// push/fold charts · 9-max · 3 bb

9-max push/fold at 3 bb

At 3 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 90.0% of hands from UTG, widening to 100.0% 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 90.0% first in

22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o

UTG+1

shoves 90.0% first in

22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o

UTG+2

shoves 90.0% first in

22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o

LJ

shoves 90.0% first in

22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o

HJ

shoves 90.0% first in

22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o

CO

shoves 90.0% first in

22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o

BTN

shoves 89.4% first in

22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 43s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o

SB

shoves 100.0% first in

22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
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 100.0% against a BTN shove of 89.4%

always (≥80%) mixed, % shown never (≤20%)

Call vs fold, closest hands

BB facing BTN: the hands nearest indifference

HandCall freqCall vs fold (bb)
32o100%+0.744
42o100%+0.775
62o100%+0.791
72o100%+0.795
52o100%+0.824
43o100%+0.874
82o100%+0.893
63o100%+0.894
73o100%+0.897
83o100%+0.920
22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o

Every calling range at 3 bb

SpotCallsRange
UTG+1 vs UTG90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
UTG+2 vs UTG90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
LJ vs UTG90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
HJ vs UTG90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
CO vs UTG90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
BTN vs UTG90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
SB vs UTG100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
BB vs UTG100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
UTG+2 vs UTG+190.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
LJ vs UTG+190.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
HJ vs UTG+190.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
CO vs UTG+190.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
BTN vs UTG+190.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
SB vs UTG+1100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
BB vs UTG+1100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
LJ vs UTG+290.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
HJ vs UTG+290.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
CO vs UTG+290.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
BTN vs UTG+290.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
SB vs UTG+2100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
BB vs UTG+2100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
HJ vs LJ90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
CO vs LJ90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
BTN vs LJ90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
SB vs LJ100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
BB vs LJ100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
CO vs HJ90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
BTN vs HJ90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
SB vs HJ100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
BB vs HJ100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
BTN vs CO90.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 54o
SB vs CO100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
BB vs CO100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
SB vs BTN100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
BB vs BTN100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
BB vs SB100.0%22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o
All 169 hands at 3 bb: shove EV by seat
HandUTGUTG+1UTG+2LJHJCOBTNSB
AA+4.231+4.231+4.231+4.230+4.226+4.186+3.817+2.761
KK+3.970+3.970+3.970+3.969+3.965+3.929+3.593+2.620
QQ+3.733+3.733+3.733+3.733+3.729+3.697+3.394+2.497
JJ+3.497+3.497+3.497+3.496+3.493+3.464+3.196+2.373
TT+3.263+3.263+3.263+3.263+3.260+3.235+3.001+2.251
99+2.978+2.978+2.978+2.978+2.976+2.955+2.763+2.102
88+2.718+2.718+2.718+2.718+2.716+2.700+2.532+1.958
77+2.471+2.471+2.471+2.470+2.469+2.454+2.300+1.812
66+2.215+2.215+2.215+2.215+2.214+2.200+2.061+1.663
55+1.966+1.966+1.966+1.966+1.965+1.953+1.826+1.516
44+1.695+1.695+1.695+1.694+1.693+1.682+1.563+1.352
33+1.449+1.449+1.449+1.449+1.448+1.437+1.295+1.184
22+1.223+1.223+1.223+1.223+1.221+1.207+1.026+1.016
AKs+2.695+2.695+2.695+2.695+2.691+2.659+2.364+1.853
AQs+2.613+2.613+2.613+2.613+2.609+2.579+2.297+1.810
AJs+2.533+2.533+2.533+2.533+2.529+2.500+2.231+1.769
ATs+2.458+2.458+2.458+2.458+2.455+2.427+2.169+1.731
A9s+2.286+2.286+2.286+2.285+2.282+2.257+2.022+1.638
A8s+2.198+2.198+2.198+2.198+2.196+2.173+1.956+1.598
A7s+2.112+2.112+2.112+2.112+2.110+2.088+1.879+1.550
A6s+2.017+2.017+2.017+2.017+2.015+1.994+1.793+1.495
A5s+2.012+2.012+2.012+2.011+2.009+1.989+1.794+1.496
A4s+1.936+1.936+1.936+1.936+1.934+1.914+1.722+1.451
A3s+1.847+1.847+1.847+1.847+1.845+1.829+1.658+1.411
A2s+1.786+1.786+1.786+1.786+1.784+1.768+1.590+1.369
KQs+2.343+2.343+2.343+2.343+2.340+2.314+2.072+1.670
KJs+2.264+2.264+2.264+2.264+2.261+2.236+2.007+1.629
KTs+2.187+2.187+2.187+2.187+2.184+2.161+1.944+1.590
K9s+2.019+2.019+2.019+2.019+2.016+1.995+1.799+1.500
K8s+1.856+1.856+1.856+1.856+1.854+1.836+1.665+1.415
K7s+1.786+1.786+1.786+1.786+1.784+1.767+1.602+1.376
K6s+1.708+1.708+1.708+1.708+1.706+1.690+1.531+1.332
K5s+1.634+1.634+1.634+1.634+1.633+1.617+1.465+1.290
K4s+1.555+1.555+1.555+1.555+1.554+1.538+1.392+1.245
K3s+1.467+1.467+1.467+1.467+1.466+1.454+1.325+1.203
K2s+1.404+1.404+1.404+1.404+1.403+1.391+1.256+1.160
QJs+2.036+2.036+2.036+2.035+2.033+2.012+1.819+1.512
QTs+1.960+1.960+1.960+1.960+1.958+1.938+1.756+1.472
Q9s+1.792+1.792+1.792+1.792+1.790+1.773+1.613+1.383
Q8s+1.636+1.636+1.636+1.636+1.635+1.621+1.482+1.301
Q7s+1.483+1.483+1.483+1.483+1.481+1.469+1.345+1.215
Q6s+1.421+1.421+1.421+1.421+1.420+1.407+1.288+1.180
Q5s+1.347+1.347+1.347+1.347+1.345+1.334+1.222+1.139
Q4s+1.268+1.268+1.268+1.268+1.267+1.256+1.149+1.093
Q3s+1.182+1.182+1.182+1.182+1.181+1.173+1.081+1.051
Q2s+1.122+1.122+1.122+1.122+1.121+1.112+1.014+1.009
JTs+1.771+1.771+1.771+1.771+1.769+1.753+1.602+1.377
J9s+1.597+1.597+1.597+1.597+1.596+1.582+1.452+1.283
J8s+1.443+1.443+1.443+1.443+1.442+1.430+1.321+1.200
J7s+1.291+1.291+1.291+1.291+1.290+1.281+1.186+1.116
J6s+1.141+1.141+1.141+1.141+1.140+1.131+1.049+1.031
J5s+1.083+1.083+1.083+1.083+1.082+1.075+0.999+0.999
J4s+1.004+1.004+1.004+1.004+1.003+0.996+0.925+0.953
J3s+0.925+0.925+0.925+0.925+0.924+0.919+0.859+0.912
J2s+0.863+0.863+0.863+0.863+0.863+0.857+0.791+0.870
T9s+1.437+1.437+1.437+1.437+1.436+1.425+1.323+1.202
T8s+1.282+1.282+1.282+1.282+1.281+1.272+1.187+1.117
T7s+1.129+1.129+1.129+1.129+1.128+1.121+1.050+1.031
T6s+0.978+0.978+0.978+0.978+0.978+0.972+0.916+0.947
T5s+0.825+0.825+0.825+0.825+0.825+0.820+0.777+0.861
T4s+0.767+0.767+0.767+0.767+0.767+0.763+0.723+0.827
T3s+0.688+0.688+0.688+0.688+0.688+0.685+0.655+0.784
T2s+0.629+0.629+0.629+0.629+0.628+0.625+0.588+0.742
98s+1.134+1.134+1.134+1.134+1.133+1.127+1.064+1.040
97s+0.985+0.985+0.985+0.985+0.984+0.979+0.930+0.956
96s+0.834+0.834+0.834+0.834+0.833+0.830+0.794+0.871
95s+0.680+0.680+0.680+0.680+0.680+0.678+0.656+0.785
94s+0.520+0.520+0.520+0.520+0.520+0.519+0.508+0.693
93s+0.468+0.468+0.468+0.468+0.468+0.468+0.462+0.664
92s+0.407+0.407+0.407+0.407+0.407+0.406+0.393+0.621
87s+0.885+0.885+0.885+0.885+0.884+0.880+0.836+0.898
86s+0.740+0.740+0.740+0.740+0.739+0.736+0.700+0.812
85s+0.592+0.592+0.592+0.592+0.592+0.590+0.564+0.728
84s+0.436+0.436+0.436+0.436+0.436+0.434+0.417+0.636
83s+0.284+0.284+0.284+0.284+0.284+0.283+0.271+0.544
82s+0.244+0.244+0.244+0.244+0.244+0.242+0.222+0.514
76s+0.689+0.689+0.689+0.689+0.689+0.684+0.629+0.768
75s+0.546+0.546+0.546+0.546+0.546+0.541+0.494+0.684
74s+0.389+0.389+0.389+0.389+0.388+0.385+0.347+0.592
73s+0.250+0.250+0.250+0.250+0.250+0.246+0.204+0.502
72s+0.101+0.101+0.101+0.101+0.101+0.097+0.053+0.408
65s+0.527+0.527+0.527+0.527+0.526+0.519+0.451+0.657
64s+0.375+0.375+0.375+0.375+0.374+0.368+0.307+0.567
63s+0.242+0.242+0.242+0.242+0.242+0.235+0.163+0.477
62s+0.096+0.096+0.096+0.095+0.095+0.088+0.014+0.384
54s+0.405+0.405+0.405+0.405+0.404+0.396+0.317+0.573
53s+0.285+0.285+0.285+0.285+0.284+0.275+0.177+0.486
52s+0.138+0.138+0.138+0.138+0.137+0.128+0.028+0.393
43s+0.208+0.208+0.208+0.208+0.207+0.197+0.092+0.433
42s+0.065+0.065+0.065+0.065+0.064+0.054−0.053+0.342
32s+0.018+0.018+0.018+0.018+0.017+0.007−0.121+0.300
AKo+2.547+2.547+2.547+2.547+2.543+2.513+2.226+1.766
AQo+2.460+2.460+2.460+2.459+2.456+2.427+2.154+1.721
AJo+2.375+2.375+2.375+2.375+2.372+2.344+2.084+1.677
ATo+2.293+2.293+2.293+2.293+2.290+2.263+2.017+1.636
A9o+2.112+2.112+2.112+2.111+2.109+2.085+1.862+1.539
A8o+2.015+2.015+2.015+2.015+2.013+1.992+1.790+1.494
A7o+1.921+1.921+1.921+1.921+1.919+1.899+1.706+1.441
A6o+1.821+1.821+1.821+1.821+1.819+1.800+1.614+1.384
A5o+1.814+1.814+1.814+1.814+1.812+1.794+1.614+1.384
A4o+1.733+1.733+1.733+1.733+1.731+1.713+1.538+1.336
A3o+1.637+1.637+1.637+1.637+1.635+1.621+1.468+1.292
A2o+1.571+1.571+1.571+1.571+1.569+1.554+1.394+1.246
KQo+2.174+2.174+2.174+2.174+2.171+2.146+1.916+1.573
KJo+2.089+2.089+2.089+2.088+2.086+2.062+1.845+1.528
KTo+2.008+2.008+2.008+2.008+2.005+1.983+1.779+1.487
K9o+1.829+1.829+1.829+1.828+1.826+1.807+1.625+1.391
K8o+1.654+1.654+1.654+1.654+1.652+1.636+1.482+1.301
K7o+1.579+1.579+1.579+1.579+1.578+1.562+1.415+1.259
K6o+1.495+1.495+1.495+1.494+1.493+1.478+1.338+1.211
K5o+1.414+1.414+1.414+1.414+1.413+1.399+1.266+1.166
K4o+1.329+1.329+1.329+1.328+1.327+1.314+1.186+1.116
K3o+1.233+1.233+1.233+1.233+1.232+1.222+1.115+1.072
K2o+1.168+1.168+1.168+1.168+1.167+1.156+1.042+1.026
QJo+1.852+1.852+1.852+1.852+1.850+1.830+1.651+1.407
QTo+1.769+1.769+1.769+1.769+1.767+1.749+1.582+1.364
Q9o+1.590+1.590+1.590+1.590+1.588+1.573+1.429+1.268
Q8o+1.422+1.422+1.422+1.422+1.421+1.409+1.289+1.180
Q7o+1.255+1.255+1.255+1.255+1.254+1.243+1.139+1.087
Q6o+1.191+1.191+1.191+1.191+1.190+1.180+1.081+1.051
Q5o+1.111+1.111+1.111+1.111+1.110+1.100+1.009+1.006
Q4o+1.025+1.025+1.025+1.025+1.024+1.016+0.930+0.956
Q3o+0.935+0.935+0.935+0.935+0.934+0.928+0.858+0.911
Q2o+0.867+0.867+0.867+0.867+0.867+0.859+0.783+0.864
JTo+1.569+1.569+1.569+1.569+1.568+1.553+1.420+1.263
J9o+1.385+1.385+1.385+1.384+1.383+1.371+1.260+1.163
J8o+1.221+1.221+1.221+1.221+1.220+1.211+1.121+1.076
J7o+1.056+1.056+1.056+1.056+1.055+1.047+0.974+0.984
J6o+0.894+0.894+0.894+0.894+0.894+0.888+0.829+0.893
J5o+0.835+0.835+0.835+0.835+0.835+0.829+0.776+0.860
J4o+0.749+0.749+0.749+0.749+0.749+0.744+0.695+0.810
J3o+0.661+0.661+0.661+0.661+0.661+0.658+0.622+0.764
J2o+0.593+0.593+0.593+0.593+0.593+0.589+0.547+0.717
T9o+1.214+1.214+1.214+1.214+1.213+1.204+1.123+1.077
T8o+1.051+1.051+1.051+1.051+1.050+1.043+0.979+0.987
T7o+0.886+0.886+0.886+0.886+0.885+0.880+0.833+0.896
T6o+0.724+0.724+0.724+0.724+0.724+0.720+0.688+0.805
T5o+0.562+0.562+0.562+0.562+0.562+0.560+0.541+0.713
T4o+0.497+0.497+0.497+0.497+0.497+0.496+0.481+0.676
T3o+0.413+0.413+0.413+0.413+0.413+0.413+0.408+0.630
T2o+0.345+0.345+0.345+0.345+0.345+0.344+0.333+0.583
98o+0.892+0.892+0.892+0.892+0.892+0.888+0.848+0.905
97o+0.732+0.732+0.732+0.732+0.732+0.729+0.704+0.815
96o+0.572+0.572+0.572+0.572+0.572+0.571+0.560+0.725
95o+0.408+0.408+0.408+0.408+0.408+0.408+0.413+0.633
94o+0.235+0.235+0.235+0.235+0.235+0.237+0.254+0.534
93o+0.178+0.178+0.178+0.178+0.178+0.180+0.202+0.501
92o+0.113+0.113+0.113+0.113+0.113+0.114+0.129+0.456
87o+0.625+0.625+0.625+0.625+0.624+0.623+0.604+0.753
86o+0.470+0.470+0.470+0.470+0.470+0.469+0.459+0.662
85o+0.313+0.313+0.313+0.313+0.313+0.313+0.315+0.572
84o+0.144+0.144+0.144+0.144+0.145+0.146+0.155+0.472
83o−0.019−0.019−0.019−0.019−0.019−0.017−0.001+0.374
82o−0.062−0.062−0.062−0.062−0.062−0.061−0.054+0.341
76o+0.420+0.420+0.420+0.420+0.420+0.417+0.386+0.616
75o+0.266+0.266+0.266+0.266+0.265+0.263+0.241+0.525
74o+0.099+0.099+0.099+0.099+0.098+0.097+0.083+0.427
73o−0.055−0.055−0.055−0.055−0.055−0.057−0.073+0.329
72o−0.214−0.214−0.214−0.214−0.214−0.215−0.234+0.229
65o+0.245+0.245+0.245+0.245+0.244+0.240+0.194+0.496
64o+0.084+0.084+0.084+0.084+0.083+0.080+0.041+0.401
63o−0.061−0.061−0.061−0.061−0.061−0.066−0.114+0.304
62o−0.219−0.219−0.219−0.219−0.220−0.224−0.274+0.204
54o+0.117+0.117+0.117+0.117+0.116+0.111+0.053+0.408
53o−0.015−0.015−0.015−0.015−0.015−0.022−0.099+0.313
52o−0.170−0.170−0.170−0.170−0.171−0.178−0.257+0.215
43o−0.096−0.096−0.096−0.096−0.097−0.104−0.188+0.257
42o−0.250−0.250−0.250−0.250−0.251−0.258−0.345+0.159
32o−0.299−0.299−0.299−0.299−0.300−0.308−0.416+0.115

Reading the chart is the easy half. The trainer deals you real hands at 3 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 9-max at 3 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 0.000 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.