// push/fold charts · 9-max · 12 bb

9-max push/fold at 12 bb

At 12 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 12.5% of hands from UTG, widening to 69.9% 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 12.5% first in

44+, A9s+, K9s+, QTs+, JTs, T9s, AJo+, KQo

UTG+1

shoves 14.6% first in

44+, A7s+, K9s+, Q9s+, J9s+, T9s, ATo+, KQo

UTG+2

shoves 16.7% first in

22+, A7s+, A5s, K9s+, Q9s+, J9s+, T9s, 98s, ATo+, KJo+

LJ

shoves 20.3% first in

22+, A2s+, K9s+, Q9s+, J9s+, T8s+, 98s, A9o+, KJo+

HJ

shoves 26.0% first in

22+, A2s+, K9s+, Q9s+, J8s+, T8s+, 98s, A5o+, KTo+, QJo, JTo

CO

shoves 31.8% first in

22+, A2s+, K6s+, Q8s+, J8s+, T8s+, 97s+, 87s, 76s, A2o+, KTo+, QTo+, JTo

BTN

shoves 39.6% first in

22+, A2s+, K2s+, Q6s+, J7s+, T7s+, 96s+, 86s+, 75s+, 65s, A2o+, K7o+, Q9o+, JTo, T9o

SB

shoves 69.9% first in

22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 93s+, 84s+, 74s+, 63s+, 53s+, 43s, A2o+, K2o+, Q2o+, J6o+, T7o+, 96o+, 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 32.1% against a BTN shove of 39.6%

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

Call vs fold, closest hands

BB facing BTN: the hands nearest indifference

HandCall freqCall vs fold (bb)
Q8s81%0.000
JTo100%+0.046
K8o100%+0.058
K4s0%−0.067
T9s100%+0.091
K5s100%+0.104
J8s0%−0.177
K3s0%−0.202
J9s100%+0.206
K7o0%−0.233
22+, A2s+, K5s+, Q8s+, J9s+, T9s, A2o+, K8o+, QTo+, JTo

Every calling range at 12 bb

SpotCallsRange
UTG+1 vs UTG7.4%77+, ATs+, AJo+
UTG+2 vs UTG7.4%77+, ATs+, AJo+
LJ vs UTG7.4%77+, ATs+, AJo+
HJ vs UTG7.4%77+, ATs+, AJo+
CO vs UTG7.4%77+, ATs+, AJo+
BTN vs UTG7.4%77+, ATs+, AJo+
SB vs UTG8.3%66+, ATs+, KQs, AJo+
BB vs UTG8.6%66+, A9s+, KQs, AJo+
UTG+2 vs UTG+18.3%66+, ATs+, KQs, AJo+
LJ vs UTG+18.3%66+, ATs+, KQs, AJo+
HJ vs UTG+18.3%66+, ATs+, KQs, AJo+
CO vs UTG+18.3%66+, ATs+, KQs, AJo+
BTN vs UTG+18.3%66+, ATs+, KQs, AJo+
SB vs UTG+19.2%66+, ATs+, KQs, ATo+
BB vs UTG+111.2%55+, A9s+, KJs+, ATo+, KQo
LJ vs UTG+210.0%55+, A9s+, KQs, ATo+
HJ vs UTG+210.0%55+, A9s+, KQs, ATo+
CO vs UTG+210.0%55+, A9s+, KQs, ATo+
BTN vs UTG+210.0%55+, A9s+, KQs, ATo+
SB vs UTG+211.2%55+, A9s+, KJs+, ATo+, KQo
BB vs UTG+212.8%44+, A7s+, A5s, KJs+, ATo+, KQo
HJ vs LJ12.5%44+, A8s+, KJs+, A9o+, KQo
CO vs LJ12.5%44+, A8s+, KJs+, A9o+, KQo
BTN vs LJ12.5%44+, A8s+, KJs+, A9o+, KQo
SB vs LJ13.1%44+, A7s+, KJs+, A9o+, KQo
BB vs LJ16.0%33+, A4s+, KTs+, QJs, A8o+, KQo
CO vs HJ15.4%33+, A5s+, KTs+, A8o+, KQo
BTN vs HJ15.4%33+, A5s+, KTs+, A8o+, KQo
SB vs HJ17.6%33+, A4s+, KTs+, QJs, A7o+, KJo+
BB vs HJ19.4%22+, A2s+, KTs+, QTs+, JTs, A7o+, KJo+
BTN vs CO18.4%33+, A2s+, KTs+, QJs, A7o+, KJo+
SB vs CO22.2%22+, A2s+, K9s+, QTs+, A5o+, KTo+
BB vs CO25.8%22+, A2s+, K8s+, Q9s+, JTs, A3o+, KTo+, QJo
SB vs BTN28.7%22+, A2s+, K7s+, Q9s+, JTs, A2o+, K9o+, QTo+
BB vs BTN32.1%22+, A2s+, K5s+, Q8s+, J9s+, T9s, A2o+, K8o+, QTo+, JTo
BB vs SB49.8%22+, A2s+, K2s+, Q2s+, J6s+, T7s+, 97s+, A2o+, K2o+, Q5o+, J8o+, T9o
All 169 hands at 12 bb: shove EV by seat
HandUTGUTG+1UTG+2LJHJCOBTNSB
AA+5.390+5.445+5.542+5.701+5.788+5.764+5.644+5.549
KK+4.373+4.469+4.586+4.736+4.819+4.819+4.822+4.931
QQ+3.555+3.688+3.902+4.090+4.246+4.303+4.321+4.429
JJ+2.746+2.929+3.242+3.490+3.711+3.825+3.899+4.058
TT+2.107+2.327+2.638+2.968+3.244+3.384+3.488+3.750
99+1.473+1.740+2.036+2.368+2.715+2.913+3.022+3.362
88+0.980+1.298+1.627+1.932+2.288+2.553+2.685+3.024
77+0.456+0.833+1.222+1.560+1.907+2.207+2.397+2.727
66+0.161+0.385+0.828+1.216+1.574+1.892+2.134+2.458
55+0.102+0.138+0.436+0.876+1.258+1.592+1.887+2.214
44+0.044+0.056+0.164+0.489+0.907+1.259+1.591+1.953
33−0.028−0.013+0.073+0.244+0.572+0.933+1.293+1.700
22−0.098−0.081+0.002+0.144+0.343+0.659+0.995+1.442
AKs+2.466+2.554+2.742+2.990+3.217+3.432+3.554+3.636
AQs+1.602+1.793+2.088+2.429+2.730+3.010+3.222+3.407
AJs+0.785+1.016+1.405+1.827+2.239+2.636+2.939+3.196
ATs+0.293+0.509+0.806+1.302+1.784+2.245+2.670+3.039
A9s+0.006+0.187+0.314+0.712+1.227+1.729+2.214+2.743
A8s−0.074+0.113+0.190+0.423+0.869+1.406+1.923+2.571
A7s−0.175+0.024+0.103+0.294+0.619+1.124+1.670+2.397
A6s−0.264−0.0850.000+0.193+0.457+0.896+1.448+2.235
A5s−0.132−0.002+0.065+0.267+0.510+0.897+1.419+2.216
A4s−0.172−0.049−0.030+0.161+0.408+0.782+1.296+2.112
A3s−0.208−0.084−0.074+0.078+0.315+0.695+1.219+2.046
A2s−0.259−0.134−0.124+0.020+0.230+0.605+1.132+1.978
KQs+0.470+0.602+0.674+0.814+0.996+1.269+1.748+2.705
KJs+0.300+0.353+0.426+0.492+0.655+0.940+1.502+2.512
KTs+0.275+0.308+0.294+0.337+0.441+0.647+1.266+2.352
K9s+0.026+0.085+0.099+0.057+0.133+0.296+0.830+2.060
K8s−0.168−0.098−0.062−0.083−0.067+0.087+0.528+1.778
K7s−0.237−0.157−0.111−0.100−0.072+0.041+0.441+1.620
K6s−0.295−0.237−0.171−0.149−0.108+0.009+0.383+1.484
K5s−0.320−0.305−0.264−0.227−0.180−0.067+0.305+1.363
K4s−0.368−0.360−0.359−0.342−0.275−0.151+0.221+1.251
K3s−0.406−0.398−0.405−0.422−0.370−0.243+0.139+1.183
K2s−0.455−0.447−0.455−0.478−0.451−0.321+0.055+1.111
QJs+0.238+0.302+0.389+0.421+0.501+0.618+0.996+1.885
QTs+0.225+0.277+0.291+0.344+0.424+0.505+0.787+1.743
Q9s−0.022+0.054+0.098+0.072+0.159+0.246+0.429+1.449
Q8s−0.217−0.137−0.074−0.078−0.052+0.047+0.235+1.178
Q7s−0.443−0.345−0.273−0.252−0.217−0.143+0.070+0.920
Q6s−0.473−0.400−0.312−0.275−0.225−0.147+0.059+0.820
Q5s−0.500−0.468−0.403−0.354−0.298−0.223−0.011+0.721
Q4s−0.541−0.517−0.494−0.465−0.391−0.307−0.093+0.635
Q3s−0.585−0.562−0.545−0.549−0.489−0.402−0.180+0.565
Q2s−0.628−0.603−0.587−0.597−0.563−0.475−0.261+0.500
JTs+0.194+0.267+0.308+0.391+0.469+0.522+0.681+1.359
J9s−0.058+0.038+0.111+0.116+0.209+0.287+0.405+1.065
J8s−0.252−0.148−0.056−0.0310.000+0.093+0.231+0.802
J7s−0.486−0.371−0.271−0.220−0.175−0.105+0.062+0.589
J6s−0.662−0.575−0.464−0.403−0.345−0.270−0.099+0.410
J5s−0.660−0.614−0.528−0.452−0.390−0.318−0.140+0.371
J4s−0.696−0.656−0.608−0.555−0.477−0.397−0.221+0.311
J3s−0.745−0.704−0.664−0.637−0.569−0.486−0.301+0.245
J2s−0.789−0.749−0.710−0.694−0.651−0.566−0.390+0.174
T9s+0.017+0.107+0.135+0.166+0.273+0.362+0.456+0.951
T8s−0.197−0.096−0.037+0.018+0.066+0.172+0.291+0.725
T7s−0.425−0.314−0.248−0.170−0.109−0.027+0.121+0.545
T6s−0.609−0.523−0.447−0.358−0.284−0.196−0.043+0.374
T5s−0.762−0.716−0.672−0.577−0.501−0.415−0.244+0.201
T4s−0.774−0.735−0.732−0.654−0.556−0.461−0.294+0.172
T3s−0.816−0.777−0.781−0.732−0.652−0.556−0.379+0.103
T2s−0.870−0.828−0.833−0.794−0.736−0.635−0.466+0.031
98s−0.196−0.076+0.009+0.028+0.097+0.226+0.339+0.718
97s−0.397−0.268−0.180−0.141−0.061+0.043+0.186+0.564
96s−0.575−0.471−0.375−0.328−0.237−0.130+0.017+0.401
95s−0.729−0.669−0.602−0.548−0.457−0.353−0.192+0.225
94s−0.900−0.845−0.820−0.792−0.686−0.572−0.406+0.051
93s−0.906−0.851−0.833−0.836−0.741−0.624−0.453+0.011
92s−0.950−0.894−0.878−0.889−0.817−0.699−0.538−0.059
87s−0.366−0.232−0.121−0.058−0.001+0.124+0.281+0.612
86s−0.544−0.430−0.309−0.237−0.172−0.044+0.117+0.464
85s−0.689−0.621−0.531−0.453−0.386−0.259−0.088+0.291
84s−0.862−0.799−0.756−0.701−0.619−0.480−0.303+0.109
83s−1.041−0.975−0.941−0.922−0.856−0.715−0.524−0.081
82s−1.046−0.981−0.948−0.935−0.895−0.755−0.574−0.122
76s−0.518−0.393−0.260−0.167−0.088+0.022+0.196+0.535
75s−0.660−0.585−0.480−0.378−0.298−0.186+0.001+0.369
74s−0.834−0.763−0.707−0.630−0.536−0.415−0.220+0.182
73s−1.015−0.940−0.893−0.853−0.774−0.650−0.439−0.007
72s−1.188−1.110−1.065−1.038−0.990−0.867−0.664−0.204
65s−0.607−0.531−0.412−0.292−0.199−0.084+0.094+0.443
64s−0.761−0.694−0.626−0.529−0.424−0.301−0.112+0.267
63s−0.952−0.882−0.820−0.763−0.673−0.544−0.339+0.072
62s−1.132−1.061−1.000−0.954−0.894−0.765−0.565−0.125
54s−0.619−0.628−0.557−0.446−0.331−0.209−0.018+0.362
53s−0.796−0.800−0.738−0.665−0.565−0.437−0.231+0.177
52s−0.976−0.975−0.915−0.856−0.790−0.660−0.459−0.021
43s−0.841−0.857−0.869−0.794−0.676−0.536−0.325+0.103
42s−1.014−1.026−1.039−0.978−0.895−0.756−0.550−0.092
32s−1.072−1.080−1.104−1.097−1.007−0.862−0.645−0.169
AKo+2.219+2.311+2.504+2.758+2.992+3.224+3.363+3.463
AQo+1.305+1.507+1.812+2.162+2.474+2.774+3.006+3.217
AJo+0.425+0.666+1.072+1.511+1.943+2.368+2.697+2.982
ATo−0.109+0.119+0.432+0.948+1.455+1.946+2.410+2.812
A9o−0.411−0.225−0.097+0.319+0.858+1.394+1.920+2.499
A8o−0.510−0.316−0.240−0.001+0.472+1.043+1.601+2.306
A7o−0.621−0.415−0.338−0.149+0.192+0.733+1.324+2.113
A6o−0.718−0.529−0.446−0.252+0.022+0.493+1.089+1.944
A5o−0.565−0.432−0.367−0.167+0.082+0.494+1.059+1.922
A4o−0.608−0.482−0.472−0.284−0.029+0.369+0.927+1.807
A3o−0.655−0.527−0.525−0.378−0.130+0.275+0.840+1.736
A2o−0.708−0.580−0.577−0.437−0.222+0.180+0.752+1.664
KQo+0.068+0.207+0.272+0.411+0.595+0.890+1.417+2.474
KJo−0.117−0.0640.000+0.055+0.222+0.531+1.146+2.253
KTo−0.153−0.116−0.136−0.1050.000+0.223+0.900+2.084
K9o−0.416−0.354−0.349−0.402−0.327−0.155+0.424+1.770
K8o−0.621−0.550−0.526−0.559−0.545−0.381+0.104+1.469
K7o−0.693−0.610−0.569−0.573−0.550−0.427+0.013+1.299
K6o−0.759−0.696−0.636−0.627−0.591−0.465−0.053+1.148
K5o−0.793−0.777−0.740−0.716−0.676−0.554−0.143+1.017
K4o−0.832−0.826−0.837−0.831−0.770−0.640−0.232+0.897
K3o−0.881−0.875−0.896−0.928−0.877−0.743−0.322+0.820
K2o−0.928−0.922−0.941−0.981−0.957−0.819−0.404+0.749
QJo−0.167−0.102−0.021−0.001+0.078+0.201+0.617+1.594
QTo−0.199−0.144−0.133−0.089−0.013+0.071+0.385+1.434
Q9o−0.470−0.391−0.356−0.389−0.307−0.2140.000+1.119
Q8o−0.675−0.591−0.535−0.551−0.529−0.424−0.211+0.826
Q7o−0.912−0.810−0.745−0.738−0.711−0.635−0.399+0.546
Q6o−0.938−0.861−0.778−0.755−0.712−0.631−0.401+0.441
Q5o−0.974−0.942−0.883−0.844−0.793−0.715−0.478+0.332
Q4o−1.019−0.995−0.980−0.959−0.889−0.802−0.565+0.240
Q3o−1.066−1.043−1.036−1.051−0.993−0.904−0.656+0.168
Q2o−1.116−1.092−1.085−1.108−1.077−0.986−0.747+0.095
JTo−0.227−0.147−0.110−0.039+0.036+0.092+0.277+1.025
J9o−0.499−0.399−0.337−0.341−0.251−0.168−0.024+0.709
J8o−0.700−0.592−0.510−0.500−0.468−0.368−0.209+0.427
J7o−0.941−0.821−0.728−0.693−0.653−0.580−0.394+0.196
J6o−1.139−1.045−0.939−0.893−0.843−0.761−0.565+0.004
J5o−1.138−1.089−1.006−0.944−0.887−0.809−0.608−0.038
J4o−1.183−1.142−1.102−1.058−0.980−0.894−0.691−0.102
J3o−1.233−1.191−1.159−1.151−1.085−0.997−0.786−0.179
J2o−1.285−1.242−1.211−1.214−1.175−1.085−0.884−0.258
T9o−0.429−0.333−0.311−0.283−0.180−0.085+0.032+0.587
T8o−0.645−0.536−0.479−0.433−0.387−0.276−0.137+0.348
T7o−0.884−0.764−0.702−0.636−0.580−0.491−0.322+0.153
T6o−1.088−0.992−0.920−0.844−0.776−0.679−0.500−0.031
T5o−1.251−1.201−1.160−1.075−1.008−0.916−0.720−0.217
T4o−1.262−1.220−1.223−1.155−1.063−0.965−0.772−0.252
T3o−1.308−1.264−1.276−1.241−1.166−1.064−0.862−0.327
T2o−1.359−1.315−1.328−1.301−1.251−1.147−0.954−0.403
98o−0.640−0.517−0.438−0.426−0.357−0.224−0.095+0.341
97o−0.852−0.719−0.636−0.606−0.532−0.425−0.262+0.171
96o−1.041−0.930−0.840−0.802−0.714−0.602−0.4350.000
95o−1.210−1.146−1.085−1.040−0.956−0.845−0.662−0.189
94o−1.394−1.338−1.325−1.305−1.201−1.082−0.893−0.381
93o−1.396−1.339−1.336−1.351−1.259−1.139−0.945−0.422
92o−1.450−1.391−1.386−1.409−1.343−1.221−1.038−0.499
87o−0.823−0.684−0.581−0.529−0.474−0.343−0.166+0.217
86o−1.012−0.890−0.775−0.712−0.648−0.514−0.333+0.062
85o−1.172−1.101−1.013−0.942−0.876−0.744−0.552−0.120
84o−1.355−1.290−1.255−1.208−1.125−0.984−0.784−0.316
83o−1.547−1.479−1.455−1.451−1.384−1.238−1.020−0.522
82o−1.555−1.487−1.460−1.465−1.427−1.279−1.074−0.566
76o−0.983−0.849−0.719−0.635−0.563−0.446−0.252+0.136
75o−1.143−1.064−0.962−0.870−0.796−0.675−0.463−0.042
74o−1.323−1.250−1.202−1.131−1.037−0.910−0.692−0.239
73o−1.515−1.438−1.402−1.375−1.299−1.168−0.932−0.447
72o−1.707−1.626−1.589−1.576−1.532−1.402−1.172−0.656
65o−1.079−0.998−0.881−0.772−0.684−0.561−0.361+0.039
64o−1.249−1.178−1.116−1.028−0.925−0.794−0.582−0.150
63o−1.439−1.364−1.315−1.269−1.181−1.048−0.821−0.358
62o−1.639−1.562−1.512−1.479−1.424−1.288−1.063−0.569
54o−1.096−1.105−1.037−0.931−0.818−0.687−0.473−0.044
53o−1.273−1.278−1.224−1.165−1.068−0.936−0.707−0.245
52o−1.472−1.472−1.418−1.370−1.309−1.172−0.946−0.454
43o−1.321−1.338−1.361−1.297−1.182−1.039−0.803−0.324
42o−1.515−1.526−1.551−1.501−1.421−1.275−1.042−0.533
32o−1.568−1.577−1.613−1.620−1.533−1.385−1.142−0.612

Reading the chart is the easy half. The trainer deals you real hands at 12 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 9-max at 12 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 0.015 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.