ICM equity
Malmuth-Harville model: your chance of finishing first equals your share of the chips, and the chance of each lower place follows from the stacks left. Exact for up to 10 players.
An ICM calculator turns chips into money, and the answer is rarely the one people expect. Four players are left: 6,000, 4,000, 3,000 and 2,000 chips, paying $500, $300 and $200. The chip leader has 40% of the chips but only 33.3% of the prize money, $332.63. The short stack has 13.3% of the chips and is worth $166.26, 16.6% of the pool.
Enter your own stacks and payouts in the free calculator above. Add up to ten players, and type payouts as amounts or percentages.
ICM calculator: why chips aren’t money
In a cash game, 1,000 chips are worth $10 whether you have 1,000 or 100,000 of them. In a tournament the chip leader can never win more than first place, and a short stack in the money is already guaranteed the lowest payout. Each extra chip is worth a little less to a big stack than to a small one. ICM, the Independent Chip Model, puts a number on that.
The model used here is Malmuth-Harville. Your chance of winning is your share of the chips. Your chance of second is worked out by taking each other player out as the winner, in turn, and re-running the sum with the stacks that are left. The calculator does this exactly for every finishing order.
Using ICM for a deal
Final tables often agree a deal instead of playing on. The two usual ways:
- Chip chop. Each player gets their share of the chips times the remaining pool. It pays the chip leader too much.
- ICM deal. Each player gets their ICM equity. In the example, the leader takes $332.63 instead of the $400 a chip chop would give, and the short stack takes $166.26 instead of $133.33.
Many deals land in between, with something left over for the winner. Whatever you agree, it helps to know your ICM figure before you start talking.
ICM and push or fold
ICM is why calling an all-in near the bubble needs a much stronger hand than chip odds suggest. Losing costs you your equity, while winning adds less than the chips you take. A medium stack calling the chip leader with four left can be a clear chip-EV call and a clear ICM fold. If you want the hand-against-hand side, the poker odds calculator works out your equity once the cards are known.
Tournament poker swings hard. Play buy-ins your bankroll can take many times over. BeGambleAware.org is free and confidential if it stops being fun.