6-max push/fold at 21 bb

At 21 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 13.2% of hands from UTG, widening to 53.5% 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 13.2% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9s23%Q8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4474%43s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

44+, A8s+, K9s+, QTs+, J9s+, T9s, AJo+, KQo

HJ

shoves 16.6% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s25%97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

33+, A7s+, A5s-A4s, K9s+, Q9s+, J9s+, T9s, ATo+, KJo+

CO

shoves 22.6% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8s37%Q7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K9s+, Q9s+, J8s+, T8s+, 98s, A8o+, KJo+, QJo, JTo

BTN

shoves 32.4% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K6s+, Q8s+, J8s+, T7s+, 97s+, 86s+, 76s, A2o+, KTo+, QTo+, JTo

SB

shoves 53.5% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K2s+, Q2s+, J4s+, T5s+, 95s+, 85s+, 74s+, 64s+, 53s+, A2o+, K3o+, Q8o+, 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 18.4% against a BTN shove of 32.4%

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)
A2s	100%	+0.011
A6o	0%	−0.123
QTs	0%	−0.184
22	0%	−0.243
A3s	100%	+0.290
K9s	0%	−0.305
A5o	0%	−0.308
KTo	0%	−0.350
KJo	100%	+0.403
QJs	100%	+0.501

33+, A2s+, KTs+, QJs, A7o+, KJo+

Every calling range at 21 bb

Spot	Calls	Range
HJ vs UTG	6.1%	77+, AJs+, AQo+
CO vs UTG	6.1%	77+, AJs+, AQo+
BTN vs UTG	6.1%	77+, AJs+, AQo+
SB vs UTG	7.3%	77+, AJs+, AJo+
BB vs UTG	7.8%	77+, ATs+, KQs, AJo+
CO vs HJ	8.3%	66+, ATs+, KQs, AJo+
BTN vs HJ	8.3%	66+, ATs+, KQs, AJo+
SB vs HJ	8.3%	66+, ATs+, KQs, AJo+
BB vs HJ	9.6%	66+, A9s+, KQs, ATo+
BTN vs CO	10.5%	55+, A8s+, KJs+, ATo+
SB vs CO	12.4%	55+, A8s+, KJs+, A9o+, KQo
BB vs CO	12.8%	44+, A8s+, KJs+, A9o+, KQo
SB vs BTN	17.8%	33+, A4s+, KTs+, QJs, A7o+, KJo+
BB vs BTN	18.4%	33+, A2s+, KTs+, QJs, A7o+, KJo+
BB vs SB	32.7%	22+, A2s+, K5s+, Q8s+, J9s+, A2o+, K7o+, QTo+, JTo

All 169 hands at 21 bb: shove EV by seat

Hand	UTG	HJ	CO	BTN	SB
AA	+5.618	+5.733	+5.922	+6.031	+6.082
KK	+4.592	+4.813	+5.001	+5.139	+5.306
QQ	+3.615	+3.995	+4.296	+4.585	+4.829
JJ	+2.766	+3.200	+3.634	+4.024	+4.383
TT	+2.108	+2.565	+3.046	+3.558	+3.966
99	+1.399	+1.937	+2.403	+3.048	+3.506
88	+0.811	+1.461	+1.942	+2.629	+3.150
77	+0.281	+0.957	+1.536	+2.212	+2.816
66	+0.063	+0.472	+1.152	+1.868	+2.526
55	+0.058	+0.200	+0.770	+1.557	+2.271
44	0.000	+0.114	+0.464	+1.196	+1.970
33	−0.076	+0.041	+0.337	+0.848	+1.672
22	−0.151	−0.032	+0.257	+0.617	+1.374
AKs	+2.475	+2.748	+3.165	+3.572	+3.972
AQs	+1.464	+1.944	+2.535	+3.094	+3.635
AJs	+0.701	+1.131	+1.872	+2.652	+3.376
ATs	+0.361	+0.596	+1.283	+2.166	+3.121
A9s	+0.108	+0.258	+0.698	+1.626	+2.660
A8s	+0.018	+0.178	+0.447	+1.272	+2.404
A7s	−0.090	+0.083	+0.339	+0.968	+2.157
A6s	−0.170	−0.034	+0.245	+0.764	+1.914
A5s	−0.015	+0.050	+0.323	+0.818	+1.887
A4s	−0.058	+0.002	+0.227	+0.713	+1.763
A3s	−0.094	−0.035	+0.172	+0.619	+1.685
A2s	−0.146	−0.089	+0.120	+0.532	+1.602
KQs	+0.537	+0.701	+0.928	+1.297	+2.291
KJs	+0.432	+0.469	+0.582	+0.892	+2.053
KTs	+0.369	+0.425	+0.415	+0.604	+1.819
K9s	+0.081	+0.184	+0.156	+0.305	+1.369
K8s	−0.132	−0.011	−0.001	+0.104	+1.031
K7s	−0.208	−0.076	−0.025	+0.054	+0.864
K6s	−0.259	−0.162	−0.081	+0.047	+0.760
K5s	−0.268	−0.241	−0.167	−0.024	+0.676
K4s	−0.320	−0.298	−0.273	−0.128	+0.591
K3s	−0.359	−0.338	−0.331	−0.222	+0.511
K2s	−0.410	−0.390	−0.383	−0.310	+0.427
QJs	+0.338	+0.422	+0.511	+0.654	+1.404
QTs	+0.283	+0.392	+0.431	+0.593	+1.195
Q9s	0.000	+0.150	+0.170	+0.330	+0.814
Q8s	−0.215	−0.052	0.000	+0.116	+0.581
Q7s	−0.450	−0.275	−0.186	−0.100	+0.379
Q6s	−0.472	−0.335	−0.217	−0.078	+0.383
Q5s	−0.486	−0.415	−0.302	−0.150	+0.316
Q4s	−0.529	−0.466	−0.404	−0.254	+0.239
Q3s	−0.577	−0.513	−0.467	−0.351	+0.152
Q2s	−0.621	−0.557	−0.511	−0.431	+0.073
JTs	+0.293	+0.378	+0.462	+0.630	+1.037
J9s	+0.005	+0.131	+0.198	+0.373	+0.712
J8s	−0.220	−0.067	+0.032	+0.157	+0.502
J7s	−0.462	−0.306	−0.170	−0.064	+0.315
J6s	−0.636	−0.524	−0.368	−0.211	+0.163
J5s	−0.613	−0.574	−0.424	−0.254	+0.125
J4s	−0.653	−0.617	−0.515	−0.354	+0.049
J3s	−0.703	−0.669	−0.580	−0.443	−0.031
J2s	−0.749	−0.716	−0.632	−0.533	−0.121
T9s	+0.053	+0.199	+0.241	+0.456	+0.761
T8s	−0.191	−0.017	+0.073	+0.244	+0.576
T7s	−0.425	−0.251	−0.129	+0.018	+0.386
T6s	−0.607	−0.475	−0.333	−0.135	+0.227
T5s	−0.751	−0.689	−0.566	−0.360	+0.023
T4s	−0.763	−0.708	−0.632	−0.424	−0.021
T3s	−0.810	−0.753	−0.692	−0.519	−0.105
T2s	−0.867	−0.808	−0.748	−0.611	−0.192
98s	−0.218	0.000	+0.094	+0.288	+0.630
97s	−0.426	−0.206	−0.086	+0.082	+0.461
96s	−0.596	−0.425	−0.287	−0.074	+0.298
95s	−0.740	−0.645	−0.521	−0.301	+0.083
94s	−0.920	−0.832	−0.760	−0.548	−0.132
93s	−0.929	−0.838	−0.784	−0.599	−0.180
92s	−0.973	−0.884	−0.831	−0.684	−0.265
87s	−0.411	−0.169	−0.012	+0.155	+0.547
86s	−0.580	−0.382	−0.204	+0.002	+0.389
85s	−0.713	−0.594	−0.434	−0.217	+0.180
84s	−0.897	−0.784	−0.681	−0.466	−0.040
83s	−1.087	−0.973	−0.890	−0.709	−0.268
82s	−1.093	−0.979	−0.896	−0.756	−0.318
76s	−0.566	−0.344	−0.135	+0.062	+0.467
75s	−0.694	−0.558	−0.361	−0.152	+0.266
74s	−0.880	−0.746	−0.611	−0.410	+0.041
73s	−1.070	−0.937	−0.820	−0.654	−0.185
72s	−1.255	−1.118	−1.008	−0.886	−0.419
65s	−0.618	−0.502	−0.275	−0.029	+0.371
64s	−0.784	−0.674	−0.511	−0.273	+0.160
63s	−0.989	−0.876	−0.730	−0.530	−0.073
62s	−1.184	−1.068	−0.924	−0.767	−0.307
54s	−0.606	−0.612	−0.427	−0.171	+0.267
53s	−0.800	−0.797	−0.629	−0.409	+0.045
52s	−0.992	−0.985	−0.822	−0.650	−0.190
43s	−0.848	−0.857	−0.769	−0.528	−0.049
42s	−1.035	−1.038	−0.953	−0.764	−0.281
32s	−1.095	−1.097	−1.035	−0.877	−0.377
AKo	+2.211	+2.492	+2.926	+3.352	+3.780
AQo	+1.140	+1.642	+2.257	+2.841	+3.411
AJo	+0.309	+0.762	+1.539	+2.363	+3.128
ATo	−0.056	+0.186	+0.906	+1.838	+2.854
A9o	−0.321	−0.176	+0.281	+1.260	+2.360
A8o	−0.431	−0.274	+0.001	+0.877	+2.076
A7o	−0.552	−0.381	−0.126	+0.543	+1.809
A6o	−0.640	−0.502	−0.221	+0.326	+1.548
A5o	−0.462	−0.405	−0.130	+0.385	+1.521
A4o	−0.507	−0.457	−0.239	+0.271	+1.384
A3o	−0.555	−0.505	−0.301	+0.170	+1.298
A2o	−0.609	−0.561	−0.354	+0.074	+1.213
KQo	+0.121	+0.283	+0.508	+0.889	+1.963
KJo	−0.001	+0.027	+0.127	+0.451	+1.702
KTo	−0.074	−0.024	−0.047	+0.145	+1.456
K9o	−0.378	−0.282	−0.322	−0.175	+0.964
K8o	−0.602	−0.492	−0.499	−0.395	+0.608
K7o	−0.686	−0.557	−0.518	−0.443	+0.429
K6o	−0.744	−0.650	−0.581	−0.456	+0.311
K5o	−0.761	−0.745	−0.678	−0.542	+0.218
K4o	−0.803	−0.795	−0.787	−0.645	+0.127
K3o	−0.853	−0.847	−0.860	−0.751	+0.037
K2o	−0.903	−0.897	−0.907	−0.839	−0.044
QJo	−0.085	−0.004	+0.069	+0.212	+1.014
QTo	−0.154	−0.055	−0.024	+0.130	+0.780
Q9o	−0.468	−0.322	−0.312	−0.157	+0.370
Q8o	−0.693	−0.534	−0.496	−0.383	+0.119
Q7o	−0.945	−0.770	−0.694	−0.618	−0.107
Q6o	−0.964	−0.824	−0.718	−0.589	−0.097
Q5o	−0.980	−0.920	−0.816	−0.669	−0.172
Q4o	−1.029	−0.976	−0.925	−0.778	−0.254
Q3o	−1.077	−1.026	−0.994	−0.881	−0.344
Q2o	−1.129	−1.078	−1.045	−0.972	−0.434
JTo	−0.148	−0.062	+0.012	+0.175	+0.620
J9o	−0.458	−0.333	−0.281	−0.108	+0.264
J8o	−0.692	−0.539	−0.461	−0.330	+0.040
J7o	−0.944	−0.784	−0.665	−0.565	−0.162
J6o	−1.141	−1.023	−0.882	−0.734	−0.327
J5o	−1.118	−1.080	−0.939	−0.775	−0.365
J4o	−1.165	−1.135	−1.047	−0.881	−0.444
J3o	−1.218	−1.187	−1.118	−0.984	−0.540
J2o	−1.273	−1.241	−1.175	−1.083	−0.636
T9o	−0.413	−0.270	−0.233	−0.020	+0.317
T8o	−0.658	−0.486	−0.403	−0.231	+0.126
T7o	−0.913	−0.731	−0.618	−0.475	−0.078
T6o	−1.112	−0.975	−0.843	−0.652	−0.251
T5o	−1.261	−1.209	−1.089	−0.893	−0.474
T4o	−1.272	−1.227	−1.160	−0.957	−0.522
T3o	−1.323	−1.275	−1.226	−1.059	−0.612
T2o	−1.377	−1.329	−1.281	−1.152	−0.705
98o	−0.684	−0.470	−0.386	−0.188	+0.174
97o	−0.904	−0.688	−0.576	−0.413	−0.010
96o	−1.089	−0.914	−0.787	−0.576	−0.181
95o	−1.248	−1.156	−1.040	−0.825	−0.412
94o	−1.441	−1.360	−1.303	−1.089	−0.646
93o	−1.442	−1.361	−1.325	−1.145	−0.697
92o	−1.499	−1.417	−1.377	−1.238	−0.791
87o	−0.893	−0.650	−0.509	−0.342	+0.079
86o	−1.075	−0.873	−0.708	−0.499	−0.086
85o	−1.221	−1.109	−0.954	−0.732	−0.309
84o	−1.416	−1.310	−1.220	−0.999	−0.545
83o	−1.622	−1.512	−1.447	−1.264	−0.790
82o	−1.628	−1.521	−1.453	−1.315	−0.843
76o	−1.060	−0.831	−0.629	−0.437	−0.004
75o	−1.202	−1.071	−0.880	−0.676	−0.219
74o	−1.395	−1.269	−1.144	−0.936	−0.455
73o	−1.599	−1.470	−1.371	−1.205	−0.703
72o	−1.805	−1.672	−1.574	−1.456	−0.951
65o	−1.122	−1.002	−0.782	−0.539	−0.110
64o	−1.305	−1.192	−1.040	−0.801	−0.335
63o	−1.507	−1.393	−1.264	−1.065	−0.582
62o	−1.722	−1.604	−1.477	−1.326	−0.833
54o	−1.112	−1.125	−0.942	−0.682	−0.214
53o	−1.302	−1.311	−1.155	−0.940	−0.457
52o	−1.516	−1.519	−1.363	−1.198	−0.705
43o	−1.355	−1.374	−1.301	−1.063	−0.553
42o	−1.564	−1.576	−1.507	−1.320	−0.800
32o	−1.620	−1.632	−1.586	−1.434	−0.902

Reading the chart is the easy half. The trainer deals you real hands at 21 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 6-max at 21 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 0.028 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: 6max.json (summary) and one file per depth, e.g. 6max/10.json.