ICM with 5 players left: even stacks, 3 paid

How much is each stack worth with 5 players left?

The stacks are even stacks: every player holds 10,000 chips. That makes 50,000 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.

Prize money flattens the stacks. Seat 5 gives up 0.00 points of equity compared with its share of the chips, and Seat 1 gains 0.00 points.

How often does each seat finish in the money?

ICM gets each equity from the chance of finishing in every place. The Seat 5 stack (10,000 chips) is paid 60.0% of the time, and the Seat 1 stack (10,000 chips) is paid 60.0% of the time.

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 1.54 with Seat 1 facing Seat 2; the smallest is 1.54 with Seat 1 facing Seat 2.

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 1.54. A call that needs 50% in chips needs 60.6% once prize money counts, which is 10.6 points more. The same all-in the other way, with the biggest stack calling the smallest, has a bubble factor of 1.54 and needs 60.6%, 10.6 points over the chip figure. Here the bigger stack pays the larger premium: losing costs it 20.00% of the prize pool and winning adds 13.00%.

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?

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 5 players left?

Seat 1 holds 10,000 chips, 20.0% of the chips in play, and is worth 20.0% 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?

60.6%. In chips alone the call breaks even at 50%, but the bubble factor of 1.54 raises the requirement because losing costs the smallest stack 20.00% 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 20.0% of the prize pool for 20.0% of the chips.