Three-handed, in the money push/fold at 6 bb
Three players left, paid 50 / 30 / 20, everyone on 6 big blinds. Under ICM the small blind open-shoves 74.3% of hands, up from 68.5% at chip EV, and BTN shoves 31.8% (chip EV 39.1%). The big blind calls a small-blind shove with 35.5% of hands, because the call needs 49.2% equity instead of 41.7%. Every chart below shows both answers, so you can see exactly which hands the payout structure changes.
Open-shove ranges, folded to you
One chart per seat, everyone in front folded and everyone behind defending with their ICM equilibrium calling range. Gold hands shove only because of ICM (the callers have tightened up so much that stealing is worth more); red dashed hands are chip-EV shoves that ICM folds. A percentage marks a hand the equilibrium mixes.
Each seat starts this hand worth 33.33% of the prize pool.
BTN
shoves 31.8% under ICM · 39.1% at chip EV
AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
22+, A2s+, K5s+, Q7s+, J7s+, T7s+, 97s+, 87s, A3o+, KTo+, QTo+, JToSB
shoves 74.3% under ICM · 68.5% at chip EV
AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 83s+, 73s+, 63s+, 52s+, 42s+, A2o+, K2o+, Q3o+, J6o+, T6o+, 96o+, 85o+, 75o+, 65o, 54o shoves either way shoves under ICM only chip EV shoves, ICM folds folds either way
Calling a shove
Pick who shoved and who is deciding. Under ICM the chips you could win are worth less than the chips you could lose, so the equity a call needs rises well above the chip-EV price. The working is printed in prize-pool shares.
BB calls 35.5% under ICM (54.4% at chip EV) against a SB shove of 74.3%
AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8s79%J7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
calls either way calls under ICM only chip EV calls, ICM folds folds either way
The price of the call
BB’s share of the prize pool after each outcome
call and win: 43.33%
call and lose: 20.00%
fold: 31.49%
needs (fold − lose) ÷ (win − lose) = (31.49% − 20.00%) ÷ (43.33% − 20.00%) = 49.2% equity
at chip EV the same call needs 41.7%
| Hand | Call freq | Call vs fold (% of pool) |
|---|---|---|
| J8s | 79% | 0.00% |
| K2s | 0% | −0.01% |
| K5o | 0% | −0.03% |
| Q8o | 0% | −0.04% |
| Q6s | 0% | −0.06% |
| T9s | 100% | +0.13% |
| 22 | 0% | −0.13% |
| Q7s | 100% | +0.13% |
33+, A2s+, K3s+, Q7s+, J8s+, T9s, A2o+, K6o+, Q9o+, JToEvery calling range at 6 bb
| Spot | ICM calls | Needs | Chip EV calls | Needs | ICM range |
|---|---|---|---|---|---|
| SB vs BTN | 8.7% | 53.2% | 30.9% | 42.3% | 77+, A9s+, ATo+ |
| BB vs BTN | 14.0% | 48.3% | 36.8% | 40.0% | 44+, A7s+, KJs+, A8o+, KQo |
| BB vs SB | 35.5% | 49.2% | 54.4% | 41.7% | 33+, A2s+, K3s+, Q7s+, J8s+, T9s, A2o+, K6o+, Q9o+, JTo |
All 169 hands at 6 bb: ICM shove EV by seat (% of pool)
| Hand | BTN | SB |
|---|---|---|
| AA | +2.45% | +4.16% |
| KK | +1.99% | +3.62% |
| +1.73% | +3.24% | |
| JJ | +1.46% | +2.96% |
| TT | +1.23% | +2.71% |
| 99 | +0.97% | +2.40% |
| 88 | +0.77% | +2.16% |
| 77 | +0.59% | +1.95% |
| 66 | +0.45% | +1.75% |
| 55 | +0.37% | +1.58% |
| 44 | +0.28% | +1.39% |
| 33 | +0.20% | +1.21% |
| 22 | +0.17% | +1.04% |
| AKs | +1.40% | +2.83% |
| AQs | +1.15% | +2.60% |
| AJs | +0.89% | +2.43% |
| ATs | +0.66% | +2.29% |
| A9s | +0.43% | +2.02% |
| A8s | +0.32% | +1.84% |
| A7s | +0.25% | +1.70% |
| A6s | +0.20% | +1.57% |
| A5s | +0.25% | +1.53% |
| A4s | +0.22% | +1.46% |
| A3s | +0.19% | +1.41% |
| A2s | +0.17% | +1.35% |
| KQs | +0.43% | +1.82% |
| KJs | +0.33% | +1.67% |
| KTs | +0.27% | +1.53% |
| K9s | +0.17% | +1.27% |
| K8s | +0.09% | +1.03% |
| K7s | +0.07% | +0.92% |
| K6s | +0.05% | +0.83% |
| K5s | +0.03% | +0.76% |
| K4s | 0.00% | +0.70% |
| K3s | −0.03% | +0.65% |
| K2s | −0.05% | +0.60% |
| QJs | +0.31% | +1.19% |
| QTs | +0.27% | +1.07% |
| Q9s | +0.17% | +0.81% |
| Q8s | +0.09% | +0.62% |
| Q7s | +0.01% | +0.49% |
| Q6s | 0.00% | +0.47% |
| Q5s | −0.02% | +0.43% |
| Q4s | −0.05% | +0.38% |
| Q3s | −0.09% | +0.33% |
| Q2s | −0.11% | +0.28% |
| JTs | +0.27% | +0.91% |
| J9s | +0.17% | +0.69% |
| J8s | +0.09% | +0.55% |
| J7s | +0.01% | +0.43% |
| J6s | −0.07% | +0.32% |
| J5s | −0.08% | +0.30% |
| J4s | −0.11% | +0.25% |
| J3s | −0.14% | +0.20% |
| J2s | −0.16% | +0.15% |
| T9s | +0.18% | +0.70% |
| T8s | +0.10% | +0.58% |
| T7s | +0.02% | +0.46% |
| T6s | −0.06% | +0.34% |
| T5s | −0.14% | +0.22% |
| T4s | −0.15% | +0.20% |
| T3s | −0.19% | +0.14% |
| T2s | −0.21% | +0.09% |
| 98s | +0.10% | +0.60% |
| 97s | +0.03% | +0.49% |
| 96s | −0.05% | +0.38% |
| 95s | −0.13% | +0.25% |
| 94s | −0.21% | +0.12% |
| 93s | −0.23% | +0.09% |
| 92s | −0.25% | +0.03% |
| 87s | +0.05% | +0.54% |
| 86s | −0.03% | +0.42% |
| 85s | −0.10% | +0.30% |
| 84s | −0.19% | +0.16% |
| 83s | −0.28% | +0.02% |
| 82s | −0.29% | −0.01% |
| 76s | −0.01% | +0.47% |
| 75s | −0.08% | +0.36% |
| 74s | −0.17% | +0.21% |
| 73s | −0.26% | +0.07% |
| 72s | −0.34% | −0.07% |
| 65s | −0.06% | +0.41% |
| 64s | −0.14% | +0.28% |
| 63s | −0.24% | +0.13% |
| 62s | −0.31% | −0.01% |
| 54s | −0.09% | +0.34% |
| 53s | −0.18% | +0.21% |
| 52s | −0.26% | +0.06% |
| 43s | −0.22% | +0.15% |
| 42s | −0.29% | +0.01% |
| 32s | −0.34% | −0.05% |
| AKo | +1.31% | +2.72% |
| AQo | +1.05% | +2.47% |
| AJo | +0.76% | +2.28% |
| ATo | +0.52% | +2.12% |
| A9o | +0.28% | +1.84% |
| A8o | +0.16% | +1.64% |
| A7o | +0.08% | +1.49% |
| A6o | +0.03% | +1.34% |
| A5o | +0.08% | +1.30% |
| A4o | +0.05% | +1.23% |
| A3o | +0.01% | +1.17% |
| A2o | −0.01% | +1.11% |
| KQo | +0.27% | +1.63% |
| KJo | +0.15% | +1.46% |
| KTo | +0.09% | +1.31% |
| K9o | −0.01% | +1.03% |
| K8o | −0.10% | +0.78% |
| K7o | −0.11% | +0.66% |
| K6o | −0.14% | +0.56% |
| K5o | −0.16% | +0.48% |
| K4o | −0.20% | +0.43% |
| K3o | −0.24% | +0.37% |
| K2o | −0.25% | +0.32% |
| QJo | +0.14% | +0.96% |
| QTo | +0.10% | +0.82% |
| Q9o | −0.02% | +0.54% |
| Q8o | −0.10% | +0.34% |
| Q7o | −0.19% | +0.19% |
| Q6o | −0.20% | +0.17% |
| Q5o | −0.22% | +0.13% |
| Q4o | −0.25% | +0.08% |
| Q3o | −0.29% | +0.02% |
| Q2o | −0.31% | −0.03% |
| JTo | +0.10% | +0.65% |
| J9o | −0.01% | +0.42% |
| J8o | −0.10% | +0.27% |
| J7o | −0.18% | +0.13% |
| J6o | −0.27% | +0.01% |
| J5o | −0.28% | 0.00% |
| J4o | −0.31% | −0.05% |
| J3o | −0.35% | −0.11% |
| J2o | −0.37% | −0.17% |
| T9o | 0.00% | +0.43% |
| T8o | −0.08% | +0.30% |
| T7o | −0.17% | +0.17% |
| T6o | −0.26% | +0.05% |
| T5o | −0.34% | −0.08% |
| T4o | −0.36% | −0.12% |
| T3o | −0.39% | −0.17% |
| T2o | −0.41% | −0.23% |
| 98o | −0.08% | +0.31% |
| 97o | −0.16% | +0.20% |
| 96o | −0.24% | +0.08% |
| 95o | −0.33% | −0.05% |
| 94o | −0.42% | −0.20% |
| 93o | −0.44% | −0.23% |
| 92o | −0.46% | −0.29% |
| 87o | −0.14% | +0.25% |
| 86o | −0.22% | +0.13% |
| 85o | −0.30% | 0.00% |
| 84o | −0.40% | −0.15% |
| 83o | −0.49% | −0.30% |
| 82o | −0.50% | −0.33% |
| 76o | −0.20% | +0.18% |
| 75o | −0.28% | +0.05% |
| 74o | −0.37% | −0.09% |
| 73o | −0.48% | −0.25% |
| 72o | −0.55% | −0.40% |
| 65o | −0.25% | +0.11% |
| 64o | −0.34% | −0.03% |
| 63o | −0.44% | −0.18% |
| 62o | −0.52% | −0.34% |
| 54o | −0.29% | +0.05% |
| 53o | −0.38% | −0.10% |
| 52o | −0.46% | −0.26% |
| 43o | −0.42% | −0.16% |
| 42o | −0.50% | −0.32% |
| 32o | −0.55% | −0.38% |
Stacks are never this even at a real bubble. Put in your actual stacks and payouts and the ICM calculator prices the call in front of you. For the same seats without a payout structure, see the chip-EV 6-max chart at 6 bb.
Open the ICM calculator →// 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 0.00000013% of the prize pool per hand by deviating (chip EV: 0 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.