6-max push/fold at 22 bb

At 22 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 12.9% of hands from UTG, widening to 52.8% 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 12.9% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJo45%QJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

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

HJ

shoves 16.1% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3366%32sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

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

CO

shoves 21.4% first in

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

BTN

shoves 31.1% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7s66%T6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K6s+, Q8s+, J8s+, T7s+, 97s+, 87s, 76s, A3o+, KTo+, QTo+, JTo

SB

shoves 52.8% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o20%6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K2s+, Q2s+, J4s+, T5s+, 95s+, 85s+, 74s+, 64s+, 53s+, A2o+, K4o+, 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 18.1% against a BTN shove of 31.1%

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	100%	+0.061
A2s	0%	−0.183
33	100%	+0.291
KJo	100%	+0.305
A4s	100%	+0.332
QJs	100%	+0.333
A7o	100%	+0.420
QTs	0%	−0.423
A6o	0%	−0.450
22	0%	−0.488

33+, A3s+, KTs+, QJs, A7o+, KJo+

Every calling range at 22 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	6.3%	77+, AJs+, AQo+
BB vs UTG	7.7%	77+, ATs+, KQs, AJo+
CO vs HJ	8.2%	66+, ATs+, KQs, AJo+
BTN vs HJ	8.2%	66+, ATs+, KQs, AJo+
SB vs HJ	8.3%	66+, ATs+, KQs, AJo+
BB vs HJ	8.3%	66+, ATs+, KQs, AJo+
BTN vs CO	10.0%	55+, A9s+, KQs, ATo+
SB vs CO	11.5%	55+, A8s+, KJs+, ATo+, KQo
BB vs CO	12.3%	44+, A8s+, KJs+, ATo+, KQo
SB vs BTN	16.4%	44+, A4s+, KTs+, QJs, A7o+, KQo
BB vs BTN	18.1%	33+, A3s+, KTs+, QJs, A7o+, KJo+
BB vs SB	31.5%	22+, A2s+, K5s+, Q8s+, J9s+, A2o+, K8o+, QTo+, JTo

All 169 hands at 22 bb: shove EV by seat

Hand	UTG	HJ	CO	BTN	SB
AA	+5.609	+5.768	+5.922	+6.000	+6.090
KK	+4.550	+4.828	+4.999	+5.127	+5.337
QQ	+3.523	+3.977	+4.261	+4.556	+4.840
JJ	+2.671	+3.148	+3.576	+4.011	+4.396
TT	+2.000	+2.517	+2.964	+3.544	+3.975
99	+1.263	+1.885	+2.350	+3.012	+3.504
88	+0.644	+1.393	+1.908	+2.578	+3.133
77	+0.191	+0.866	+1.490	+2.139	+2.824
66	+0.062	+0.379	+1.091	+1.779	+2.546
55	+0.056	+0.136	+0.694	+1.453	+2.282
44	0.000	+0.075	+0.380	+1.078	+1.972
33	−0.078	−0.001	+0.251	+0.784	+1.664
22	−0.153	−0.074	+0.173	+0.623	+1.357
AKs	+2.431	+2.714	+3.080	+3.566	+3.976
AQs	+1.369	+1.872	+2.428	+3.085	+3.642
AJs	+0.633	+1.027	+1.726	+2.595	+3.366
ATs	+0.343	+0.521	+1.124	+2.122	+3.097
A9s	+0.091	+0.233	+0.606	+1.565	+2.634
A8s	−0.004	+0.157	+0.441	+1.196	+2.364
A7s	−0.104	+0.057	+0.340	+0.879	+2.084
A6s	−0.159	−0.062	+0.242	+0.670	+1.866
A5s	−0.006	+0.027	+0.315	+0.725	+1.837
A4s	−0.049	−0.014	+0.215	+0.618	+1.708
A3s	−0.085	−0.052	+0.159	+0.530	+1.629
A2s	−0.136	−0.106	+0.107	+0.464	+1.543
KQs	+0.508	+0.685	+0.906	+1.201	+2.217
KJs	+0.433	+0.450	+0.564	+0.851	+1.968
KTs	+0.352	+0.429	+0.411	+0.619	+1.726
K9s	+0.057	+0.173	+0.200	+0.308	+1.274
K8s	−0.160	−0.029	+0.023	+0.100	+0.931
K7s	−0.228	−0.097	−0.013	+0.046	+0.804
K6s	−0.255	−0.186	−0.074	+0.040	+0.736
K5s	−0.266	−0.262	−0.164	−0.033	+0.647
K4s	−0.318	−0.312	−0.273	−0.139	+0.558
K3s	−0.356	−0.353	−0.332	−0.225	+0.475
K2s	−0.407	−0.405	−0.384	−0.290	+0.389
QJs	+0.324	+0.396	+0.507	+0.674	+1.377
QTs	+0.250	+0.388	+0.416	+0.585	+1.158
Q9s	−0.040	+0.132	+0.203	+0.319	+0.780
Q8s	−0.257	−0.076	+0.012	+0.100	+0.542
Q7s	−0.482	−0.305	−0.181	−0.121	+0.371
Q6s	−0.481	−0.367	−0.219	−0.098	+0.356
Q5s	−0.496	−0.444	−0.309	−0.172	+0.284
Q4s	−0.538	−0.488	−0.413	−0.278	+0.203
Q3s	−0.587	−0.536	−0.477	−0.367	+0.114
Q2s	−0.631	−0.580	−0.522	−0.424	+0.032
JTs	+0.275	+0.366	+0.447	+0.642	+1.014
J9s	−0.019	+0.104	+0.228	+0.377	+0.701
J8s	−0.252	−0.100	+0.041	+0.158	+0.487
J7s	−0.483	−0.345	−0.170	−0.072	+0.327
J6s	−0.635	−0.564	−0.374	−0.220	+0.154
J5s	−0.611	−0.611	−0.433	−0.265	+0.113
J4s	−0.651	−0.647	−0.527	−0.364	+0.033
J3s	−0.701	−0.699	−0.595	−0.445	−0.050
J2s	−0.747	−0.747	−0.645	−0.513	−0.141
T9s	+0.016	+0.186	+0.263	+0.447	+0.751
T8s	−0.234	−0.040	+0.073	+0.230	+0.561
T7s	−0.457	−0.279	−0.137	0.000	+0.399
T6s	−0.614	−0.507	−0.346	−0.152	+0.220
T5s	−0.760	−0.718	−0.580	−0.380	+0.010
T4s	−0.771	−0.729	−0.651	−0.446	−0.038
T3s	−0.819	−0.775	−0.712	−0.532	−0.125
T2s	−0.876	−0.831	−0.768	−0.601	−0.213
98s	−0.270	−0.031	+0.120	+0.267	+0.616
97s	−0.466	−0.241	−0.068	+0.056	+0.472
96s	−0.609	−0.462	−0.272	−0.099	+0.289
95s	−0.754	−0.678	−0.508	−0.328	+0.070
94s	−0.936	−0.860	−0.750	−0.577	−0.152
93s	−0.945	−0.866	−0.773	−0.620	−0.201
92s	−0.988	−0.913	−0.820	−0.683	−0.288
87s	−0.458	−0.208	−0.008	+0.123	+0.558
86s	−0.599	−0.423	−0.202	−0.027	+0.380
85s	−0.732	−0.632	−0.434	−0.251	+0.165
84s	−0.917	−0.816	−0.682	−0.503	−0.059
83s	−1.108	−1.006	−0.892	−0.737	−0.292
82s	−1.114	−1.012	−0.899	−0.761	−0.342
76s	−0.588	−0.389	−0.141	+0.029	+0.475
75s	−0.715	−0.599	−0.370	−0.190	+0.269
74s	−0.902	−0.781	−0.621	−0.450	+0.039
73s	−1.092	−0.974	−0.831	−0.687	−0.192
72s	−1.280	−1.157	−1.016	−0.896	−0.429
65s	−0.597	−0.545	−0.290	−0.066	+0.367
64s	−0.765	−0.711	−0.528	−0.311	+0.152
63s	−0.972	−0.916	−0.748	−0.562	−0.086
62s	−1.169	−1.109	−0.940	−0.774	−0.324
54s	−0.587	−0.644	−0.447	−0.211	+0.255
53s	−0.785	−0.831	−0.652	−0.444	+0.030
52s	−0.978	−1.022	−0.843	−0.660	−0.210
43s	−0.833	−0.880	−0.795	−0.566	−0.067
42s	−1.023	−1.064	−0.978	−0.775	−0.303
32s	−1.082	−1.123	−1.062	−0.891	−0.402
AKo	+2.166	+2.454	+2.836	+3.344	+3.780
AQo	+1.039	+1.563	+2.145	+2.833	+3.416
AJo	+0.235	+0.648	+1.384	+2.302	+3.115
ATo	−0.075	+0.102	+0.738	+1.791	+2.826
A9o	−0.338	−0.207	+0.182	+1.196	+2.329
A8o	−0.454	−0.299	−0.005	+0.797	+2.032
A7o	−0.568	−0.411	−0.123	+0.449	+1.726
A6o	−0.627	−0.535	−0.224	+0.226	+1.495
A5o	−0.451	−0.433	−0.137	+0.287	+1.465
A4o	−0.497	−0.477	−0.248	+0.171	+1.324
A3o	−0.545	−0.526	−0.313	+0.075	+1.235
A2o	−0.597	−0.582	−0.367	−0.001	+1.147
KQo	+0.092	+0.264	+0.489	+0.784	+1.880
KJo	0.000	+0.006	+0.112	+0.402	+1.605
KTo	−0.090	−0.024	−0.047	+0.158	+1.350
K9o	−0.402	−0.296	−0.277	−0.173	+0.857
K8o	−0.629	−0.511	−0.471	−0.401	+0.495
K7o	−0.707	−0.581	−0.501	−0.454	+0.358
K6o	−0.738	−0.678	−0.569	−0.466	+0.280
K5o	−0.757	−0.770	−0.672	−0.553	+0.181
K4o	−0.799	−0.811	−0.783	−0.659	+0.086
K3o	−0.849	−0.864	−0.857	−0.759	−0.007
K2o	−0.897	−0.915	−0.904	−0.820	−0.090
QJo	−0.099	−0.033	+0.069	+0.230	+0.983
QTo	−0.186	−0.063	−0.035	+0.125	+0.738
Q9o	−0.507	−0.344	−0.280	−0.168	+0.331
Q8o	−0.735	−0.561	−0.480	−0.400	+0.076
Q7o	−0.978	−0.803	−0.685	−0.639	−0.122
Q6o	−0.972	−0.860	−0.717	−0.610	−0.128
Q5o	−0.989	−0.952	−0.819	−0.692	−0.207
Q4o	−1.038	−1.001	−0.931	−0.802	−0.293
Q3o	−1.085	−1.051	−1.003	−0.898	−0.387
Q2o	−1.137	−1.104	−1.054	−0.965	−0.479
JTo	−0.168	−0.078	−0.001	+0.186	+0.590
J9o	−0.484	−0.362	−0.250	−0.106	+0.249
J8o	−0.726	−0.574	−0.445	−0.332	+0.021
J7o	−0.970	−0.825	−0.661	−0.575	−0.156
J6o	−1.140	−1.068	−0.883	−0.745	−0.340
J5o	−1.116	−1.122	−0.945	−0.788	−0.382
J4o	−1.164	−1.169	−1.057	−0.895	−0.464
J3o	−1.216	−1.222	−1.129	−0.991	−0.562
J2o	−1.272	−1.277	−1.185	−1.065	−0.663
T9o	−0.451	−0.288	−0.213	−0.028	+0.302
T8o	−0.700	−0.515	−0.400	−0.246	+0.109
T7o	−0.947	−0.765	−0.624	−0.494	−0.070
T6o	−1.117	−1.013	−0.852	−0.670	−0.262
T5o	−1.267	−1.244	−1.101	−0.915	−0.492
T4o	−1.279	−1.254	−1.176	−0.980	−0.543
T3o	−1.330	−1.302	−1.245	−1.073	−0.636
T2o	−1.384	−1.357	−1.300	−1.142	−0.730
98o	−0.735	−0.505	−0.359	−0.210	+0.157
97o	−0.946	−0.727	−0.556	−0.438	−0.004
96o	−1.102	−0.955	−0.771	−0.601	−0.192
95o	−1.262	−1.195	−1.026	−0.854	−0.429
94o	−1.456	−1.391	−1.292	−1.121	−0.668
93o	−1.457	−1.392	−1.314	−1.169	−0.721
92o	−1.513	−1.450	−1.367	−1.236	−0.817
87o	−0.942	−0.692	−0.503	−0.375	+0.084
86o	−1.092	−0.919	−0.704	−0.531	−0.097
85o	−1.239	−1.152	−0.951	−0.768	−0.328
84o	−1.436	−1.345	−1.220	−1.037	−0.568
83o	−1.644	−1.550	−1.446	−1.295	−0.817
82o	−1.648	−1.559	−1.452	−1.320	−0.872
76o	−1.083	−0.881	−0.633	−0.472	−0.001
75o	−1.224	−1.117	−0.887	−0.715	−0.223
74o	−1.418	−1.308	−1.152	−0.978	−0.462
73o	−1.624	−1.511	−1.380	−1.241	−0.715
72o	−1.831	−1.716	−1.581	−1.466	−0.968
65o	−1.099	−1.051	−0.794	−0.578	−0.118
64o	−1.285	−1.234	−1.054	−0.841	−0.347
63o	−1.489	−1.436	−1.279	−1.100	−0.598
62o	−1.706	−1.651	−1.492	−1.335	−0.853
54o	−1.093	−1.162	−0.961	−0.726	−0.229
53o	−1.286	−1.350	−1.175	−0.978	−0.476
52o	−1.502	−1.561	−1.383	−1.208	−0.727
43o	−1.340	−1.401	−1.324	−1.104	−0.575
42o	−1.550	−1.606	−1.530	−1.333	−0.826
32o	−1.606	−1.662	−1.613	−1.450	−0.929

Reading the chart is the easy half. The trainer deals you real hands at 22 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 6-max at 22 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 0.025 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.