ICM push/fold charts
Chip-EV charts assume a chip won is worth as much as a chip lost. Near the money it is not, and the ranges move a long way: on a 50/30/20 bubble at 10 bb each, the small blind goes from shoving 58.3% to 100.0% and the big blind’s call goes from needing 45.0% equity to 60.9%. These are solved equilibria for three common structures, every depth from 2 to 25 bb, each printed next to its chip-EV twin.
SNG bubble
Four players left, three paid 50 / 30 / 20. At 10 bb: small blind shoves 100.0% (chip EV 58.3%); the big blind calls 11.6% (37.4%), needing 60.9% equity.
Satellite bubble
Four players left, three equal seats. At 10 bb: small blind shoves 100.0% (chip EV 58.3%); the big blind calls 2.7% (37.4%), needing 71.2% equity.
Three-handed, in the money
Three players left, paid 50 / 30 / 20. At 10 bb: small blind shoves 64.5% (chip EV 58.3%); the big blind calls 23.3% (37.4%), needing 52.4% equity.
Why the ranges move
Prize money is not linear in chips. Doubling up on a bubble does not double your share of the pool, but busting takes all of it. So every caller needs more equity than the pot odds say, and because the callers tighten, the shover can often steal with more hands, not fewer. Both effects are on every chart: gold cells shove only because of ICM, red dashed cells are chip-EV plays ICM folds.
The satellite bubble is the extreme case. Every seat pays the same, so a player who already has a seat nearly locked gains almost nothing by doubling up; calling risks the whole seat for almost no reward. Three-handed in the money is the mild case: the pay jumps are still there, but nobody busts out with nothing.
Each structure assumes equal stacks, which is the cleanest way to show the effect and the least realistic part of the model. For a spot with the stacks you actually have, the ICM calculator prices the single call exactly. For the chip-EV game, see the heads-up, 6-max and 9-max charts.
- Three structures: SNG bubble, four players left, three paid 50 / 30 / 20; Satellite bubble, four players left, three equal seats; Three-handed, in the money, three players left, paid 50 / 30 / 20. Blinds 0.5 / 1, no ante. Assumption: every player has the same stack, counted before the blinds go in. Real bubbles are rarely that tidy; with unequal stacks the big stack shoves wider and the medium stacks call tighter than any chart here.
- ICM is Malmuth-Harville: a player finishes first with probability equal to their share of the chips, and each later place goes the same way among the players left. Every EV on these pages is in percent of the prize pool, valued at the end of this one hand. ICM does not know that blinds come round again or that you can outplay anyone; it prices chips, nothing else.
- The first player in may only shove or fold; each player behind may only call or fold. Once one player calls, everyone behind folds (no three-way all-ins). Players who folded are treated as holding random cards.
- Folding is not free under ICM: your prize equity changes when the players behind you clash. The solver values every fold as the rest of the hand, played out by everyone behind at their equilibrium ranges, so seats were solved from the small blind backwards.
- Assumption: a split pot is valued as half a win and half a loss. The equity matrix stores wins plus half the ties, and under ICM half-and-half is a slight mispricing of the 2–3% of all-ins that tie. Chip EV, where it is exact, is unaffected.
- Solved by regret matching (CFR+, linearly averaged) over a 169×169 all-in equity matrix from our engine, 200,000 sampled runouts per matchup, card removal corrected, 10,000 iterations per seat. Measured, not assumed: no seat could gain more than 0.00052% of the prize pool per hand by deviating (chip EV: 0.0010 mbb). With three or more players there is no guarantee such a method finds the only equilibrium, or that there is only one; what is guaranteed is that nobody can profit by switching away from it.
- Checked: given a linear payoff (prize equity = chips), the same solver reproduces our chip-EV N-handed solver at 3 and 4 players: the same action for every hand not within 0.01 bb of indifference, and every EV within 0.03 bb. Each solved hand's prize equities add up to the whole pool, and every big-blind price is re-derived from our ICM calculator’s code in the test suite. We have not compared these ranges with a commercial ICM solver.
- Raw data: sng-bubble.json (summary) and one file per depth, e.g. sng-bubble/10.json.