This article keeps every input visible. We calculate a three-player example, check that finish probabilities and equities add up, compare two simplified all-ins involving the same middle stack, then vary the payouts and stacks separately. The examples are educational models, not push/fold recommendations for a real tournament.
What ICM Models—And What It Leaves Out
ICM takes a stack vector and a payout ladder. It assigns each player a probability of finishing in each place, then multiplies each place probability by that place's prize. In the basic model, the probability of finishing first is the player's stack divided by all chips in play. Conditional on a player finishing first, that stack leaves the calculation and the remaining players' relative stack sizes determine second place; the same logic continues down the ladder.
PokerNews gives a brief English-language introduction to ICM and tournament stack decisions. English captions are available. The full payout calculation and assumptions remain in the article below.
The model assumes players are equally skilled for this calculation and that future finishing chances can be represented by those chip proportions. It does not directly include positional advantage, different playing skill, changing blinds, table dynamics, or a particular opponent's hand. It is an estimate under a model, not the actual probability that a named player wins. GTO Wizard identifies those omitted factors in its discussion of basic ICM.
Chip EV Is Not the Same Unit as Prize Equity
In a cash game without rake or other complications, an extra chip has a direct cash value. In a tournament, chips are useful for competing for a payout ladder; they are not freely cashable at face value. Suppose first, second and third pay 55, 27 and 18 prize units. Every surviving player is already assured at least 18 in this three-player snapshot. Winning more chips can increase first-place probability, but it changes your share of the fixed 100-unit pool, not the pool's size.
Chip EV measures expected chip change. ICM prize EV (often written $EV) measures expected payout share after the model maps each possible resulting stack vector to the prizes. Here the payouts are abstract prize units, not a claim about real-money winnings or buy-ins. Both measures require clear timing: are we comparing a fold now with a call now, or a post-hand stack? A decision's stack outcomes, their probabilities and the payout ladder must be supplied before any EV claim is meaningful.
A Three-Player Calculation With Every Input Disclosed
Players A, B and C have 460, 340 and 200 chips, respectively, for a total of 1,000. The prizes for first, second and third are 55, 27 and 18 units, totaling 100. No bounties, rake, re-entries, future blinds or skill differences are modeled. These are invented teaching inputs, not a real tournament result.
The first-place probabilities are immediate: A 460/1000 = 46%, B 340/1000 = 34%, C 200/1000 = 20%. Second place requires considering who finished first. For example, A finishes second if B finishes first and A then wins among the 660 remaining chips, or if C finishes first and A then wins among the 800 remaining chips:
P(A second) = (340/1000 × 460/660) + (200/1000 × 460/800)
= 0.2369696970 + 0.115 = 0.3519696970, or 35.196970%. A third-place probability is the residual 18.803030%. Repeat that branch calculation for B and C.
| Player | Stack | First | Second | Third | ICM prize equity |
|---|---|---|---|---|---|
| A | 460 | 46.000000% | 35.196970% | 18.803030% | 38.187727 |
| B | 340 | 34.000000% | 37.462963% | 28.537037% | 33.951667 |
| C | 200 | 20.000000% | 27.340067% | 52.659933% | 27.860606 |
| Check | 1,000 | 100% | 100% | 100% | 100.000000 |
A's equity is 0.46×55 + 0.3519696970×27 + 0.1880303030×18 = 38.187727 units. The same method gives B and C's rows. Every player's three place probabilities add to 100%; each finish-position column adds to 100%; all three equities add to the 100-unit prize pool. These are stronger checks than copying a calculator's final number.
The Middle Stack Versus the Leader: Positive Chip EV, Negative Prize EV
Keep the same three stacks and 55/27/18 payouts. Now suppose middle stack B contests an all-in against leader A for B's 340-chip stack, with no dead money, antes or side pot. If B wins, the post-hand stacks are A 120, B 680, C 200, and B's model prize equity is 45.524545. If B loses, the stacks are A 800, B 0, C 200; B receives third-place 18. Without this contest in the static comparison, B's original equity is 33.951667.
Let w be B's hypothetical probability of winning this all-in, with no tie. Its chip change is +340 on a win and −340 on a loss, so the chip-EV break-even share is 50%. Its model prize EV from taking the contest is w×45.524545… + (1−w)×18. Equating that with the original 33.951667… gives:
w = (33.951666… − 18) / (45.524545… − 18) ≈ 57.9543%.
For a toy w = 56%, chip EV is 0.56×340 − 0.44×340 = +40.8 chips. Model prize EV is 0.56×45.524545… + 0.44×18 = 33.413745 units, 0.537921 units below the static no-contest baseline. Thus a chip-positive gamble can be ICM-negative in this precise three-player model. This is not a claim that a 56% all-in should always be folded: the real decision includes blinds, positions, ranges, payout conditions and alternatives that the toy comparison excludes.
| B's choice or outcome against A | Resulting stacks A/B/C | B chip change | B model prize equity |
|---|---|---|---|
| Static no-contest baseline | 460 / 340 / 200 | 0 | 33.951667 |
| B wins the 340-chip contest | 120 / 680 / 200 | +340 | 45.524545 |
| B loses the contest | 800 / 0 / 200 | −340 | 18.000000 |
| Contest with 56% win share | Win or lose as above | +40.8 EV chips | 33.413745 EV units |
Same Win Share, Different Stack at Risk
Change only the opponent and the amount B risks: suppose B instead contests 200 chips against C, again with no dead money, and assign the same hypothetical 56% chance of winning. A stays at 460. If B wins, stacks become 460 / 540 / 0, and B's model prize equity is 42.120000. If B loses, stacks become 460 / 140 / 400, and B's equity is 25.093333. C's elimination on a win and B's survival on a loss create a different payout-risk profile from the B-versus-A contest.
Here the chip-EV break-even share is again 50%. The model prize-EV threshold is (33.951666… − 25.093333…) / (42.12 − 25.093333…) ≈ 52.0262%. At 56%, B gains 24 expected chips and reaches 34.628267 expected prize units, 0.676600 above the static baseline. The difference is not that C is always a better target: we held a hypothetical win share constant to isolate the stack-outcome and payout arithmetic. Actual win shares, ranges, table position and the price of each confrontation need separate evidence.
| Hypothetical B contest | Chips at risk | Prize-EV break-even win share | B chip EV at 56% | B prize EV at 56% | Change from baseline |
|---|---|---|---|---|---|
| Against A | 340 | 57.9543% | +40.8 | 33.413745 | −0.537921 |
| Against C | 200 | 52.0262% | +24.0 | 34.628267 | +0.676600 |
Change One Input and Watch the Answer Move
The result is not a universal “ICM percentage.” Keep stacks 460/340/200, but change the payout ladder from 55/27/18 to 70/20/10. The place probabilities do not change because stacks did not change. The prize equities do: A 41.119697, B 34.146296, C 24.734007. The total is still 100. A more top-heavy structure rewards the first-place probability more strongly; it does not retroactively alter the first-place probabilities.
Alternatively, keep payouts 55/27/18 but redistribute the same 1,000 chips to 520/280/200. Now both the first-place and conditional later-place probabilities change. The equities become A 40.230000, B 31.720000, C 28.050000, again summing to 100. These are sensitivity examples, not forecasts about how a particular player will perform.
| Controlled scenario | Stacks A/B/C | Payouts 1st/2nd/3rd | A equity | B equity | C equity |
|---|---|---|---|---|---|
| Baseline | 460 / 340 / 200 | 55 / 27 / 18 | 38.187727 | 33.951667 | 27.860606 |
| Payout-only change | 460 / 340 / 200 | 70 / 20 / 10 | 41.119697 | 34.146296 | 24.734007 |
| Stack-only change | 520 / 280 / 200 | 55 / 27 / 18 | 40.230000 | 31.720000 | 28.050000 |
When Basic ICM Needs Caution
Earlier in a tournament, when payouts are distant and many players remain, calculating a full payout equity for every action can be less intuitive than the three-player illustration. The model still has defined inputs, but the strategic importance of a small difference depends on the actual format. Do not transfer either break-even threshold above to another field, payout ladder or stack vector.
Near a bubble or pay jump, losing a stack can carry a pronounced payout cost. But bounties, satellites, equal stacks, hand-for-hand procedures and seat-dependent future blinds can change the relevant objective. A plain 55/27/18 model is not a bounty or satellite model. The GTO Wizard ICM basics article specifically cautions that skill, position and rising blinds are not encoded in its simple formulation.
At a table, you cannot infer a decision solely from the stack-to-prize conversion. You still need hand equity against a credible range, available alternative lines, the price of the decision and operator rules on tools during play. An off-table ICM calculator can support study; its output is not permission for in-play assistance. ICM converts stack outcomes to modeled payout equity; it does not calculate the price of a call.
For a completed hand, the hand-review worksheet helps separate the decision and its known inputs from the eventual result; its process does not validate an ICM model or authorize live tool use.
Quick Answers
What does ICM stand for? Independent Chip Model: a mathematical mapping from tournament stacks and payouts to estimated finishing probabilities and prize equity.
Are tournament chips worth their face value? Not as a cash claim. The example's 340-chip middle stack has model prize equity 33.951667 of 100 units, not “340 cash units.” A cash-game chip analogy does not transfer to a payout ladder.
Can a chip-positive call be ICM-negative? Yes, in a specified model. Our 56%-to-win, 340-chip-risk toy contest yields +40.8 expected chips but −0.537921 prize units relative to the baseline. With the same hypothetical win share against a different stack, the modeled sign reverses. Those numbers belong only to the exact stated stacks, payouts and no-dead-money assumptions.
What mistakes make a basic ICM comparison misleading? Treating chip count as cash value, using an assumed win share as if it were an observed opponent range, or carrying this payout ladder into a bounty or satellite event. State the stacks, prizes, contest outcomes and omitted factors before comparing chip EV with model prize EV.
Is an ICM output the true probability of finishing first? No. It is a model-based probability derived from stack shares under an equal-skill assumption. Real future play is not determined by that one number.
Sources and Scope
- GTO Wizard: ICM Basics — Explains stack-based finish probabilities, payout equity and omitted skill, position and blind effects. It is the model reference, not the source of our invented tournament inputs.
The 460/340/200 stacks, 55/27/18 prizes and both 56% contests are original teaching inputs. Their displayed calculations are reproducible above and are not measured tournament outcomes.
About the Editorial Team
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