ABC Tools

ICM and Deal Making, Explained

After reading this you can turn tournament chip stacks into prize-money equity, tell an ICM deal apart from a chip chop, and know exactly how much a proposed split costs or earns you.

What ICM measures

The Independent Chip Model (ICM) answers one question: given the current chip stacks and the remaining prizes, how much money is each player worth right now? Chips are not money. A payout ladder caps what first place can win, so the last chips you gather are worth less than the first ones. ICM prices that in.

Here is the hook. Four players are left. Stacks are 5000, 3000, 1500, 500, and the remaining prizes are 100, 60 and 40 (fourth pays nothing). The big stack holds half the chips but is nowhere near half the money. ICM values Alice at about 68.72, not 100. Carol, with 15% of the chips, is worth about 39.30, far more than 15% of the 200 in prizes would suggest. The short stack still has meaningful equity because someone else has to bust first.

When to use it, and when not

Use ICM whenever a chip lead does not convert one-for-one into money: pay jumps at a final table, a bubble, satellite seats, or any deal discussion. It gives everyone a fair starting number that respects the payout structure.

ICM ignores everything about how hands actually play out. It assumes every chip is equally likely to be won by anyone, so it knows nothing about skill, position, or the blinds bearing down on a short stack. That last point matters. A stack of 500 with the big blind arriving next hand is worth less than its ICM figure, because it is about to be forced all-in on bad terms.

ICM is a static snapshot. It does not model future blind pressure, antes, or a strong player's edge. Treat its numbers as a fair baseline for a deal, then adjust by hand for anything the model cannot see.

The formula and the intuition

ICM uses the Malmuth-Harville recursion. The chance a player finishes first is simply their share of the chips:

P_i(\text{1st}) = \frac{s_i}{\sum_j s_j}

Here s_i is player i's stack and the denominator is the total chips in play. Second place is where the recursion earns its keep. To finish second, some other player k takes first, then you win the race among everyone left. So you remove k's chips from the pool and repeat:

P_i(\text{2nd}) = \sum_{k \ne i} P_k(\text{1st}) \cdot \frac{s_i}{\left(\sum_j s_j\right) - s_k}

The same idea extends to third, fourth and beyond: condition on who took each higher place, remove their chips, and renormalize. Each finish probability is exact, not simulated. Once you have the full table of finish probabilities, equity is the weighted sum over the paid positions:

E_i = \sum_{p=1}^{m} P_i(\text{place } p) \cdot \text{prize}_p

where m is the number of paid finishes and \text{prize}_p is the money for place p. The cost of the recursion grows with the number of players, which is why the tool caps out at 12.

Worked example: reproducing the demo

Four stacks, three prizes

Load the demo: stacks Alice 5000, Bob 3000, Carol 1500, Dave 500, payouts 100 / 60 / 40, leave 0. Total chips are 10000.

  1. First-place odds are chip shares: Alice 0.5, Bob 0.3, Carol 0.15, Dave 0.05.
  2. For Alice's second place, sum over each possible winner. If Bob wins first (prob 0.3), Alice has 5000 of the remaining 7000, so 0.3 * 5000/7000 = 0.2143. Adding the Carol and Dave branches gives Alice a second-place chance near 0.3072.
  3. Repeat for third place across all winner-and-runner-up orderings.
  4. Multiply each player's place probabilities by 100, 60 and 40, then add.

The equities come out roughly as below. They sum to the full prize pool of 200.

ICM equity and a chip chop for the demo data
PlayerChipsChip %Chip chopICM equityICM minus chop
Alice500050%100.068.72-31.28
Bob300030%60.056.55-3.45
Carol150015%30.039.30+9.30
Dave5005%10.015.43+5.43

Notice the chip chop hands Alice the entire first prize of 100 just for having half the chips, even though she cannot be guaranteed to win. ICM trims her to 68.72 and redistributes that money down the ladder. The short stacks gain the most in relative terms.

A quick sanity check: the ICM column and the chip-chop column must each sum to the full prize pool. Here both total 200. If a proposed deal does not add up to the pool, something is wrong.

Reading the two deals

The tool shows both splits side by side. The chip chop is proportional to chips. The ICM deal is proportional to equity. The interesting number is the difference per player, the last column above.

The chip chop overpays the big stack and underpays everyone below. ICM shifts money down the ladder.

The pattern is always the same direction. A chip chop overpays big stacks and underpays short ones, because it treats the marginal chip as fully valuable when the ladder caps its worth. If you are the chip leader, you prefer the chip chop. If you are short, you prefer ICM. That is why deal talks so often stall on the big stack: they are being asked to accept less than a naive chip count promises.

Leaving money for the winner

Players sometimes agree to lock in most of the prize pool now but keep playing for a bonus. The Leave for winner field sets aside a fixed amount paid to whoever actually finishes first. The deal then splits only the remainder.

Say the four players carve out 40 for the eventual winner. The pool drops to 160 for the immediate split, run through ICM on the reduced payouts, and the 40 rides on the last hands. This keeps some competitive incentive while removing most of the variance. The larger the leave, the more the outcome still depends on play, and the closer the arrangement sits to just finishing the tournament.

Common mistakes

Three errors show up again and again.

Chopping by chips at a final table
This is the default in casual games and it is wrong whenever the payouts are top-heavy. The short stack is being robbed. In the demo, Dave gets 10 from a chip chop but is worth 15.43.
Forgetting the blinds
A 500-chip stack with 200-chip blinds is not worth its full ICM number. It is about to be committed. Shade the shortest stacks down and give that money to the medium stacks.
Ignoring skill
If one player is clearly the strongest and stacks are deep, pure ICM understates that player. Deals are negotiations, and a strong player can reasonably ask for a little above their ICM figure.

With stacks 5000, 3000, 1500, 500 and payouts 100/60/40, the chip leader's chip-chop share is 100 while their ICM equity is only 68.72. As you move chips from the short stacks onto the leader, the gap between the two widens: the more chips the leader piles up, the more the chip chop overpays them relative to ICM.

Related tools

ICM prices a deal, but it assumes no skill edge. To estimate the edge it ignores, work with the actual hands. The Texas Hold'em Odds Calculator gives exact win and tie odds for a matchup, and the Hold'em Hand vs Range Equity tool does the same against a whole range. For short-stack final tables, the Push/Fold Nash Charts show the jam and call ranges that ICM pressure distorts. If you play other games, the Omaha Odds Calculator and Seven-Card Stud Odds Calculator cover those, with split-pot versions in the Stud Hi/Lo and Omaha Hi/Lo tools, plus the Razz Odds Calculator. When you are weighing a call, the Poker Pot Odds and Outs tool turns outs into equity.

Frequently asked questions

Why is the chip leader worth less than their chip percentage?

Because the payout ladder caps the top prize. In the demo Alice holds 50% of the chips but first place is only 100 out of 200, so she cannot capture 50% of the pool with certainty. She sometimes finishes second or third for less. ICM averages over all those outcomes and lands at 68.72.

Does ICM account for skill or position?

No. It assumes every chip is equally likely to be won by anyone. Skill, position and blind pressure are outside the model. Use ICM as a baseline, then adjust: shade short stacks facing the blinds down, and give a genuinely stronger player a little more.

What does "leave for winner" do?

It removes a fixed amount from the pool before the deal and pays it to whoever finishes first. The players split the rest now. A leave of 40 in the demo means 160 gets divided immediately and 40 is decided at the table.

Why cap at 12 players?

The Malmuth-Harville recursion sums over every ordering of finishes, and that work grows fast with player count. Twelve players keeps the exact computation quick. Real deals almost always happen with far fewer players left anyway.

Should I ever accept a chip chop?

Only if you are the big stack, or the payouts are nearly flat. When prizes are top-heavy, a chip chop overpays the leader and underpays everyone else. If you are short or medium, ask for the ICM split.

Gambling math here is informational only, not betting advice. Gambling involves risk of loss. Only play with money you can afford to lose, and only if you are 18+ or of legal age where you live.

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