ICM Deal Calculator

What this ICM deal calculator does

Enter the chip stacks and the remaining payouts and it returns each player's tournament equity under the Independent Chip Model: the amount a mathematically fair deal would pay each player right now. It also shows the chip chop, which splits the prize pool in proportion to chips, so you can see exactly how much the chip leader is asking for when they propose one.

Why chips are not worth their face value

In a cash game every chip is worth the same. In a tournament the prize pool is fixed and paid by finishing position, so chips only matter through the finishing positions they make likely. A player holding half the chips at a three-handed final table cannot win more than first prize, however many more chips they accumulate, and a player with 10% of the chips has already locked up at least third. The result is that each additional chip is worth a little less than the one before. ICM is the standard way to put a dollar figure on that.

How ICM works: the Malmuth-Harville method

ICM assumes a player's chance of finishing first equals their share of the chips. The chance of finishing second is computed by taking each other player as the winner in turn, removing their chips, and asking what share of the remaining chips the player then holds. Third follows the same way, and so on down the payouts. A player's equity is the sum of each finishing probability multiplied by that position's prize.

Take three players with 50,000, 30,000 and 20,000 chips playing for $500, $300 and $200:

• The chip leader has 50% of the chips, so a 50% chance of first.
• If the 30,000 stack wins (30% of the time), the leader holds 50,000 of the remaining 70,000, a 71.4% chance of second; if the 20,000 stack wins (20%), the leader holds 50,000 of 80,000, or 62.5%. Combined: 0.3 × 0.714 + 0.2 × 0.625 = 33.9% for second.
• Third is what is left: 16.1%.
• Equity = 0.5 × $500 + 0.339 × $300 + 0.161 × $200 = $384.

The same arithmetic gives $328 to the 30,000 stack and $289 to the 20,000 stack. The three figures add up to the $1,000 prize pool, as they must.

ICM deal versus chip chop

A chip chop would pay the same three players $500, $300 and $200: it hands the chip leader the entire first prize for having half the chips, even though they win the tournament only half the time. ICM moves $116 from the leader to the two shorter stacks. That is the general pattern: a chip chop favours the leader, ICM favours the short stacks, and the gap grows as the payouts get more top-heavy and the stacks more uneven.

A four-handed example with a larger spread shows how far the two can diverge. Stacks of 120,000, 60,000, 40,000 and 20,000 playing for $1,000, $600 and $400 (fourth gets nothing) have ICM equities of $747, $559, $446 and $248; a chip chop would pay $1,000, $500, $333 and $167. The short stack's ICM equity is half as much again as their chip share, because fourth place pays nothing and they only need to outlast one player to cash.

Negotiating a deal

ICM is the fair baseline, not the final word. Deals are agreed by people, and a few patterns are worth knowing:

• Leave something to play for. Most venues require a portion of first prize, often $100 or 10%, to stay on the table so there is still a tournament to finish. Enter the remaining payouts after that amount is removed.
• The chip leader will ask for more than ICM. They have the most to gain from a chip chop and usually open there. Short stacks should know their ICM number before anyone speaks; it is the figure to accept nothing below.
• A common compromise is ICM plus a premium for the leader. If the leader is also the strongest player, giving them some of the gap between ICM and chip chop is reasonable; giving them all of it is not.
• Skill is not in the model. ICM assumes every player is equally likely to win each chip. A clearly weaker player should take an ICM deal gladly; a clearly stronger one, with a workable stack, can decline it.
• Stack depth matters. With stacks under ten big blinds the tournament is close to a lottery and ICM is a good description of it. With deep stacks skill has more room, which weakens the case for a deal at ICM for the better players.

ICM beyond deal-making

The same model explains why tournament play tightens near pay jumps: a chip lost costs more equity than a chip won gains. Our push/fold charts show the effect directly, with final-table and bubble ranges computed under ICM beside the chip-EV ranges, and the ICM fundamentals article covers the strategy side.

Questions

What is an ICM deal? A split of the remaining prize pool in which each player receives their tournament equity under the Independent Chip Model: the sum, over every finishing position, of the probability of finishing there times that position's prize. It is the standard fair-deal calculation at final tables.

What is the difference between an ICM deal and a chip chop? A chip chop divides the prize pool in proportion to chip counts, which pays the chip leader as if they had already won. ICM accounts for the fact that the leader wins only some of the time and that short stacks have locked up lower prizes. ICM pays short stacks more and the leader less than a chip chop.

How is ICM calculated? By the Malmuth-Harville method: a player's chance of first is their share of the chips; their chance of second is computed by assuming each other player wins in turn, removing that player's chips and taking the remaining share; and so on for each paid position. Equity is each probability times its prize.

Is ICM fair if one player is much better than the others? No. ICM assumes equal skill. A stronger player with a playable stack gives up equity by accepting an ICM deal, and a weaker player gains it. Negotiate from the ICM number, then adjust for skill if everyone agrees it is real.

Should money be left to play for? Usually yes, and many card rooms insist on it. Take the amount off first prize before entering the payouts, and the calculator splits what is left.

Does ICM work for more than three players? Yes. The calculator takes up to nine players and nine payouts. With many players the probabilities get small and the computation grows quickly, which is why larger fields use approximations, but at a final table the exact method is fine.