ICM & risk premium
Cash-game EV math counts chips. Tournament EV counts money, and the bridge between them is the Independent Chip Model (ICM): given every player's stack and the prize structure, it estimates the probability of each possible finishing order and converts placements times payouts into a dollar value for every stack. Its defining property is decreasing marginal value — the ten thousandth chip you win is worth less than the ten thousandth chip you lose, because chips only matter insofar as they climb you up a payout ladder that flattens as it rises.
The operational takeaway is the risk premium: the extra all-in equity a decision needs beyond its chip-EV break-even before it is profitable in money terms. Bust risk sits almost entirely on the caller — the player whose tournament life ends on a showdown — so calling ranges tighten first and hardest, jamming ranges tighten second, and the big stack, whose premium is smallest, gains leverage over everyone without playing a single hand better.
- Convert chips to money.Ask what finishing positions this stack realistically produces, and what each is worth.
- Find who bears the premium.Whoever risks elimination pays; whoever cannot be eliminated collects leverage.
- Price calls with the premium added.Add the premium to the raw pot odds before comparing a hand’s equity.
- Discount thin chip-EV edges.A marginally profitable shove in chips is frequently a money-loser near payouts.
Worked example: three players, one ladder
Three players, prize pool $1000 paying $500 / $300 / $200. The table compares each stack's straight chip-proportional share with its ICM value — computed live above from the standard formula, not quoted.
| Player | Chips | Chip-proportional share | ICM value |
|---|---|---|---|
| A | 5,000 | $500 | $383.93 |
| B | 3,000 | $300 | $327.50 |
| C | 2,000 | $200 | $288.57 |
Now player C wins 2,000 chips straight from player A — stacks become 3k / 3k / 4k. C's ICM value rises by only $65.71, far short of the $200 the raw chips suggest, and A falls by just $61.07. Even player B, who never played a hand, drifts because ICM value depends on the whole distribution, not your stack alone. Winning chips is taxed; losing them is subsidized. That asymmetry is the risk premium.
Put a number on the premium: calling a 10bb shove costs 10bb to win a 30bb final pot, a chip-EV price of 33% equity. On a typical bubble, published ICM solves report risk premiums in the neighborhood of 15–19% for short and medium stacks — meaning the same call now needs roughly 48–52% equity. Hands that were easy calls at 33% become clear folds, and that is the equilibrium behaving correctly, not cowardice.
Honesty note: this app has no prize-pool model — every grade it prints, including all push/fold drills below, is chip EV. The benchmark numbers above come from published postflop-ICM solver work (GTO Wizard's ICM articles, 2024–2026) and tools of the Hold'em Resources Calculator class, not from anything computed here. Those benchmarks report that playing pure chip-EV strategy on bubbles and final tables leaks on the order of tens of percent of buy-in across a session's key pots. Treat this app's marginal chip-EV verdicts as the optimistic boundary of the real decision.