// push/fold charts · 9-max · 13 bb
9-max push/fold at 13 bb
At 13 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 12.2% of hands from UTG, widening to 66.8% from the small blind. Below: every seat's shoving range, every seat's calling range against every shove, and each hand's EV against folding. Solved, not remembered, and the assumptions are printed at the bottom so you can argue with them.
Open-shove ranges, folded to you
One chart per seat. Each assumes everyone in front has folded and everyone behind defends with their equilibrium calling range. Mixed hands show their shove frequency.
UTG
shoves 12.2% first in
AAAKsAQsAJsATsA9sA8s76%A7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5571%54s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
55+, A8s+, K9s+, QTs+, JTs, T9s, AJo+, KQoUTG+1
shoves 13.1% first in
AAAKsAQsAJsATsA9sA8s61%A7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9s62%Q8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3355%32sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
33+, A8s+, K9s+, Q9s+, JTs, T9s, AJo+, KQoUTG+2
shoves 16.1% first in
AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJo64%QJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o2232%
33+, A7s+, A5s, K9s+, Q9s+, J9s+, T9s, ATo+, KJo+LJ
shoves 19.7% first in
AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJo64%JJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
22+, A3s+, K9s+, Q9s+, J9s+, T8s+, 98s, A9o+, KJo+, QJoHJ
shoves 24.3% first in
AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
22+, A2s+, K9s+, Q9s+, J8s+, T8s+, 98s, A7o+, A5o, KJo+, QJo, JToCO
shoves 31.1% first in
AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s46%96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
22+, A2s+, K7s+, Q8s+, J8s+, T8s+, 98s, 87s, A2o+, KTo+, QTo+, JToBTN
shoves 37.8% first in
AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9o76%T9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
22+, A2s+, K3s+, Q6s+, J7s+, T7s+, 96s+, 86s+, 75s+, 65s, A2o+, K9o+, QTo+, J9o+, T9oSB
shoves 66.8% first in
AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
22+, A2s+, K2s+, Q2s+, J2s+, T3s+, 94s+, 84s+, 74s+, 63s+, 53s+, 43s, A2o+, K2o+, Q3o+, J7o+, T7o+, 97o+, 86o+, 76o, 65o always (≥80%) mixed, % shown never (≤20%)
Calling a shove
Pick who shoved and who is deciding. The caller is the first player to act after the shove with everyone between them folded; under this model, once someone calls, everyone behind folds.
BB calls 29.4% against a BTN shove of 37.8%
AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22
always (≥80%) mixed, % shown never (≤20%)
Call vs fold, closest hands
BB facing BTN: the hands nearest indifference
| Hand | Call freq | Call vs fold (bb) |
|---|---|---|
| Q8s | 12% | +0.001 |
| K5s | 0% | −0.007 |
| JTo | 0% | −0.013 |
| J9s | 100% | +0.099 |
| T9s | 0% | −0.121 |
| K6s | 100% | +0.195 |
| K4s | 0% | −0.196 |
| K8o | 0% | −0.249 |
| QTo | 100% | +0.311 |
| K3s | 0% | −0.346 |
22+, A2s+, K6s+, Q9s+, J9s+, A2o+, K9o+, QTo+Every calling range at 13 bb
| Spot | Calls | Range |
|---|---|---|
| UTG+1 vs UTG | 6.4% | 77+, AJs+, AQo+ |
| UTG+2 vs UTG | 6.4% | 77+, AJs+, AQo+ |
| LJ vs UTG | 6.4% | 77+, AJs+, AQo+ |
| HJ vs UTG | 6.4% | 77+, AJs+, AQo+ |
| CO vs UTG | 6.4% | 77+, AJs+, AQo+ |
| BTN vs UTG | 6.4% | 77+, AJs+, AQo+ |
| SB vs UTG | 7.8% | 77+, ATs+, KQs, AJo+ |
| BB vs UTG | 7.8% | 77+, ATs+, KQs, AJo+ |
| UTG+2 vs UTG+1 | 7.8% | 77+, ATs+, KQs, AJo+ |
| LJ vs UTG+1 | 7.8% | 77+, ATs+, KQs, AJo+ |
| HJ vs UTG+1 | 7.8% | 77+, ATs+, KQs, AJo+ |
| CO vs UTG+1 | 7.8% | 77+, ATs+, KQs, AJo+ |
| BTN vs UTG+1 | 7.8% | 77+, ATs+, KQs, AJo+ |
| SB vs UTG+1 | 8.3% | 66+, ATs+, KQs, AJo+ |
| BB vs UTG+1 | 9.9% | 55+, A9s+, KQs, ATo+ |
| LJ vs UTG+2 | 8.7% | 66+, ATs+, KQs, AJo+ |
| HJ vs UTG+2 | 8.7% | 66+, ATs+, KQs, AJo+ |
| CO vs UTG+2 | 8.7% | 66+, ATs+, KQs, AJo+ |
| BTN vs UTG+2 | 8.7% | 66+, ATs+, KQs, AJo+ |
| SB vs UTG+2 | 10.0% | 55+, A9s+, KQs, ATo+ |
| BB vs UTG+2 | 11.7% | 44+, A8s+, KJs+, ATo+, KQo |
| HJ vs LJ | 10.6% | 55+, A8s+, KQs, ATo+ |
| CO vs LJ | 10.6% | 55+, A8s+, KQs, ATo+ |
| BTN vs LJ | 10.6% | 55+, A8s+, KQs, ATo+ |
| SB vs LJ | 12.8% | 44+, A8s+, KJs+, A9o+, KQo |
| BB vs LJ | 14.5% | 33+, A5s+, KTs+, A9o+, KQo |
| CO vs HJ | 13.1% | 44+, A7s+, KJs+, A9o+, KQo |
| BTN vs HJ | 13.1% | 44+, A7s+, KJs+, A9o+, KQo |
| SB vs HJ | 15.7% | 33+, A5s+, KTs+, QJs, A8o+, KQo |
| BB vs HJ | 18.8% | 22+, A3s+, KTs+, QTs+, A7o+, KJo+ |
| BTN vs CO | 18.1% | 33+, A3s+, KTs+, QJs, A7o+, KJo+ |
| SB vs CO | 20.0% | 22+, A2s+, KTs+, QTs+, A6o+, KJo+ |
| BB vs CO | 24.3% | 22+, A2s+, K9s+, QTs+, JTs, A4o+, KTo+, QJo |
| SB vs BTN | 26.7% | 22+, A2s+, K8s+, Q9s+, JTs, A2o+, KTo+, QJo |
| BB vs BTN | 29.4% | 22+, A2s+, K6s+, Q9s+, J9s+, A2o+, K9o+, QTo+ |
| BB vs SB | 47.3% | 22+, A2s+, K2s+, Q3s+, J7s+, T7s+, 98s, A2o+, K2o+, Q7o+, J8o+, T9o |
All 169 hands at 13 bb: shove EV by seat
| Hand | UTG | UTG+1 | UTG+2 | LJ | HJ | CO | BTN | SB |
|---|---|---|---|---|---|---|---|---|
| AA | +5.329 | +5.478 | +5.483 | +5.649 | +5.761 | +5.882 | +5.659 | +5.675 |
| KK | +4.303 | +4.478 | +4.539 | +4.693 | +4.815 | +4.937 | +4.836 | +5.003 |
| +3.383 | +3.662 | +3.799 | +4.013 | +4.192 | +4.398 | +4.347 | +4.518 | |
| JJ | +2.583 | +2.856 | +3.082 | +3.379 | +3.617 | +3.879 | +3.921 | +4.138 |
| TT | +1.970 | +2.222 | +2.466 | +2.818 | +3.125 | +3.420 | +3.518 | +3.810 |
| 99 | +1.312 | +1.596 | +1.872 | +2.223 | +2.564 | +2.937 | +3.074 | +3.405 |
| 88 | +0.764 | +1.117 | +1.445 | +1.795 | +2.141 | +2.563 | +2.753 | +3.048 |
| 77 | +0.239 | +0.610 | +0.999 | +1.400 | +1.761 | +2.193 | +2.467 | +2.739 |
| 66 | +0.008 | +0.277 | +0.570 | +1.027 | +1.422 | +1.853 | +2.194 | +2.471 |
| 55 | +0.004 | +0.158 | +0.291 | +0.654 | +1.099 | +1.547 | +1.934 | +2.242 |
| 44 | −0.049 | +0.073 | +0.154 | +0.357 | +0.733 | +1.201 | +1.624 | +1.980 |
| 33 | −0.119 | +0.001 | +0.072 | +0.209 | +0.460 | +0.865 | +1.306 | +1.712 |
| 22 | −0.188 | −0.070 | +0.002 | +0.108 | +0.296 | +0.593 | +0.989 | +1.444 |
| AKs | +2.291 | +2.558 | +2.664 | +2.904 | +3.140 | +3.446 | +3.571 | +3.716 |
| AQs | +1.335 | +1.728 | +1.946 | +2.297 | +2.626 | +3.011 | +3.236 | +3.457 |
| AJs | +0.626 | +0.903 | +1.208 | +1.635 | +2.074 | +2.611 | +2.934 | +3.252 |
| ATs | +0.324 | +0.387 | +0.644 | +1.081 | +1.587 | +2.175 | +2.625 | +3.084 |
| A9s | +0.088 | +0.079 | +0.252 | +0.558 | +1.016 | +1.643 | +2.165 | +2.770 |
| A8s | +0.002 | −0.001 | +0.165 | +0.353 | +0.706 | +1.310 | +1.864 | +2.585 |
| A7s | −0.104 | −0.098 | +0.076 | +0.237 | +0.517 | +1.019 | +1.606 | +2.394 |
| A6s | −0.187 | −0.192 | −0.029 | +0.134 | +0.380 | +0.787 | +1.375 | +2.214 |
| A5s | −0.040 | −0.071 | +0.052 | +0.202 | +0.448 | +0.802 | +1.337 | +2.197 |
| A4s | −0.080 | −0.120 | −0.008 | +0.108 | +0.346 | +0.692 | +1.210 | +2.106 |
| A3s | −0.114 | −0.156 | −0.048 | +0.051 | +0.262 | +0.600 | +1.127 | +2.036 |
| A2s | −0.163 | −0.207 | −0.099 | −0.008 | +0.193 | +0.510 | +1.033 | +1.961 |
| KQs | +0.487 | +0.525 | +0.659 | +0.755 | +0.952 | +1.220 | +1.603 | +2.694 |
| KJs | +0.393 | +0.312 | +0.421 | +0.460 | +0.602 | +0.865 | +1.348 | +2.503 |
| KTs | +0.333 | +0.285 | +0.333 | +0.328 | +0.421 | +0.582 | +1.081 | +2.331 |
| K9s | +0.061 | +0.043 | +0.134 | +0.102 | +0.131 | +0.251 | +0.695 | +2.022 |
| K8s | −0.139 | −0.149 | −0.046 | −0.068 | −0.027 | +0.050 | +0.439 | +1.724 |
| K7s | −0.214 | −0.214 | −0.100 | −0.095 | −0.053 | +0.006 | +0.382 | +1.550 |
| K6s | −0.268 | −0.277 | −0.172 | −0.152 | −0.088 | −0.030 | +0.330 | +1.396 |
| K5s | −0.277 | −0.314 | −0.244 | −0.237 | −0.162 | −0.090 | +0.248 | +1.273 |
| K4s | −0.325 | −0.371 | −0.311 | −0.335 | −0.267 | −0.190 | +0.159 | +1.174 |
| K3s | −0.361 | −0.409 | −0.354 | −0.393 | −0.351 | −0.277 | +0.072 | +1.101 |
| K2s | −0.409 | −0.459 | −0.404 | −0.452 | −0.418 | −0.358 | −0.017 | +1.023 |
| QJs | +0.305 | +0.257 | +0.378 | +0.417 | +0.491 | +0.592 | +0.919 | +1.811 |
| QTs | +0.252 | +0.243 | +0.312 | +0.327 | +0.405 | +0.485 | +0.729 | +1.661 |
| Q9s | −0.015 | +0.002 | +0.114 | +0.109 | +0.132 | +0.217 | +0.427 | +1.351 |
| Q8s | −0.217 | −0.194 | −0.074 | −0.072 | −0.036 | +0.016 | +0.233 | +1.070 |
| Q7s | −0.442 | −0.415 | −0.278 | −0.252 | −0.219 | −0.184 | +0.067 | +0.803 |
| Q6s | −0.468 | −0.450 | −0.326 | −0.286 | −0.227 | −0.192 | +0.050 | +0.718 |
| Q5s | −0.480 | −0.489 | −0.398 | −0.371 | −0.301 | −0.252 | −0.025 | +0.644 |
| Q4s | −0.520 | −0.539 | −0.461 | −0.464 | −0.404 | −0.352 | −0.114 | +0.566 |
| Q3s | −0.565 | −0.585 | −0.509 | −0.527 | −0.491 | −0.443 | −0.206 | +0.491 |
| Q2s | −0.606 | −0.627 | −0.551 | −0.578 | −0.552 | −0.518 | −0.293 | +0.423 |
| JTs | +0.266 | +0.216 | +0.312 | +0.366 | +0.452 | +0.507 | +0.682 | +1.339 |
| J9s | −0.004 | −0.030 | +0.109 | +0.143 | +0.186 | +0.260 | +0.435 | +1.030 |
| J8s | −0.216 | −0.222 | −0.076 | −0.033 | +0.020 | +0.057 | +0.260 | +0.754 |
| J7s | −0.447 | −0.456 | −0.294 | −0.230 | −0.176 | −0.150 | +0.083 | +0.531 |
| J6s | −0.614 | −0.641 | −0.493 | −0.423 | −0.346 | −0.323 | −0.087 | +0.368 |
| J5s | −0.592 | −0.650 | −0.537 | −0.479 | −0.391 | −0.355 | −0.132 | +0.342 |
| J4s | −0.629 | −0.694 | −0.590 | −0.561 | −0.486 | −0.450 | −0.220 | +0.270 |
| J3s | −0.676 | −0.744 | −0.644 | −0.628 | −0.571 | −0.534 | −0.305 | +0.201 |
| J2s | −0.719 | −0.790 | −0.689 | −0.683 | −0.639 | −0.618 | −0.399 | +0.127 |
| T9s | +0.041 | +0.046 | +0.150 | +0.180 | +0.244 | +0.341 | +0.501 | +0.915 |
| T8s | −0.188 | −0.165 | −0.045 | 0.000 | +0.078 | +0.143 | +0.336 | +0.685 |
| T7s | −0.411 | −0.392 | −0.259 | −0.194 | −0.118 | −0.069 | +0.159 | +0.500 |
| T6s | −0.584 | −0.585 | −0.464 | −0.391 | −0.292 | −0.245 | −0.016 | +0.341 |
| T5s | −0.718 | −0.750 | −0.664 | −0.614 | −0.509 | −0.452 | −0.225 | +0.172 |
| T4s | −0.728 | −0.771 | −0.696 | −0.674 | −0.575 | −0.513 | −0.281 | +0.132 |
| T3s | −0.772 | −0.814 | −0.742 | −0.734 | −0.659 | −0.603 | −0.371 | +0.058 |
| T2s | −0.826 | −0.868 | −0.794 | −0.796 | −0.731 | −0.687 | −0.463 | −0.015 |
| 98s | −0.215 | −0.156 | −0.007 | +0.038 | +0.098 | +0.194 | +0.394 | +0.681 |
| 97s | −0.412 | −0.356 | −0.196 | −0.136 | −0.080 | 0.000 | +0.231 | +0.529 |
| 96s | −0.576 | −0.543 | −0.397 | −0.329 | −0.254 | −0.180 | +0.053 | +0.379 |
| 95s | −0.709 | −0.711 | −0.600 | −0.553 | −0.472 | −0.392 | −0.162 | +0.204 |
| 94s | −0.876 | −0.893 | −0.790 | −0.776 | −0.708 | −0.631 | −0.383 | +0.014 |
| 93s | −0.885 | −0.899 | −0.800 | −0.801 | −0.756 | −0.677 | −0.434 | −0.029 |
| 92s | −0.926 | −0.943 | −0.844 | −0.854 | −0.819 | −0.755 | −0.524 | −0.101 |
| 87s | −0.400 | −0.322 | −0.154 | −0.078 | −0.001 | +0.079 | +0.325 | +0.589 |
| 86s | −0.563 | −0.506 | −0.349 | −0.262 | −0.166 | −0.096 | +0.152 | +0.446 |
| 85s | −0.686 | −0.666 | −0.547 | −0.483 | −0.380 | −0.300 | −0.058 | +0.275 |
| 84s | −0.856 | −0.850 | −0.740 | −0.712 | −0.621 | −0.540 | −0.280 | +0.078 |
| 83s | −1.032 | −1.031 | −0.921 | −0.912 | −0.847 | −0.774 | −0.508 | −0.122 |
| 82s | −1.038 | −1.036 | −0.927 | −0.927 | −0.872 | −0.816 | −0.563 | −0.162 |
| 76s | −0.550 | −0.474 | −0.307 | −0.200 | −0.100 | −0.032 | +0.229 | +0.519 |
| 75s | −0.668 | −0.632 | −0.505 | −0.417 | −0.308 | −0.228 | +0.029 | +0.353 |
| 74s | −0.841 | −0.816 | −0.698 | −0.649 | −0.553 | −0.476 | −0.201 | +0.152 |
| 73s | −1.017 | −1.000 | −0.880 | −0.850 | −0.782 | −0.711 | −0.425 | −0.047 |
| 72s | −1.190 | −1.174 | −1.051 | −1.035 | −0.981 | −0.935 | −0.656 | −0.249 |
| 65s | −0.609 | −0.576 | −0.446 | −0.340 | −0.211 | −0.126 | +0.119 | +0.437 |
| 64s | −0.762 | −0.742 | −0.624 | −0.559 | −0.443 | −0.360 | −0.097 | +0.246 |
| 63s | −0.951 | −0.936 | −0.817 | −0.769 | −0.682 | −0.606 | −0.330 | +0.042 |
| 62s | −1.132 | −1.119 | −0.996 | −0.961 | −0.886 | −0.833 | −0.563 | −0.160 |
| 54s | −0.596 | −0.615 | −0.555 | −0.483 | −0.353 | −0.256 | −0.006 | +0.349 |
| 53s | −0.776 | −0.794 | −0.733 | −0.678 | −0.577 | −0.483 | −0.225 | +0.156 |
| 52s | −0.953 | −0.976 | −0.909 | −0.869 | −0.783 | −0.714 | −0.461 | −0.046 |
| 43s | −0.820 | −0.853 | −0.809 | −0.806 | −0.698 | −0.595 | −0.324 | +0.076 |
| 42s | −0.993 | −1.028 | −0.979 | −0.988 | −0.896 | −0.821 | −0.557 | −0.123 |
| 32s | −1.048 | −1.085 | −1.040 | −1.068 | −1.010 | −0.927 | −0.657 | −0.205 |
| AKo | +2.039 | +2.310 | +2.425 | +2.670 | +2.912 | +3.229 | +3.377 | +3.541 |
| AQo | +1.027 | +1.433 | +1.665 | +2.026 | +2.368 | +2.766 | +3.020 | +3.258 |
| AJo | +0.254 | +0.542 | +0.867 | +1.308 | +1.769 | +2.333 | +2.692 | +3.031 |
| ATo | −0.070 | −0.017 | +0.262 | +0.718 | +1.246 | +1.864 | +2.356 | +2.849 |
| A9o | −0.316 | −0.343 | −0.159 | +0.156 | +0.636 | +1.292 | +1.866 | +2.518 |
| A8o | −0.421 | −0.441 | −0.262 | −0.072 | +0.297 | +0.931 | +1.535 | +2.310 |
| A7o | −0.538 | −0.548 | −0.364 | −0.205 | +0.084 | +0.612 | +1.254 | +2.100 |
| A6o | −0.628 | −0.649 | −0.473 | −0.310 | −0.058 | +0.366 | +1.009 | +1.909 |
| A5o | −0.460 | −0.508 | −0.378 | −0.231 | +0.019 | +0.383 | +0.968 | +1.890 |
| A4o | −0.503 | −0.561 | −0.443 | −0.336 | −0.093 | +0.263 | +0.832 | +1.791 |
| A3o | −0.548 | −0.608 | −0.493 | −0.401 | −0.185 | +0.164 | +0.741 | +1.716 |
| A2o | −0.598 | −0.662 | −0.546 | −0.463 | −0.259 | +0.069 | +0.645 | +1.634 |
| KQo | +0.096 | +0.119 | +0.262 | +0.352 | +0.554 | +0.826 | +1.255 | +2.450 |
| KJo | −0.013 | −0.113 | 0.000 | +0.027 | +0.167 | +0.439 | +0.972 | +2.235 |
| KTo | −0.082 | −0.149 | −0.093 | −0.108 | −0.020 | +0.140 | +0.693 | +2.052 |
| K9o | −0.369 | −0.406 | −0.308 | −0.351 | −0.328 | −0.216 | +0.271 | +1.719 |
| K8o | −0.579 | −0.610 | −0.504 | −0.539 | −0.503 | −0.434 | 0.000 | +1.403 |
| K7o | −0.661 | −0.677 | −0.554 | −0.561 | −0.529 | −0.476 | −0.058 | +1.215 |
| K6o | −0.721 | −0.748 | −0.633 | −0.624 | −0.568 | −0.518 | −0.119 | +1.043 |
| K5o | −0.737 | −0.794 | −0.719 | −0.721 | −0.653 | −0.592 | −0.214 | +0.908 |
| K4o | −0.777 | −0.844 | −0.782 | −0.820 | −0.758 | −0.692 | −0.305 | +0.805 |
| K3o | −0.824 | −0.894 | −0.837 | −0.892 | −0.858 | −0.793 | −0.402 | +0.724 |
| K2o | −0.870 | −0.942 | −0.882 | −0.947 | −0.922 | −0.871 | −0.489 | +0.643 |
| QJo | −0.092 | −0.154 | −0.028 | −0.001 | +0.069 | +0.164 | +0.529 | +1.502 |
| QTo | −0.157 | −0.188 | −0.109 | −0.104 | −0.030 | +0.038 | +0.316 | +1.334 |
| Q9o | −0.453 | −0.454 | −0.334 | −0.350 | −0.331 | −0.258 | −0.011 | +1.000 |
| Q8o | −0.663 | −0.659 | −0.531 | −0.542 | −0.511 | −0.469 | −0.220 | +0.698 |
| Q7o | −0.904 | −0.891 | −0.746 | −0.733 | −0.709 | −0.691 | −0.408 | +0.407 |
| Q6o | −0.928 | −0.923 | −0.789 | −0.761 | −0.710 | −0.689 | −0.416 | +0.318 |
| Q5o | −0.942 | −0.971 | −0.874 | −0.858 | −0.793 | −0.758 | −0.499 | +0.236 |
| Q4o | −0.987 | −1.026 | −0.942 | −0.956 | −0.899 | −0.861 | −0.592 | +0.152 |
| Q3o | −1.032 | −1.074 | −0.994 | −1.026 | −0.995 | −0.960 | −0.690 | +0.076 |
| Q2o | −1.081 | −1.125 | −1.043 | −1.085 | −1.064 | −1.043 | −0.786 | −0.002 |
| JTo | −0.146 | −0.209 | −0.104 | −0.060 | +0.020 | +0.065 | +0.271 | +0.993 |
| J9o | −0.437 | −0.477 | −0.332 | −0.310 | −0.272 | −0.208 | 0.000 | +0.659 |
| J8o | −0.656 | −0.677 | −0.524 | −0.496 | −0.449 | −0.417 | −0.186 | +0.364 |
| J7o | −0.897 | −0.916 | −0.747 | −0.697 | −0.653 | −0.639 | −0.377 | +0.123 |
| J6o | −1.085 | −1.123 | −0.965 | −0.907 | −0.840 | −0.829 | −0.559 | −0.055 |
| J5o | −1.063 | −1.134 | −1.013 | −0.965 | −0.886 | −0.861 | −0.605 | −0.082 |
| J4o | −1.107 | −1.189 | −1.079 | −1.063 | −0.991 | −0.962 | −0.697 | −0.157 |
| J3o | −1.156 | −1.239 | −1.134 | −1.133 | −1.086 | −1.061 | −0.797 | −0.239 |
| J2o | −1.207 | −1.292 | −1.185 | −1.196 | −1.161 | −1.151 | −0.899 | −0.318 |
| T9o | −0.392 | −0.404 | −0.292 | −0.271 | −0.207 | −0.119 | +0.071 | +0.537 |
| T8o | −0.622 | −0.618 | −0.486 | −0.450 | −0.374 | −0.319 | −0.096 | +0.295 |
| T7o | −0.864 | −0.856 | −0.710 | −0.656 | −0.587 | −0.547 | −0.289 | +0.094 |
| T6o | −1.054 | −1.068 | −0.935 | −0.872 | −0.780 | −0.743 | −0.479 | −0.078 |
| T5o | −1.192 | −1.247 | −1.150 | −1.109 | −1.010 | −0.969 | −0.707 | −0.261 |
| T4o | −1.202 | −1.266 | −1.183 | −1.172 | −1.079 | −1.031 | −0.765 | −0.306 |
| T3o | −1.249 | −1.312 | −1.233 | −1.238 | −1.171 | −1.128 | −0.860 | −0.387 |
| T2o | −1.300 | −1.364 | −1.284 | −1.300 | −1.241 | −1.213 | −0.958 | −0.464 |
| 98o | −0.648 | −0.607 | −0.450 | −0.416 | −0.357 | −0.269 | −0.043 | +0.290 |
| 97o | −0.857 | −0.818 | −0.649 | −0.598 | −0.549 | −0.481 | −0.221 | +0.121 |
| 96o | −1.035 | −1.014 | −0.858 | −0.801 | −0.730 | −0.666 | −0.403 | −0.037 |
| 95o | −1.181 | −1.198 | −1.080 | −1.043 | −0.968 | −0.899 | −0.636 | −0.225 |
| 94o | −1.361 | −1.395 | −1.288 | −1.287 | −1.223 | −1.156 | −0.876 | −0.432 |
| 93o | −1.362 | −1.397 | −1.294 | −1.310 | −1.273 | −1.208 | −0.931 | −0.477 |
| 92o | −1.414 | −1.451 | −1.345 | −1.370 | −1.342 | −1.292 | −1.028 | −0.554 |
| 87o | −0.847 | −0.784 | −0.610 | −0.547 | −0.474 | −0.402 | −0.124 | +0.181 |
| 86o | −1.022 | −0.979 | −0.812 | −0.737 | −0.643 | −0.580 | −0.301 | +0.031 |
| 85o | −1.157 | −1.155 | −1.028 | −0.972 | −0.870 | −0.799 | −0.526 | −0.151 |
| 84o | −1.339 | −1.350 | −1.234 | −1.219 | −1.128 | −1.058 | −0.767 | −0.362 |
| 83o | −1.530 | −1.545 | −1.429 | −1.436 | −1.376 | −1.314 | −1.011 | −0.577 |
| 82o | −1.535 | −1.553 | −1.436 | −1.452 | −1.402 | −1.355 | −1.068 | −0.621 |
| 76o | −1.008 | −0.944 | −0.765 | −0.666 | −0.572 | −0.513 | −0.223 | +0.106 |
| 75o | −1.140 | −1.121 | −0.986 | −0.907 | −0.804 | −0.734 | −0.440 | −0.073 |
| 74o | −1.319 | −1.313 | −1.189 | −1.150 | −1.055 | −0.986 | −0.676 | −0.283 |
| 73o | −1.509 | −1.507 | −1.384 | −1.367 | −1.306 | −1.245 | −0.923 | −0.501 |
| 72o | −1.699 | −1.701 | −1.572 | −1.568 | −1.521 | −1.485 | −1.171 | −0.715 |
| 65o | −1.077 | −1.054 | −0.915 | −0.817 | −0.693 | −0.618 | −0.340 | +0.017 |
| 64o | −1.246 | −1.237 | −1.110 | −1.056 | −0.943 | −0.870 | −0.571 | −0.185 |
| 63o | −1.432 | −1.429 | −1.304 | −1.271 | −1.189 | −1.125 | −0.817 | −0.403 |
| 62o | −1.631 | −1.632 | −1.501 | −1.482 | −1.413 | −1.371 | −1.066 | −0.619 |
| 54o | −1.066 | −1.099 | −1.033 | −0.967 | −0.839 | −0.749 | −0.465 | −0.071 |
| 53o | −1.241 | −1.278 | −1.214 | −1.172 | −1.079 | −0.998 | −0.707 | −0.281 |
| 52o | −1.440 | −1.479 | −1.408 | −1.379 | −1.298 | −1.241 | −0.953 | −0.494 |
| 43o | −1.291 | −1.341 | −1.294 | −1.304 | −1.202 | −1.115 | −0.808 | −0.365 |
| 42o | −1.483 | −1.537 | −1.484 | −1.509 | −1.421 | −1.357 | −1.056 | −0.579 |
| 32o | −1.536 | −1.590 | −1.542 | −1.585 | −1.535 | −1.467 | −1.161 | −0.663 |
Reading the chart is the easy half. The trainer deals you real hands at 13 bb in a seat you choose and prices every wrong shove or call in big blinds.
Drill 9-max at 13 bb →// what was solved, and what was assumed
- 9-max, blinds 0.5 / 1, 1 bb big-blind ante (dead money, posted by the big blind). Every player starts the hand with the same stack, counted before posting, so the big blind has 1 bb less to play with.
- The first player in may only shove or fold. Facing a shove, each player behind may only call or fold. No limps, no raises short of all-in.
- Assumption: once one player calls, everyone behind folds. Three-way all-ins are left out of the model, because pricing them needs a 169×169×169 equity table. In real play a big blind sometimes overcalls with aces; here it cannot, so shoves into several players are priced slightly too well.
- Assumption: players who folded held random cards. Card removal is applied between the shover and each possible caller, not for the hands that folded in front. One consequence: a seat's ranges depend only on the players left behind it, which is why every 6-max chart matches the 9-max chart for the seat with the same players behind it (6-max UTG is 9-max LJ; HJ through BB are the same seats).
- Solved by fictitious play (linearly averaged) over a 169×169 all-in equity matrix from our engine, 200,000 sampled runouts per matchup, card removal corrected, 3,000 iterations per seat. Measured, not assumed: no seat, in any spot on these pages, could gain more than 0.082 mbb (thousandths of a big blind) per hand by deviating.
- Checked against our heads-up table: the same solver run with two players and no ante reproduces the heads-up charts, with no disagreement bigger than 0.1 percentage points of equity.
- EV is the aggressive action minus folding, in big blinds, against everyone else's equilibrium ranges. Chip EV only: no ICM, so near a bubble or a pay jump these ranges are too wide.
- Raw data: 9max.json (summary) and one file per depth, e.g. 9max/10.json.