6-max push/fold at 23 bb

At 23 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 12.4% of hands from UTG, widening to 51.2% 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 12.4% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJo70%QJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

55+, A9s+, K9s+, QTs+, JTs, AJo+, KJo+

HJ

shoves 15.1% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJo32%QJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

33+, A8s+, K9s+, Q9s+, J9s+, T9s, ATo+, KQo

CO

shoves 21.3% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K8s+, Q8s+, J8s+, T8s+, 98s, A9o+, KJo+, QJo

BTN

shoves 31.0% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7s27%T6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K6s+, Q8s+, J8s+, T8s+, 97s+, 87s, 76s, A3o+, KTo+, QTo+, JTo

SB

shoves 51.2% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4o55%Q4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K2s+, Q3s+, J4s+, T5s+, 95s+, 85s+, 74s+, 64s+, 53s+, A2o+, K4o+, Q9o+, J8o+, T8o+, 98o, 87o

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.

ShoverCaller

BB calls 17.8% against a BTN shove of 31.0%

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)
A3s	0%	−0.038
KJo	100%	+0.207
33	100%	+0.220
QJs	100%	+0.230
A4s	100%	+0.246
A2s	0%	−0.294
A7o	100%	+0.327
QTs	0%	−0.560
A6o	0%	−0.570
22	0%	−0.596

33+, A4s+, KTs+, QJs, A7o+, KJo+

Every calling range at 23 bb

Spot	Calls	Range
HJ vs UTG	5.9%	88+, AJs+, AQo+
CO vs UTG	5.9%	88+, AJs+, AQo+
BTN vs UTG	5.9%	88+, AJs+, AQo+
SB vs UTG	5.9%	88+, AJs+, AQo+
BB vs UTG	6.7%	77+, AJs+, AQo+
CO vs HJ	7.5%	77+, ATs+, AJo+
BTN vs HJ	7.5%	77+, ATs+, AJo+
SB vs HJ	8.0%	66+, ATs+, AJo+
BB vs HJ	8.3%	66+, ATs+, KQs, AJo+
BTN vs CO	10.0%	55+, A9s+, KQs, ATo+
SB vs CO	10.5%	55+, A8s+, KQs, ATo+
BB vs CO	11.5%	55+, A8s+, KJs+, ATo+, KQo
SB vs BTN	15.2%	44+, A5s+, KTs+, A8o+, KQo
BB vs BTN	17.8%	33+, A4s+, KTs+, QJs, A7o+, KJo+
BB vs SB	30.4%	22+, A2s+, K6s+, Q9s+, J9s+, A2o+, K8o+, QTo+

All 169 hands at 23 bb: shove EV by seat

Hand	UTG	HJ	CO	BTN	SB
AA	+5.608	+5.724	+5.873	+6.042	+6.113
KK	+4.525	+4.785	+4.976	+5.152	+5.337
QQ	+3.459	+3.930	+4.242	+4.567	+4.835
JJ	+2.597	+3.076	+3.551	+4.009	+4.418
TT	+1.915	+2.418	+2.917	+3.526	+4.009
99	+1.156	+1.758	+2.296	+2.972	+3.534
88	+0.511	+1.242	+1.848	+2.517	+3.162
77	+0.112	+0.688	+1.411	+2.091	+2.853
66	+0.055	+0.302	+0.996	+1.728	+2.567
55	+0.050	+0.169	+0.582	+1.387	+2.300
44	−0.007	+0.107	+0.308	+1.009	+1.986
33	−0.085	+0.031	+0.235	+0.722	+1.668
22	−0.161	−0.044	+0.158	+0.568	+1.351
AKs	+2.394	+2.701	+3.039	+3.540	+3.997
AQs	+1.284	+1.812	+2.363	+3.033	+3.650
AJs	+0.560	+0.949	+1.648	+2.523	+3.360
ATs	+0.310	+0.425	+1.026	+2.041	+3.078
A9s	+0.070	+0.140	+0.519	+1.469	+2.624
A8s	−0.030	+0.062	+0.370	+1.091	+2.334
A7s	−0.127	−0.042	+0.264	+0.804	+2.056
A6s	−0.160	−0.149	+0.163	+0.620	+1.830
A5s	−0.008	−0.029	+0.235	+0.678	+1.792
A4s	−0.051	−0.072	+0.135	+0.573	+1.665
A3s	−0.088	−0.109	+0.097	+0.487	+1.584
A2s	−0.139	−0.164	+0.045	+0.420	+1.494
KQs	+0.484	+0.632	+0.856	+1.191	+2.152
KJs	+0.435	+0.442	+0.567	+0.822	+1.891
KTs	+0.346	+0.425	+0.425	+0.586	+1.638
K9s	+0.042	+0.160	+0.221	+0.271	+1.196
K8s	−0.179	−0.047	+0.034	+0.060	+0.838
K7s	−0.243	−0.120	−0.006	+0.032	+0.721
K6s	−0.249	−0.195	−0.070	+0.008	+0.655
K5s	−0.261	−0.242	−0.164	−0.067	+0.570
K4s	−0.313	−0.293	−0.271	−0.168	+0.481
K3s	−0.352	−0.333	−0.311	−0.255	+0.395
K2s	−0.402	−0.386	−0.364	−0.323	+0.305
QJs	+0.314	+0.380	+0.524	+0.648	+1.293
QTs	+0.232	+0.376	+0.424	+0.574	+1.065
Q9s	−0.066	+0.112	+0.220	+0.304	+0.699
Q8s	−0.287	−0.097	+0.020	+0.080	+0.475
Q7s	−0.508	−0.335	−0.178	−0.116	+0.318
Q6s	−0.485	−0.382	−0.220	−0.112	+0.304
Q5s	−0.501	−0.430	−0.312	−0.187	+0.235
Q4s	−0.544	−0.474	−0.414	−0.288	+0.148
Q3s	−0.593	−0.522	−0.461	−0.377	+0.056
Q2s	−0.636	−0.567	−0.505	−0.438	−0.030
JTs	+0.264	+0.339	+0.445	+0.629	+0.989
J9s	−0.038	+0.070	+0.236	+0.359	+0.711
J8s	−0.278	−0.135	+0.041	+0.136	+0.499
J7s	−0.505	−0.385	−0.174	−0.070	+0.332
J6s	−0.636	−0.588	−0.380	−0.237	+0.153
J5s	−0.611	−0.607	−0.444	−0.283	+0.115
J4s	−0.652	−0.644	−0.535	−0.377	+0.030
J3s	−0.702	−0.697	−0.587	−0.459	−0.055
J2s	−0.748	−0.744	−0.636	−0.531	−0.150
T9s	−0.008	+0.153	+0.264	+0.427	+0.764
T8s	−0.266	−0.077	+0.065	+0.207	+0.577
T7s	−0.483	−0.320	−0.148	0.000	+0.406
T6s	−0.619	−0.533	−0.360	−0.172	+0.226
T5s	−0.767	−0.716	−0.597	−0.402	+0.014
T4s	−0.778	−0.729	−0.666	−0.463	−0.038
T3s	−0.827	−0.774	−0.710	−0.549	−0.128
T2s	−0.882	−0.832	−0.765	−0.623	−0.220
98s	−0.309	−0.074	+0.114	+0.239	+0.629
97s	−0.500	−0.289	−0.077	+0.051	+0.479
96s	−0.620	−0.495	−0.284	−0.122	+0.293
95s	−0.765	−0.682	−0.524	−0.353	+0.075
94s	−0.948	−0.866	−0.763	−0.598	−0.153
93s	−0.958	−0.872	−0.769	−0.642	−0.203
92s	−1.000	−0.919	−0.816	−0.708	−0.294
87s	−0.498	−0.255	−0.022	+0.113	+0.568
86s	−0.614	−0.460	−0.222	−0.055	+0.385
85s	−0.747	−0.639	−0.456	−0.280	+0.170
84s	−0.934	−0.824	−0.703	−0.529	−0.060
83s	−1.127	−1.016	−0.894	−0.764	−0.296
82s	−1.132	−1.021	−0.901	−0.792	−0.350
76s	−0.610	−0.432	−0.164	+0.018	+0.478
75s	−0.737	−0.608	−0.396	−0.203	+0.274
74s	−0.926	−0.793	−0.645	−0.459	+0.036
73s	−1.117	−0.988	−0.836	−0.697	−0.198
72s	−1.306	−1.172	−1.022	−0.911	−0.438
65s	−0.582	−0.556	−0.320	−0.090	+0.373
64s	−0.752	−0.721	−0.556	−0.331	+0.149
63s	−0.961	−0.928	−0.756	−0.583	−0.094
62s	−1.161	−1.122	−0.949	−0.800	−0.335
54s	−0.575	−0.603	−0.479	−0.232	+0.253
53s	−0.775	−0.793	−0.664	−0.466	+0.024
52s	−0.970	−0.986	−0.855	−0.687	−0.220
43s	−0.824	−0.842	−0.815	−0.587	−0.076
42s	−1.017	−1.028	−0.997	−0.801	−0.317
32s	−1.075	−1.089	−1.053	−0.918	−0.418
AKo	+2.127	+2.439	+2.793	+3.315	+3.800
AQo	+0.949	+1.500	+2.078	+2.774	+3.423
AJo	+0.156	+0.570	+1.302	+2.222	+3.106
ATo	−0.111	+0.002	+0.637	+1.704	+2.803
A9o	−0.359	−0.301	+0.091	+1.091	+2.318
A8o	−0.481	−0.396	−0.077	+0.683	+1.998
A7o	−0.594	−0.512	−0.200	+0.365	+1.695
A6o	−0.628	−0.626	−0.305	+0.170	+1.456
A5o	−0.453	−0.488	−0.219	+0.235	+1.413
A4o	−0.499	−0.533	−0.331	+0.119	+1.278
A3o	−0.547	−0.583	−0.375	+0.023	+1.186
A2o	−0.598	−0.640	−0.430	−0.050	+1.095
KQo	+0.067	+0.206	+0.435	+0.771	+1.806
KJo	+0.001	−0.001	+0.115	+0.369	+1.518
KTo	−0.095	−0.031	−0.031	+0.122	+1.253
K9o	−0.417	−0.311	−0.255	−0.214	+0.772
K8o	−0.647	−0.531	−0.460	−0.444	+0.392
K7o	−0.726	−0.606	−0.493	−0.472	+0.266
K6o	−0.731	−0.691	−0.564	−0.502	+0.191
K5o	−0.751	−0.749	−0.671	−0.590	+0.092
K4o	−0.794	−0.791	−0.781	−0.691	0.000
K3o	−0.843	−0.844	−0.834	−0.792	−0.095
K2o	−0.891	−0.894	−0.882	−0.858	−0.182
QJo	−0.110	−0.048	+0.089	+0.201	+0.886
QTo	−0.204	−0.075	−0.027	+0.111	+0.632
Q9o	−0.534	−0.365	−0.263	−0.188	+0.241
Q8o	−0.765	−0.584	−0.471	−0.423	−0.003
Q7o	−1.008	−0.835	−0.681	−0.638	−0.183
Q6o	−0.977	−0.878	−0.716	−0.627	−0.189
Q5o	−0.994	−0.939	−0.822	−0.711	−0.265
Q4o	−1.044	−0.987	−0.934	−0.815	−0.357
Q3o	−1.090	−1.038	−0.985	−0.912	−0.455
Q2o	−1.142	−1.091	−1.036	−0.983	−0.551
JTo	−0.181	−0.108	0.000	+0.170	+0.558
J9o	−0.505	−0.400	−0.241	−0.127	+0.255
J8o	−0.754	−0.613	−0.442	−0.357	+0.029
J7o	−0.997	−0.869	−0.663	−0.575	−0.158
J6o	−1.143	−1.097	−0.887	−0.765	−0.347
J5o	−1.119	−1.120	−0.954	−0.810	−0.386
J4o	−1.166	−1.167	−1.065	−0.911	−0.474
J3o	−1.219	−1.221	−1.116	−1.008	−0.575
J2o	−1.276	−1.276	−1.172	−1.087	−0.679
T9o	−0.478	−0.324	−0.212	−0.052	+0.310
T8o	−0.733	−0.556	−0.407	−0.273	+0.120
T7o	−0.979	−0.811	−0.633	−0.499	−0.068
T6o	−1.123	−1.044	−0.864	−0.694	−0.263
T5o	−1.273	−1.244	−1.116	−0.940	−0.494
T4o	−1.285	−1.255	−1.191	−1.000	−0.549
T3o	−1.337	−1.304	−1.240	−1.095	−0.646
T2o	−1.391	−1.358	−1.295	−1.168	−0.742
98o	−0.775	−0.551	−0.366	−0.242	+0.167
97o	−0.984	−0.777	−0.565	−0.448	0.000
96o	−1.114	−0.995	−0.783	−0.629	−0.192
95o	−1.275	−1.201	−1.041	−0.883	−0.427
94o	−1.470	−1.399	−1.306	−1.145	−0.675
93o	−1.470	−1.400	−1.308	−1.194	−0.729
92o	−1.526	−1.458	−1.361	−1.266	−0.828
87o	−0.985	−0.744	−0.516	−0.390	+0.090
86o	−1.107	−0.963	−0.722	−0.562	−0.096
85o	−1.255	−1.160	−0.973	−0.802	−0.325
84o	−1.455	−1.355	−1.241	−1.068	−0.573
83o	−1.664	−1.562	−1.445	−1.327	−0.826
82o	−1.667	−1.571	−1.452	−1.356	−0.884
76o	−1.108	−0.930	−0.655	−0.487	−0.002
75o	−1.249	−1.128	−0.913	−0.733	−0.223
74o	−1.445	−1.321	−1.179	−0.992	−0.470
73o	−1.652	−1.527	−1.383	−1.257	−0.726
72o	−1.861	−1.733	−1.584	−1.487	−0.983
65o	−1.085	−1.065	−0.824	−0.606	−0.116
64o	−1.272	−1.249	−1.083	−0.865	−0.355
63o	−1.480	−1.453	−1.287	−1.125	−0.611
62o	−1.698	−1.670	−1.499	−1.366	−0.869
54o	−1.082	−1.121	−0.994	−0.750	−0.236
53o	−1.277	−1.311	−1.185	−1.004	−0.487
52o	−1.495	−1.525	−1.393	−1.240	−0.742
43o	−1.331	−1.363	−1.344	−1.128	−0.589
42o	−1.544	−1.572	−1.549	−1.363	−0.845
32o	−1.599	−1.629	−1.601	−1.481	−0.952

Reading the chart is the easy half. The trainer deals you real hands at 23 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 6-max at 23 bb →

// what was solved, and what was assumed

6-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 0.027 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: 6max.json (summary) and one file per depth, e.g. 6max/10.json.