19	3.88	10.07%
Seat 6	3.10	2.03	5.13%

What is the bubble factor for each seat with 6 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 1.03 (Seat 1 calling Seat 6) up to 1.33 (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	vs Seat 6
Seat 1	none	1.28	1.19	1.12	1.07	1.03
Seat 2	1.33	none	1.19	1.12	1.07	1.03
Seat 3	1.26	1.22	none	1.12	1.07	1.03
Seat 4	1.19	1.16	1.14	none	1.07	1.03
Seat 5	1.12	1.11	1.09	1.08	none	1.03
Seat 6	1.06	1.05	1.05	1.04	1.04	none

How much equity does a call need?

When the smallest stack (Seat 6) calls an all-in from the biggest (Seat 1), the bubble factor is 1.06. A call that needs 50% in chips needs 51.5% once prize money counts, which is 1.5 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.03 and needs 50.8%, 0.8 points over the chip figure. The smaller stack is the one that pays the larger ICM premium, because losing the all-in costs it 5.13% of the prize pool and winning adds 4.84%.

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	1.0603	50.0%	51.5%	5.13%	9.96%	0.00%
Biggest stack calls smallest	5,000	1.0310	50.0%	50.8%	27.27%	31.23%	23.18%

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?

Under the Malmuth-Harville model a stack wins first place in proportion to its chips, then the next place is awarded among the rest in the same proportion, and so on. Equity adds up the payout of each place weighted by those chances. For the bubble factor, a player whose stack falls to 0 busts into the lowest place and the other stacks stay put.

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 6 players left?: Seat 1 holds 30,000 chips, 28.6% of the chips in play, and is worth 27.3% of the prize pool when 2 places pay 65/35 percent. That is -1.30 points against its chip share.
What equity does the smallest stack need to call the biggest stack's all-in?: 51.5%. In chips alone the call breaks even at 50%, but the bubble factor of 1.06 raises the requirement because losing costs the smallest stack 5.13% 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 27.3% of the prize pool for 28.6% of the chips.