// push/fold charts · 9-max · 10 bb

9-max push/fold at 10 bb

At 10 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 14.9% of hands from UTG, widening to 73.9% 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 14.9% first in

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

UTG+1

shoves 16.6% first in

33+, A5s+, K9s+, Q9s+, J9s+, T9s, ATo+, KJo+

UTG+2

shoves 19.2% first in

22+, A2s+, K9s+, Q9s+, J9s+, T9s, 98s, A9o+, KJo+

LJ

shoves 23.3% first in

22+, A2s+, K9s+, Q9s+, J9s+, T8s+, 98s, A7o+, A5o, KJo+, QJo

HJ

shoves 28.5% first in

22+, A2s+, K9s+, Q9s+, J8s+, T8s+, 98s, 87s, A3o+, KTo+, QJo, JTo

CO

shoves 33.5% first in

22+, A2s+, K5s+, Q8s+, J8s+, T7s+, 97s+, 87s, 76s, A2o+, K9o+, QTo+, JTo

BTN

shoves 43.6% first in

22+, A2s+, K2s+, Q4s+, J7s+, T7s+, 96s+, 86s+, 75s+, 65s, 54s, A2o+, K5o+, Q9o+, J9o+, T9o

SB

shoves 73.9% first in

22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 84s+, 73s+, 63s+, 52s+, 43s, A2o+, K2o+, Q2o+, J4o+, T6o+, 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 37.3% against a BTN shove of 43.6%

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

Call vs fold, closest hands

BB facing BTN: the hands nearest indifference

HandCall freqCall vs fold (bb)
K5o0%−0.033
Q6s100%+0.057
J9o0%−0.074
Q5s0%−0.079
98s100%+0.085
87s0%−0.093
J7s0%−0.113
T8s100%+0.119
Q7s100%+0.146
Q4s0%−0.172
22+, A2s+, K2s+, Q6s+, J8s+, T8s+, 98s, A2o+, K6o+, Q9o+, JTo

Every calling range at 10 bb

SpotCallsRange
UTG+1 vs UTG8.8%66+, ATs+, KQs, ATo+
UTG+2 vs UTG8.8%66+, ATs+, KQs, ATo+
LJ vs UTG8.8%66+, ATs+, KQs, ATo+
HJ vs UTG8.8%66+, ATs+, KQs, ATo+
CO vs UTG8.8%66+, ATs+, KQs, ATo+
BTN vs UTG8.8%66+, ATs+, KQs, ATo+
SB vs UTG10.3%55+, A9s+, KJs+, ATo+
BB vs UTG13.1%44+, A7s+, A5s, KTs+, QJs, ATo+, KQo
UTG+2 vs UTG+110.0%55+, A9s+, KQs, ATo+
LJ vs UTG+110.0%55+, A9s+, KQs, ATo+
HJ vs UTG+110.0%55+, A9s+, KQs, ATo+
CO vs UTG+110.0%55+, A9s+, KQs, ATo+
BTN vs UTG+110.0%55+, A9s+, KQs, ATo+
SB vs UTG+112.0%44+, A8s+, KJs+, ATo+, KQo
BB vs UTG+115.3%44+, A3s+, KTs+, QJs, A9o+, KQo
LJ vs UTG+212.3%44+, A8s+, KQs, A9o+, KQo
HJ vs UTG+212.3%44+, A8s+, KQs, A9o+, KQo
CO vs UTG+212.3%44+, A8s+, KQs, A9o+, KQo
BTN vs UTG+212.3%44+, A8s+, KQs, A9o+, KQo
SB vs UTG+213.9%33+, A7s+, A5s, KJs+, A9o+, KQo
BB vs UTG+218.3%22+, A3s+, KTs+, QTs+, JTs, A8o+, KJo+
HJ vs LJ14.6%33+, A7s+, KJs+, A8o+, KQo
CO vs LJ14.6%33+, A7s+, KJs+, A8o+, KQo
BTN vs LJ14.6%33+, A7s+, KJs+, A8o+, KQo
SB vs LJ16.6%33+, A4s+, KTs+, QJs, A8o+, KJo+
BB vs LJ22.6%22+, A2s+, K9s+, QTs+, JTs, A5o+, KTo+
CO vs HJ18.6%22+, A3s+, KTs+, QJs, A7o+, KJo+
BTN vs HJ18.6%22+, A3s+, KTs+, QJs, A7o+, KJo+
SB vs HJ21.3%22+, A2s+, KTs+, QTs+, JTs, A5o+, KJo+
BB vs HJ26.8%22+, A2s+, K7s+, Q9s+, JTs, A2o+, KTo+, QJo
BTN vs CO23.1%22+, A2s+, K9s+, QTs+, A4o+, KTo+
SB vs CO26.4%22+, A2s+, K8s+, QTs+, JTs, A2o+, KTo+, QJo
BB vs CO30.8%22+, A2s+, K5s+, Q8s+, J9s+, T9s, A2o+, K9o+, QTo+, JTo
SB vs BTN33.0%22+, A2s+, K4s+, Q8s+, J9s+, A2o+, K7o+, QTo+, JTo
BB vs BTN37.3%22+, A2s+, K2s+, Q6s+, J8s+, T8s+, 98s, A2o+, K6o+, Q9o+, JTo
BB vs SB56.6%22+, A2s+, K2s+, Q2s+, J3s+, T6s+, 96s+, 87s, A2o+, K2o+, Q2o+, J7o+, T8o+, 98o
All 169 hands at 10 bb: shove EV by seat
HandUTGUTG+1UTG+2LJHJCOBTNSB
AA+5.341+5.386+5.580+5.634+5.728+5.643+5.453+5.273
KK+4.360+4.428+4.594+4.649+4.741+4.709+4.658+4.764
QQ+3.639+3.773+3.948+4.072+4.218+4.222+4.159+4.292
JJ+2.936+3.143+3.349+3.541+3.720+3.794+3.761+3.928
TT+2.326+2.568+2.850+3.080+3.281+3.377+3.391+3.635
99+1.746+1.987+2.277+2.554+2.816+2.926+2.957+3.271
88+1.336+1.593+1.863+2.123+2.453+2.601+2.624+2.940
77+0.903+1.206+1.509+1.756+2.094+2.305+2.321+2.639
66+0.486+0.832+1.180+1.444+1.776+2.018+2.053+2.379
55+0.225+0.460+0.852+1.141+1.484+1.740+1.819+2.155
44+0.097+0.189+0.478+0.797+1.152+1.409+1.550+1.907
33+0.014+0.077+0.230+0.469+0.826+1.096+1.283+1.653
22−0.0540.000+0.106+0.254+0.516+0.795+1.019+1.402
AKs+2.542+2.658+2.870+3.058+3.279+3.437+3.444+3.448
AQs+1.835+2.037+2.333+2.572+2.852+3.066+3.119+3.271
AJs+1.117+1.385+1.722+2.068+2.464+2.749+2.881+3.077
ATs+0.557+0.816+1.226+1.620+2.039+2.429+2.660+2.935
A9s+0.172+0.332+0.666+1.071+1.527+1.938+2.252+2.670
A8s+0.093+0.196+0.409+0.714+1.203+1.634+2.019+2.538
A7s+0.003+0.106+0.288+0.488+0.920+1.368+1.794+2.372
A6s−0.104+0.003+0.192+0.357+0.698+1.129+1.587+2.216
A5s−0.023+0.064+0.261+0.419+0.715+1.096+1.550+2.200
A4s−0.079−0.028+0.156+0.318+0.604+0.965+1.445+2.118
A3s−0.121−0.077+0.075+0.226+0.514+0.882+1.370+2.053
A2s−0.170−0.129+0.013+0.144+0.417+0.790+1.295+1.978
KQs+0.580+0.644+0.754+0.909+1.103+1.382+1.950+2.698
KJs+0.354+0.413+0.428+0.588+0.762+1.113+1.733+2.519
KTs+0.254+0.285+0.303+0.399+0.502+0.839+1.529+2.377
K9s+0.062+0.088+0.041+0.097+0.196+0.450+1.135+2.117
K8s−0.114−0.068−0.099−0.105−0.005+0.218+0.822+1.879
K7s−0.168−0.112−0.115−0.092−0.054+0.167+0.661+1.731
K6s−0.238−0.171−0.163−0.128−0.079+0.114+0.554+1.598
K5s−0.307−0.258−0.242−0.199−0.153+0.029+0.462+1.490
K4s−0.367−0.350−0.352−0.295−0.242−0.065+0.381+1.402
K3s−0.411−0.401−0.430−0.390−0.334−0.136+0.309+1.334
K2s−0.459−0.450−0.489−0.466−0.420−0.223+0.234+1.254
QJs+0.294+0.372+0.386+0.448+0.515+0.723+1.102+2.019
QTs+0.222+0.271+0.303+0.368+0.433+0.567+0.921+1.887
Q9s+0.036+0.080+0.045+0.107+0.170+0.292+0.568+1.624
Q8s−0.147−0.086−0.105−0.099−0.032+0.102+0.343+1.390
Q7s−0.348−0.276−0.270−0.240−0.227−0.075+0.147+1.136
Q6s−0.394−0.313−0.294−0.249−0.221−0.096+0.135+1.025
Q5s−0.462−0.399−0.373−0.321−0.294−0.175+0.079+0.920
Q4s−0.518−0.487−0.480−0.416−0.383−0.267+0.004+0.832
Q3s−0.567−0.542−0.562−0.513−0.479−0.342−0.070+0.761
Q2s−0.607−0.583−0.614−0.582−0.559−0.426−0.140+0.693
JTs+0.221+0.289+0.353+0.417+0.448+0.549+0.744+1.479
J9s+0.031+0.096+0.095+0.160+0.200+0.312+0.446+1.215
J8s−0.148−0.065−0.051−0.043+0.001+0.127+0.255+0.987
J7s−0.363−0.269−0.233−0.197−0.201−0.054+0.074+0.748
J6s−0.556−0.456−0.412−0.362−0.354−0.229−0.072+0.561
J5s−0.596−0.515−0.462−0.405−0.400−0.279−0.099+0.510
J4s−0.643−0.592−0.559−0.494−0.484−0.369−0.173+0.437
J3s−0.697−0.652−0.640−0.586−0.574−0.438−0.240+0.372
J2s−0.741−0.698−0.699−0.663−0.662−0.528−0.320+0.309
T9s+0.070+0.121+0.142+0.220+0.283+0.372+0.478+1.057
T8s−0.120−0.044−0.005+0.018+0.090+0.194+0.304+0.835
T7s−0.330−0.245−0.187−0.135−0.116+0.012+0.125+0.622
T6s−0.529−0.438−0.369−0.305−0.273−0.165−0.026+0.462
T5s−0.720−0.653−0.583−0.514−0.489−0.380−0.202+0.294
T4s−0.747−0.710−0.656−0.573−0.539−0.439−0.246+0.253
T3s−0.794−0.763−0.733−0.668−0.634−0.512−0.317+0.184
T2s−0.844−0.815−0.797−0.747−0.723−0.601−0.394+0.123
98s−0.077+0.001+0.013+0.044+0.139+0.256+0.339+0.772
97s−0.263−0.180−0.151−0.093−0.050+0.089+0.183+0.596
96s−0.457−0.368−0.330−0.264−0.211−0.093+0.031+0.441
95s−0.652−0.585−0.546−0.476−0.430−0.314−0.154+0.277
94s−0.832−0.794−0.781−0.701−0.652−0.539−0.351+0.101
93s−0.843−0.813−0.824−0.759−0.705−0.571−0.391+0.061
92s−0.885−0.857−0.879−0.830−0.788−0.657−0.465+0.001
87s−0.221−0.121−0.072−0.040+0.026+0.177+0.260+0.617
86s−0.410−0.303−0.243−0.205−0.1310.000+0.111+0.480
85s−0.599−0.515−0.455−0.413−0.343−0.213−0.069+0.322
84s−0.782−0.731−0.693−0.642−0.567−0.439−0.271+0.143
83s−0.959−0.915−0.907−0.874−0.801−0.650−0.471−0.039
82s−0.965−0.923−0.925−0.910−0.848−0.701−0.514−0.073
76s−0.370−0.255−0.175−0.115−0.068+0.073+0.181+0.533
75s−0.559−0.465−0.382−0.317−0.274−0.130+0.008+0.384
74s−0.741−0.682−0.623−0.552−0.506−0.364−0.198+0.199
73s−0.920−0.867−0.840−0.784−0.740−0.573−0.398+0.018
72s−1.086−1.035−1.023−0.990−0.964−0.800−0.605−0.162
65s−0.502−0.398−0.299−0.222−0.166−0.044+0.100+0.456
64s−0.670−0.604−0.527−0.442−0.385−0.263−0.095+0.279
63s−0.858−0.797−0.754−0.685−0.629−0.480−0.300+0.097
62s−1.033−0.972−0.942−0.896−0.856−0.710−0.508−0.085
54s−0.600−0.536−0.448−0.355−0.293−0.177+0.004+0.373
53s−0.774−0.716−0.660−0.581−0.521−0.378−0.191+0.196
52s−0.944−0.889−0.849−0.796−0.750−0.610−0.400+0.015
43s−0.842−0.839−0.784−0.695−0.625−0.481−0.276+0.121
42s−1.006−1.003−0.966−0.902−0.849−0.711−0.483−0.054
32s−1.068−1.073−1.078−1.012−0.956−0.798−0.566−0.130
AKo+2.306+2.427+2.641+2.836+3.064+3.237+3.265+3.281
AQo+1.559+1.771+2.073+2.319+2.609+2.841+2.911+3.093
AJo+0.783+1.064+1.410+1.775+2.190+2.497+2.650+2.878
ATo+0.182+0.457+0.881+1.295+1.731+2.154+2.412+2.722
A9o−0.232−0.064+0.283+0.708+1.184+1.627+1.977+2.442
A8o−0.326−0.218−0.002+0.321+0.833+1.295+1.719+2.293
A7o−0.428−0.321−0.141+0.067+0.522+1.004+1.475+2.111
A6o−0.540−0.428−0.240−0.069+0.287+0.752+1.256+1.947
A5o−0.444−0.354−0.1600.000+0.305+0.718+1.215+1.928
A4o−0.506−0.454−0.274−0.109+0.183+0.576+1.101+1.838
A3o−0.557−0.513−0.364−0.209+0.088+0.484+1.018+1.768
A2o−0.608−0.567−0.429−0.297−0.016+0.390+0.941+1.687
KQo+0.192+0.256+0.364+0.519+0.718+1.024+1.659+2.485
KJo−0.056+0.001+0.002+0.166+0.347+0.728+1.419+2.284
KTo−0.161−0.129−0.125−0.028+0.072+0.442+1.205+2.132
K9o−0.369−0.344−0.404−0.348−0.256+0.017+0.777+1.854
K8o−0.560−0.516−0.559−0.568−0.472−0.228+0.447+1.598
K7o−0.612−0.554−0.572−0.556−0.521−0.280+0.274+1.439
K6o−0.688−0.620−0.626−0.594−0.553−0.341+0.155+1.293
K5o−0.768−0.719−0.715−0.678−0.639−0.437+0.052+1.174
K4o−0.825−0.811−0.825−0.775−0.729−0.535−0.031+1.079
K3o−0.880−0.874−0.919−0.882−0.834−0.618−0.114+1.005
K2o−0.924−0.918−0.975−0.957−0.916−0.703−0.186+0.922
QJo−0.102−0.023−0.023+0.035+0.099+0.324+0.753+1.763
QTo−0.190−0.140−0.118−0.0570.000+0.149+0.551+1.613
Q9o−0.400−0.359−0.404−0.345−0.287−0.151+0.172+1.331
Q8o−0.593−0.531−0.565−0.562−0.501−0.353−0.070+1.080
Q7o−0.804−0.732−0.742−0.721−0.717−0.552−0.287+0.803
Q6o−0.845−0.764−0.760−0.721−0.702−0.564−0.294+0.684
Q5o−0.925−0.862−0.849−0.801−0.783−0.651−0.359+0.570
Q4o−0.985−0.955−0.960−0.899−0.876−0.747−0.438+0.475
Q3o−1.038−1.015−1.050−1.003−0.979−0.829−0.515+0.402
Q2o−1.086−1.064−1.110−1.082−1.067−0.921−0.594+0.325
JTo−0.184−0.116−0.063−0.002+0.021+0.135+0.368+1.178
J9o−0.398−0.335−0.347−0.286−0.252−0.125+0.045+0.894
J8o−0.585−0.502−0.504−0.498−0.458−0.319−0.157+0.652
J7o−0.804−0.711−0.691−0.661−0.674−0.514−0.355+0.391
J6o−1.016−0.915−0.886−0.843−0.844−0.703−0.511+0.191
J5o−1.059−0.976−0.938−0.885−0.889−0.754−0.539+0.137
J4o−1.118−1.068−1.047−0.983−0.979−0.849−0.616+0.060
J3o−1.173−1.129−1.137−1.087−1.082−0.932−0.697−0.016
J2o−1.223−1.181−1.202−1.172−1.177−1.030−0.783−0.089
T9o−0.360−0.308−0.296−0.218−0.162−0.058+0.082+0.725
T8o−0.549−0.471−0.444−0.420−0.356−0.240−0.099+0.490
T7o−0.769−0.684−0.639−0.591−0.578−0.436−0.292+0.260
T6o−0.986−0.893−0.840−0.779−0.754−0.631−0.454+0.088
T5o−1.192−1.123−1.067−1.002−0.987−0.865−0.648−0.094
T4o−1.219−1.182−1.142−1.063−1.039−0.926−0.696−0.139
T3o−1.270−1.240−1.226−1.165−1.140−1.004−0.772−0.214
T2o−1.319−1.291−1.289−1.244−1.229−1.098−0.854−0.281
98o−0.507−0.429−0.428−0.397−0.309−0.181−0.068+0.424
97o−0.703−0.618−0.601−0.550−0.514−0.364−0.238+0.233
96o−0.905−0.815−0.791−0.726−0.678−0.551−0.396+0.067
95o−1.117−1.050−1.024−0.959−0.918−0.789−0.596−0.111
94o−1.314−1.280−1.279−1.202−1.158−1.033−0.810−0.300
93o−1.322−1.297−1.322−1.262−1.216−1.070−0.852−0.344
92o−1.371−1.346−1.383−1.339−1.305−1.163−0.934−0.409
87o−0.663−0.564−0.529−0.500−0.438−0.274−0.160+0.253
86o−0.859−0.751−0.704−0.666−0.597−0.454−0.313+0.105
85o−1.066−0.979−0.930−0.887−0.823−0.683−0.507−0.062
84o−1.260−1.211−1.185−1.135−1.066−0.928−0.723−0.254
83o−1.451−1.409−1.419−1.387−1.320−1.155−0.937−0.450
82o−1.457−1.416−1.438−1.426−1.368−1.208−0.984−0.486
76o−0.815−0.696−0.629−0.574−0.532−0.379−0.239+0.160
75o−1.025−0.929−0.859−0.800−0.760−0.602−0.426−0.001
74o−1.216−1.158−1.109−1.039−0.997−0.841−0.642−0.193
73o−1.407−1.357−1.345−1.294−1.254−1.074−0.860−0.393
72o−1.590−1.539−1.543−1.516−1.493−1.316−1.082−0.585
65o−0.956−0.850−0.763−0.690−0.640−0.504−0.330+0.075
64o−1.140−1.074−1.009−0.928−0.876−0.739−0.536−0.109
63o−1.330−1.272−1.243−1.177−1.129−0.969−0.753−0.308
62o−1.521−1.464−1.450−1.407−1.374−1.215−0.977−0.502
54o−1.062−0.996−0.918−0.825−0.768−0.638−0.426−0.008
53o−1.240−1.184−1.144−1.068−1.017−0.862−0.638−0.200
52o−1.427−1.372−1.347−1.296−1.257−1.104−0.859−0.391
43o−1.310−1.310−1.269−1.184−1.124−0.967−0.726−0.277
42o−1.493−1.494−1.472−1.412−1.364−1.211−0.946−0.467
32o−1.553−1.562−1.583−1.523−1.473−1.304−1.033−0.546

Reading the chart is the easy half. The trainer deals you real hands at 10 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 9-max at 10 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 0.028 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.