ICM with 4 players left: even stacks, 2 paid

How much is each stack worth with 4 players left?

40,000 chips are in play in the even stacks pattern, where every player holds 10,000 chips. The prize pool pays two places paid, 65 and 35 percent, and the table converts each seat's chips into prize equity.

The chips overstate the big stacks and understate the small ones. Seat 4 is worth 0.00 points less than its chip share, while Seat 1 is worth 0.00 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 (10,000 chips) is in the money 50.0% of the time and Seat 4 (10,000 chips) 50.0%.

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

The bubble factor is the prize equity a player loses by losing an all-in divided by the equity gained by winning it. The highest figure here is 1.30, for Seat 1 calling Seat 2, and the lowest is 1.30, for Seat 1 calling 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 1.30. A call that needs 50% in chips needs 56.6% once prize money counts, which is 6.6 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 56.6%, 6.6 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 19.17%.

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 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 2 places pay 65/35 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?

56.6%. In chips alone the call breaks even at 50%, but the bubble factor of 1.30 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.