ICM Calculator

Defaults: Your Stack 1000, Opponent 1 Stack 2500, Opponent 2 Stack 1500, Prize Pool $1000, first 50 percent, second 30 percent, third 20 percent. Three players, 5000 chips in play, a 50/30/20 payout on a thousand dollars. The engine is Malmuth–Harville independent chip model for exactly three stacks. Probability you finish first is your stack over total: 1000 / 5000 = 20.00 percent. Probability you finish second uses removal: if Opponent 1 wins (2500/5000), you then take second with 1000/2500; if Opponent 2 wins (1500/5000), you take second with 1000/3500. That sums to 0.5 × 0.4 + 0.3 × (1000/3500) = 0.20 + 0.08571 = 28.57 percent. Third is the residual, 51.43 percent.

ICM dollar value is prize × (p1 × 0.50 + p2 × 0.30 + p3 × 0.20) = 1000 × (0.20 × 0.50 + 0.2857 × 0.30 + 0.5143 × 0.20) = 1000 × 0.28857 ≈ $288.57. Chip EV if the prize were winner-take-all would be only 20 percent of $1000 = $200. The flattened payout makes the short stack’s tournament dollars larger than his chip share, because third place still pays 20 percent. That is the whole point of ICM: a chip is not a dollar when more than one payout remains.

Common mistakes: treating $288.57 as cash you can pocket now; comparing it with the 1000-chip face value as if chips were money; using this three-player model at a nine-handed final table. Harville with n > 3 needs a recursive sum over every finishing permutation, which this page does not run. Another error is leaving payout percents that do not add to 100; the engine rescales them, but typing 50/50/50 will not match a real structure until you fix the sheet.

What the number is for: deal-making and bubble calls. If a deal were an ICM chop, $288.57 is your fair share of this $1000 under the model. If a call risks your 1000 to gain 1500 more, you must compare ICM after winning versus ICM after busting (zero, plus the remaining prizes you no longer contest), not the chip ratio. Next, swap your stack with Opponent 1’s 2500 and watch p(first) jump to 50 percent and dollar value climb — not linearly. Then set first to 100 and second/third to 0 to recover chip-EV ($200). Do not read $288.57 as a prediction you will finish in the money a particular way. It is a model value, not a promise.

ICM converts a stack into a share of the remaining prize pool when payouts are skewed. This page implements the three-player Malmuth–Harville independent chip model: the chance you outlast a given opponent is proportional to stacks, and finishing positions are built by successive removal. Satellite grinders, final-table deal-makers, and bubble specialists use it because chip-EV calls that look automatic in a cash game can be ICM suicides when third place still pays. Coaches use the default 1000/2500/1500 ladder to show why the short stack should not call off as wide as the chip leader.

The independent chip model was described in tournament poker by Mason Malmuth; the underlying sequential-allocation idea traces to Harville’s work on ranking probabilities (and independently to other sports-ranking literature). It became standard in MTT deal-making in the 2000s as PokerStars-era final tables needed a number that was not “chips times first prize.” Later, ICM-aware solvers (HRC, ICMIZER, Monker) replaced the back-of-envelope chop with full push/fold Nash, but they still rest on Harville probabilities.

What it does not do: four-plus players, future blinds, skill differences, or deal sweetening. There is no field for “Opponent 1 is a nit.” ICM assumes every chip is equally likely to win every future pot — a statement nobody believes and everybody uses as a baseline. It does not compute whether a specific call is +EV; it only values stacks before the hand. You still need an equity number and a model of the other stacks after the hand to price a shove.

Limitations. Three-handed only. Payout percents are rescaled if they do not sum to 100, which can hide a typing error. Prize Pool is the money still to be distributed among these three, not the original buy-in overlay. Antes, pay jumps already passed, and bounty chips are not modelled. Risk premium — the extra equity a shorter stack needs to call a chip leader — is a consequence of this value function, not an extra output.

This calculator will not tell you to deal or to fold. $288.57 is the model’s dollar equity, not cash, not a forecast of finishing order, and not financial advice. Live deals often add a “save” or a last-longer side bet that this formula does not see.

Independent-chip valuation converts a stack into a share of a skewed prize pool when more than first place still pays. Three-player exact Harville–Malmuth arithmetic is the lecture case. Stacks 1000, 2500 and 1500 sum to T = 5000. Prize 1000 is paid 50 / 30 / 20. Probability of finishing first is the chip share: P1 = 1000 / 5000 = 20 percent. Second place uses sequential removal. After stating that, P2 = (2500 / 5000) × (1000 / 2500) + (1500 / 5000) × (1000 / 3500) = 0.20 + 0.085714… ≈ 28.57 percent. Third is the residual: P3 ≈ 51.43 percent.

Dollar value under the model is the prize times the probability-weighted payout vector. After that sentence, Value = 1000 × (0.20 × 0.50 + 0.285714 × 0.30 + 0.514286 × 0.20) ≈ 288.57 dollars. Chip expected value, as if the 1000 were winner-take-all, would have been 20 percent of 1000, or 200 dollars. The extra 88.57 dollars is insurance: the short stack still collects 20 percent of the pool with probability about 51.43 percent for third, which chip-EV ignores. That gap is the entire pedagogical point of the independent chip model. A chip is not a dollar while second and third still pay.

Derivation of second place is Harville’s ranking formula, transplanted by Mason Malmuth onto poker chips. First place is assigned proportional to chips, the independence hypothesis. Conditioning on the 2500-stack taking first, the remaining race is 1000 versus 1500, so the short stack takes second with 1000 / 2500. Conditioning on the 1500-stack taking first, second is taken with 1000 / 3500. The law of total probability adds those branches. Each chip is treated as an independent lottery ticket for first, then recursively for the rest. The construction is exact for three players; four or more requires a sum over every finishing permutation.

Assumptions are known to be false and are used anyway as a baseline. No skill, no position, no blinds, chips independent, three players only, payouts claimed at the end with no bounties. Empirically the model can overvalue medium stacks in larger fields; that debate is a warning not to paste 288.57 dollars onto a nine-handed final table. Real finishing rates depend on who covers whom, who has the button, and who can wait. Two equal stacks of 2500 with a 1000 shorty do not produce the same risk premium as 1000 / 2500 / 1500 even at the same 50 / 30 / 20.

Deal-making and bubble calls are the intended applications, not a forecast of finishing order. An ICM chop of this pool would assign about 288.57 dollars to the 1000-stack. A call that risks those 1000 chips must compare model value after winning versus model value after busting, not the raw chip ratio. Setting first to 100 percent and the others to zero recovers the 200-dollar chip-EV. House edge is irrelevant: the probability caveat is independence. Do not treat 288.57 dollars as cash in pocket. It is three-player exact Harville–Malmuth independent chip model value versus 200 dollars of chip-EV on the stated stacks and payouts.