// push/fold charts · ICM · Three-handed, in the money

Three-handed, in the money push/fold charts

Three players left, paid 50 / 30 / 20, every stack equal, from 2 to 25 big blinds. Solved twice: once with prize equity as the payoff (ICM) and once with chips (chip EV), on the same table. At 10 bb the small blind shoves 64.5% under ICM against 58.3% at chip EV, and the big blind needs 52.4% equity to call it instead of 45.0%.

Open-shove range by seat and depth

Share of all 1,326 starting hands each seat shoves when folded to, ICM first and chip EV after the slash. Open a depth for the charts, every calling range and the price of each call.

StackBTN ICM / chipSB ICM / chipCharts
2 bb18.8% / 82.2%68.6% / 89.4%2 bb →
3 bb31.1% / 54.4%75.1% / 77.5%3 bb →
4 bb32.2% / 43.7%75.7% / 73.8%4 bb →
5 bb32.0% / 40.7%76.8% / 71.5%5 bb →
6 bb31.8% / 39.1%74.3% / 68.5%6 bb →
7 bb29.9% / 35.7%71.1% / 66.3%7 bb →
8 bb29.0% / 34.2%69.2% / 62.0%8 bb →
9 bb26.3% / 33.1%67.6% / 59.9%9 bb →
10 bb24.6% / 32.4%64.5% / 58.3%10 bb →
11 bb24.3% / 31.6%63.8% / 54.5%11 bb →
12 bb24.4% / 31.3%62.8% / 53.2%12 bb →
13 bb24.7% / 30.0%58.7% / 51.5%13 bb →
14 bb21.9% / 28.6%56.4% / 48.4%14 bb →
15 bb21.8% / 26.6%57.4% / 45.7%15 bb →
16 bb19.7% / 26.6%56.3% / 44.8%16 bb →
17 bb18.9% / 25.1%53.4% / 42.9%17 bb →
18 bb18.3% / 23.3%51.7% / 42.3%18 bb →
19 bb18.6% / 22.6%50.5% / 40.9%19 bb →
20 bb18.5% / 22.0%49.3% / 40.2%20 bb →
21 bb16.1% / 21.3%48.7% / 38.2%21 bb →
22 bb15.7% / 19.9%48.1% / 38.2%22 bb →
23 bb15.9% / 18.9%46.9% / 38.0%23 bb →
24 bb16.1% / 19.0%44.4% / 38.1%24 bb →
25 bb15.4% / 18.5%44.4% / 36.3%25 bb →

What the big blind needs to call

The all-in equity the big blind needs to call a small-blind shove, under ICM and at chip EV, then the share of hands the big blind calls against each seat (ICM / chip). The price comes from the stacks and the payouts, not the shover’s cards; what changes from seat to seat is the range the call is up against.

StackNeeds vs SB (ICM)Needs vs SB (chip)calls vs BTNcalls vs SB
2 bb32.1%25.0%62.9% / 100.0%94.5% / 100.0%
3 bb40.9%33.3%30.5% / 97.3%61.1% / 92.2%
4 bb45.1%37.5%22.2% / 65.6%49.1% / 74.1%
5 bb47.6%40.0%17.4% / 45.7%41.2% / 61.9%
6 bb49.2%41.7%14.0% / 36.8%35.5% / 54.4%
7 bb50.4%42.9%11.9% / 31.3%31.4% / 48.6%
8 bb51.2%43.8%9.8% / 28.6%28.2% / 44.9%
9 bb51.9%44.4%9.4% / 25.5%25.3% / 40.7%
10 bb52.4%45.0%8.7% / 24.3%23.3% / 37.4%
11 bb52.9%45.5%8.1% / 22.2%21.2% / 35.0%
12 bb53.2%45.8%7.5% / 19.5%19.4% / 33.0%
13 bb53.5%46.2%7.1% / 18.1%18.1% / 31.0%
14 bb53.8%46.4%6.8% / 17.0%17.0% / 29.3%
15 bb54.0%46.7%5.9% / 15.7%15.7% / 28.5%
16 bb54.2%46.9%5.8% / 14.8%14.7% / 26.4%
17 bb54.4%47.1%5.6% / 13.3%14.0% / 24.9%
18 bb54.5%47.2%5.4% / 12.8%13.4% / 23.8%
19 bb54.7%47.4%5.4% / 12.3%12.7% / 22.6%
20 bb54.8%47.5%5.3% / 11.5%12.1% / 21.7%
21 bb54.9%47.6%5.1% / 10.7%11.5% / 20.8%
22 bb55.0%47.7%5.0% / 10.2%11.0% / 19.9%
23 bb55.1%47.8%4.3% / 9.6%10.6% / 18.6%
24 bb55.2%47.9%4.0% / 9.5%10.2% / 17.9%
25 bb55.3%48.0%4.0% / 8.9%9.7% / 17.3%
// what was solved, and what was assumed
  • Three players left, paid 50 / 30 / 20: prizes 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 0.0000038% 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: three-handed.json (summary) and one file per depth, e.g. three-handed/10.json.