6-max push/fold at 25 bb

At 25 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 11.2% of hands from UTG, widening to 48.3% 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 11.2% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7773%76s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5571%54s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

55+, A9s+, KTs+, QTs+, JTs, AJo+, KQo

HJ

shoves 14.0% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJo56%QJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

44+, A8s+, K9s+, Q9s+, J9s+, T9s, AJo+, KJo+

CO

shoves 19.0% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8s37%K7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A4s+, K9s+, Q9s+, J9s+, T8s+, 98s, ATo+, KJo+, QJo

BTN

shoves 29.6% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6s27%K5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7s23%T6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K7s+, Q8s+, J8s+, T8s+, 97s+, 87s, A4o+, KTo+, QTo+, JTo

SB

shoves 48.3% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8o24%T8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K2s+, Q4s+, J5s+, T6s+, 95s+, 85s+, 75s+, 64s+, 54s, A2o+, K5o+, Q9o+, J9o+, 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 15.5% against a BTN shove of 29.6%

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJs74%QTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJo33%QJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

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)
QJs	74%	0.000
KJo	33%	−0.003
33	0%	−0.094
A4s	0%	−0.109
A7o	0%	−0.142
A5s	100%	+0.311
A3s	0%	−0.357
A6s	100%	+0.376
KTs	100%	+0.437
A2s	0%	−0.635

44+, A5s+, KTs+, QJs, A8o+, KQo

Every calling range at 25 bb

Spot	Calls	Range
HJ vs UTG	5.4%	88+, AQs+, AQo+
CO vs UTG	5.4%	88+, AQs+, AQo+
BTN vs UTG	5.4%	88+, AQs+, AQo+
SB vs UTG	5.6%	88+, AQs+, AQo+
BB vs UTG	5.9%	88+, AJs+, AQo+
CO vs HJ	6.5%	77+, AJs+, AQo+
BTN vs HJ	6.5%	77+, AJs+, AQo+
SB vs HJ	7.7%	77+, ATs+, AJo+
BB vs HJ	7.8%	77+, ATs+, KQs, AJo+
BTN vs CO	9.2%	66+, ATs+, KQs, ATo+
SB vs CO	10.0%	55+, A9s+, KQs, ATo+
BB vs CO	10.6%	55+, A9s+, KQs, ATo+, KQo
SB vs BTN	14.6%	44+, A6s+, KTs+, A8o+, KQo
BB vs BTN	15.5%	44+, A5s+, KTs+, QJs, A8o+, KQo
BB vs SB	28.5%	33+, A2s+, K7s+, Q9s+, JTs, A2o+, K9o+, QTo+

All 169 hands at 25 bb: shove EV by seat

Hand	UTG	HJ	CO	BTN	SB
AA	+5.654	+5.742	+5.929	+6.048	+6.145
KK	+4.504	+4.747	+5.029	+5.162	+5.400
QQ	+3.334	+3.798	+4.256	+4.531	+4.863
JJ	+2.468	+2.936	+3.525	+3.959	+4.431
TT	+1.758	+2.276	+2.840	+3.447	+3.985
99	+0.938	+1.578	+2.185	+2.855	+3.490
88	+0.307	+1.009	+1.733	+2.363	+3.146
77	−0.001	+0.408	+1.271	+1.957	+2.833
66	+0.007	+0.110	+0.822	+1.592	+2.542
55	−0.001	+0.104	+0.455	+1.241	+2.268
44	−0.056	+0.043	+0.243	+0.856	+1.936
33	−0.136	−0.035	+0.170	+0.622	+1.599
22	−0.215	−0.112	+0.091	+0.534	+1.310
AKs	+2.320	+2.607	+3.010	+3.495	+4.041
AQs	+1.111	+1.634	+2.281	+2.958	+3.693
AJs	+0.445	+0.821	+1.513	+2.395	+3.370
ATs	+0.290	+0.412	+0.848	+1.902	+3.070
A9s	+0.036	+0.145	+0.334	+1.303	+2.581
A8s	−0.064	+0.058	+0.232	+0.908	+2.253
A7s	−0.146	−0.057	+0.148	+0.671	+1.990
A6s	−0.159	−0.160	+0.039	+0.535	+1.740
A5s	−0.008	−0.001	+0.120	+0.598	+1.706
A4s	−0.052	−0.043	+0.036	+0.497	+1.574
A3s	−0.090	−0.081	−0.002	+0.415	+1.489
A2s	−0.140	−0.134	−0.058	+0.368	+1.398
KQs	+0.428	+0.595	+0.773	+1.149	+2.040
KJs	+0.431	+0.444	+0.517	+0.792	+1.757
KTs	+0.301	+0.399	+0.383	+0.581	+1.493
K9s	−0.016	+0.115	+0.184	+0.255	+1.019
K8s	−0.237	−0.098	0.000	+0.037	+0.715
K7s	−0.286	−0.181	−0.055	+0.053	+0.647
K6s	−0.272	−0.253	−0.125	0.000	+0.591
K5s	−0.285	−0.263	−0.216	−0.069	+0.510
K4s	−0.340	−0.314	−0.307	−0.174	+0.417
K3s	−0.378	−0.355	−0.349	−0.262	+0.324
K2s	−0.428	−0.408	−0.404	−0.310	+0.236
QJs	+0.287	+0.362	+0.488	+0.640	+1.251
QTs	+0.164	+0.327	+0.371	+0.548	+1.007
Q9s	−0.147	+0.047	+0.175	+0.276	+0.620
Q8s	−0.367	−0.169	−0.020	+0.046	+0.436
Q7s	−0.573	−0.417	−0.239	−0.106	+0.254
Q6s	−0.530	−0.459	−0.286	−0.131	+0.246
Q5s	−0.549	−0.472	−0.375	−0.200	+0.167
Q4s	−0.593	−0.516	−0.462	−0.304	+0.073
Q3s	−0.641	−0.565	−0.510	−0.394	−0.023
Q2s	−0.687	−0.610	−0.556	−0.437	−0.110
JTs	+0.222	+0.319	+0.385	+0.609	+0.915
J9s	−0.089	+0.033	+0.182	+0.333	+0.648
J8s	−0.338	−0.188	−0.008	+0.107	+0.483
J7s	−0.551	−0.444	−0.245	−0.060	+0.287
J6s	−0.665	−0.643	−0.459	−0.258	+0.112
J5s	−0.639	−0.620	−0.518	−0.295	+0.065
J4s	−0.681	−0.660	−0.594	−0.392	−0.027
J3s	−0.730	−0.713	−0.649	−0.477	−0.117
J2s	−0.777	−0.760	−0.699	−0.529	−0.211
T9s	−0.084	+0.096	+0.200	+0.391	+0.721
T8s	−0.345	−0.145	+0.004	+0.165	+0.560
T7s	−0.545	−0.395	−0.228	0.000	+0.362
T6s	−0.663	−0.602	−0.449	−0.203	+0.186
T5s	−0.813	−0.749	−0.682	−0.423	−0.038
T4s	−0.826	−0.761	−0.737	−0.489	−0.097
T3s	−0.875	−0.808	−0.782	−0.574	−0.192
T2s	−0.931	−0.868	−0.840	−0.630	−0.284
98s	−0.405	−0.162	+0.058	+0.190	+0.612
97s	−0.576	−0.383	−0.150	+0.042	+0.434
96s	−0.675	−0.582	−0.367	−0.159	+0.251
95s	−0.823	−0.729	−0.605	−0.382	+0.020
94s	−1.010	−0.914	−0.833	−0.630	−0.219
93s	−1.021	−0.921	−0.839	−0.676	−0.272
92s	−1.063	−0.968	−0.888	−0.723	−0.363
87s	−0.584	−0.360	−0.092	+0.094	+0.548
86s	−0.676	−0.559	−0.303	−0.101	+0.369
85s	−0.812	−0.695	−0.534	−0.320	+0.143
84s	−1.002	−0.882	−0.768	−0.573	−0.096
83s	−1.199	−1.076	−0.965	−0.809	−0.342
82s	−1.205	−1.082	−0.972	−0.815	−0.393
76s	−0.652	−0.539	−0.251	−0.002	+0.450
75s	−0.783	−0.670	−0.481	−0.217	+0.235
74s	−0.977	−0.861	−0.716	−0.475	−0.012
73s	−1.171	−1.056	−0.912	−0.716	−0.254
72s	−1.365	−1.245	−1.102	−0.910	−0.496
65s	−0.594	−0.630	−0.410	−0.120	+0.338
64s	−0.770	−0.799	−0.629	−0.363	+0.107
63s	−0.985	−1.007	−0.835	−0.616	−0.146
62s	−1.187	−1.205	−1.034	−0.813	−0.390
54s	−0.592	−0.615	−0.554	−0.261	+0.208
53s	−0.799	−0.811	−0.744	−0.498	−0.029
52s	−0.999	−1.007	−0.940	−0.698	−0.276
43s	−0.849	−0.860	−0.864	−0.625	−0.133
42s	−1.046	−1.050	−1.053	−0.814	−0.378
32s	−1.103	−1.112	−1.111	−0.941	−0.486
AKo	+2.046	+2.340	+2.755	+3.265	+3.840
AQo	+0.762	+1.311	+1.986	+2.694	+3.468
AJo	+0.025	+0.429	+1.153	+2.083	+3.113
ATo	−0.134	−0.013	+0.443	+1.556	+2.791
A9o	−0.397	−0.295	−0.111	+0.914	+2.267
A8o	−0.523	−0.401	−0.233	+0.487	+1.905
A7o	−0.621	−0.527	−0.330	+0.219	+1.620
A6o	−0.630	−0.642	−0.442	+0.079	+1.354
A5o	−0.457	−0.458	−0.348	+0.150	+1.319
A4o	−0.504	−0.504	−0.441	+0.037	+1.177
A3o	−0.551	−0.554	−0.487	−0.056	+1.082
A2o	−0.602	−0.609	−0.545	−0.106	+0.988
KQo	+0.005	+0.170	+0.337	+0.727	+1.676
KJo	−0.009	+0.001	+0.050	+0.334	+1.362
KTo	−0.147	−0.057	−0.083	+0.116	+1.088
K9o	−0.481	−0.356	−0.303	−0.230	+0.569
K8o	−0.711	−0.582	−0.506	−0.467	+0.247
K7o	−0.778	−0.669	−0.555	−0.453	+0.178
K6o	−0.760	−0.753	−0.634	−0.511	+0.110
K5o	−0.785	−0.769	−0.738	−0.592	+0.016
K4o	−0.827	−0.812	−0.830	−0.697	−0.080
K3o	−0.875	−0.864	−0.885	−0.801	−0.181
K2o	−0.924	−0.915	−0.934	−0.845	−0.269
QJo	−0.142	−0.070	+0.042	+0.191	+0.835
QTo	−0.279	−0.123	−0.091	+0.087	+0.565
Q9o	−0.622	−0.433	−0.321	−0.217	+0.147
Q8o	−0.855	−0.658	−0.525	−0.457	−0.055
Q7o	−1.084	−0.921	−0.756	−0.629	−0.259
Q6o	−1.031	−0.964	−0.796	−0.646	−0.258
Q5o	−1.049	−0.980	−0.901	−0.723	−0.344
Q4o	−1.100	−1.029	−0.996	−0.830	−0.443
Q3o	−1.145	−1.079	−1.047	−0.930	−0.547
Q2o	−1.199	−1.134	−1.101	−0.979	−0.645
JTo	−0.230	−0.132	−0.071	+0.150	+0.469
J9o	−0.565	−0.441	−0.307	−0.154	+0.176
J8o	−0.826	−0.669	−0.504	−0.390	0.000
J7o	−1.053	−0.934	−0.746	−0.568	−0.212
J6o	−1.180	−1.160	−0.980	−0.786	−0.399
J5o	−1.153	−1.137	−1.043	−0.824	−0.447
J4o	−1.201	−1.186	−1.137	−0.929	−0.544
J3o	−1.255	−1.239	−1.191	−1.029	−0.650
J2o	−1.312	−1.296	−1.248	−1.087	−0.755
T9o	−0.564	−0.380	−0.288	−0.089	+0.255
T8o	−0.822	−0.625	−0.481	−0.316	+0.091
T7o	−1.053	−0.891	−0.725	−0.502	−0.123
T6o	−1.173	−1.121	−0.968	−0.725	−0.316
T5o	−1.326	−1.275	−1.218	−0.960	−0.561
T4o	−1.341	−1.286	−1.276	−1.026	−0.620
T3o	−1.393	−1.337	−1.326	−1.124	−0.722
T2o	−1.447	−1.393	−1.383	−1.176	−0.820
98o	−0.882	−0.639	−0.434	−0.292	+0.137
97o	−1.070	−0.872	−0.652	−0.459	−0.056
96o	−1.178	−1.088	−0.879	−0.667	−0.244
95o	−1.344	−1.250	−1.137	−0.913	−0.496
94o	−1.543	−1.448	−1.390	−1.178	−0.753
93o	−1.541	−1.450	−1.392	−1.231	−0.813
92o	−1.597	−1.508	−1.447	−1.281	−0.911
87o	−1.084	−0.852	−0.599	−0.412	+0.056
86o	−1.181	−1.067	−0.816	−0.608	−0.126
85o	−1.331	−1.216	−1.067	−0.842	−0.367
84o	−1.536	−1.415	−1.320	−1.113	−0.626
83o	−1.750	−1.625	−1.530	−1.375	−0.888
82o	−1.750	−1.633	−1.537	−1.382	−0.945
76o	−1.161	−1.044	−0.757	−0.510	−0.043
75o	−1.305	−1.192	−1.014	−0.749	−0.277
74o	−1.506	−1.388	−1.264	−1.013	−0.531
73o	−1.719	−1.597	−1.474	−1.281	−0.796
72o	−1.932	−1.807	−1.681	−1.489	−1.057
65o	−1.106	−1.148	−0.929	−0.638	−0.162
64o	−1.298	−1.334	−1.170	−0.899	−0.409
63o	−1.512	−1.540	−1.379	−1.162	−0.675
62o	−1.732	−1.759	−1.597	−1.379	−0.938
54o	−1.108	−1.135	−1.086	−0.780	−0.293
53o	−1.307	−1.328	−1.281	−1.038	−0.552
52o	−1.531	−1.547	−1.495	−1.248	−0.812
43o	−1.364	−1.382	−1.407	−1.167	−0.659
42o	−1.582	−1.595	−1.619	−1.377	−0.921
32o	−1.636	−1.653	−1.673	−1.506	−1.034

Reading the chart is the easy half. The trainer deals you real hands at 25 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 6-max at 25 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 0.046 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.