ICM with 4 players left: even stacks, 3 paid

How much is each stack worth with 4 players left?

The stacks are even stacks: every player holds 10,000 chips. That makes 40,000 chips in play, and three places paid, 50, 30 and 20 percent. The table gives each seat's share of the prize pool next to its share of the chips.

ICM pays less than chip share to the stacks at the top and more to the stacks at the bottom: Seat 4 falls 0.00 points short, and Seat 1 comes out 0.00 points ahead.

How often does each seat finish in the money?

Equity comes from the places a stack can finish in. With 3 paid, Seat 1 (10,000 chips) is in the money 75.0% of the time and Seat 4 (10,000 chips) 75.0%.

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 1.88 with Seat 1 facing Seat 2; the smallest is 1.88 with Seat 1 facing Seat 2.

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 1.88. A call that needs 50% in chips needs 65.2% once prize money counts, which is 15.2 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.88 and needs 65.2%, 15.2 points over the chip figure. Here the bigger stack pays the larger premium: losing costs it 25.00% of the prize pool and winning adds 13.33%.

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 4 players left?

Seat 1 holds 10,000 chips, 25.0% of the chips in play, and is worth 25.0% of the prize pool when 3 places pay 50/30/20 percent. That is +0.00 points against its chip share.

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

65.2%. In chips alone the call breaks even at 50%, but the bubble factor of 1.88 raises the requirement because losing costs the smallest stack 25.00% 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 25.0% of the prize pool for 25.0% of the chips.