6-max push/fold at 14 bb

At 14 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 18.1% of hands from UTG, widening to 64.7% 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 18.1% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJo51%JJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A4s+, K9s+, Q9s+, J9s+, T9s, 98s, ATo+, KJo+, QJo

HJ

shoves 23.1% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJTo71%TTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K9s+, Q9s+, J8s+, T8s+, 98s, A7o+, KJo+, QJo, JTo

CO

shoves 29.7% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K8s+, Q8s+, J8s+, T8s+, 98s, 87s, A3o+, KTo+, QTo+, JTo

BTN

shoves 36.3% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K3s+, Q7s+, J7s+, T7s+, 96s+, 86s+, 76s, 65s, A2o+, K9o+, QTo+, JTo, T9o

SB

shoves 64.7% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K2s+, Q2s+, J2s+, T3s+, 95s+, 84s+, 74s+, 63s+, 53s+, 43s, A2o+, K2o+, Q4o+, J7o+, T7o+, 97o+, 86o+, 76o

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 28.6% against a BTN shove of 36.3%

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQTo73%JToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

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)
QTo	73%	0.000
K9o	100%	+0.044
K6s	0%	−0.091
J9s	0%	−0.111
K7s	100%	+0.113
Q9s	100%	+0.115
A2o	100%	+0.179
K8s	100%	+0.284
T9s	0%	−0.287
Q8s	0%	−0.305

22+, A2s+, K7s+, Q9s+, JTs, A2o+, K9o+, QTo+

Every calling range at 14 bb

Spot	Calls	Range
HJ vs UTG	10.0%	55+, A9s+, KQs, ATo+
CO vs UTG	10.0%	55+, A9s+, KQs, ATo+
BTN vs UTG	10.0%	55+, A9s+, KQs, ATo+
SB vs UTG	11.4%	55+, A8s+, KJs+, ATo+, KQo
BB vs UTG	13.2%	44+, A7s+, KJs+, A9o+, KQo
CO vs HJ	12.8%	44+, A8s+, KJs+, A9o+, KQo
BTN vs HJ	12.8%	44+, A8s+, KJs+, A9o+, KQo
SB vs HJ	13.2%	44+, A7s+, KJs+, A9o+, KQo
BB vs HJ	16.9%	33+, A4s+, KTs+, QJs, A8o+, KJo+
BTN vs CO	16.9%	33+, A4s+, KTs+, QJs, A7o+, KQo
SB vs CO	18.1%	33+, A3s+, KTs+, QJs, A7o+, KJo+
BB vs CO	22.2%	22+, A2s+, K9s+, QTs+, A5o+, KTo+
SB vs BTN	24.9%	22+, A2s+, K9s+, QTs+, JTs, A3o+, KTo+, QJo
BB vs BTN	28.6%	22+, A2s+, K7s+, Q9s+, JTs, A2o+, K9o+, QTo+
BB vs SB	45.3%	22+, A2s+, K2s+, Q4s+, J7s+, T8s+, 98s, A2o+, K2o+, Q7o+, J9o+, T9o

All 169 hands at 14 bb: shove EV by seat

Hand	UTG	HJ	CO	BTN	SB
AA	+5.657	+5.808	+5.883	+5.781	+5.808
KK	+4.714	+4.846	+4.934	+4.937	+5.087
QQ	+4.019	+4.190	+4.392	+4.432	+4.589
JJ	+3.354	+3.580	+3.883	+3.983	+4.219
TT	+2.748	+3.062	+3.426	+3.552	+3.879
99	+2.134	+2.468	+2.920	+3.093	+3.448
88	+1.708	+2.034	+2.521	+2.767	+3.091
77	+1.294	+1.666	+2.123	+2.467	+2.783
66	+0.895	+1.327	+1.780	+2.177	+2.514
55	+0.502	+0.991	+1.460	+1.901	+2.277
44	+0.221	+0.608	+1.104	+1.569	+1.997
33	+0.122	+0.356	+0.768	+1.240	+1.719
22	+0.048	+0.247	+0.526	+0.934	+1.444
AKs	+2.850	+3.125	+3.422	+3.609	+3.796
AQs	+2.197	+2.573	+2.961	+3.252	+3.514
AJs	+1.509	+1.984	+2.515	+2.935	+3.298
ATs	+0.909	+1.462	+2.085	+2.603	+3.128
A9s	+0.394	+0.874	+1.540	+2.115	+2.800
A8s	+0.239	+0.579	+1.189	+1.804	+2.584
A7s	+0.144	+0.445	+0.889	+1.545	+2.398
A6s	+0.040	+0.341	+0.671	+1.301	+2.208
A5s	+0.111	+0.414	+0.703	+1.271	+2.196
A4s	+0.015	+0.310	+0.592	+1.143	+2.099
A3s	−0.032	+0.227	+0.501	+1.057	+2.021
A2s	−0.083	+0.167	+0.415	+0.965	+1.945
KQs	+0.722	+0.944	+1.144	+1.576	+2.686
KJs	+0.457	+0.566	+0.809	+1.303	+2.482
KTs	+0.323	+0.380	+0.558	+1.015	+2.308
K9s	+0.114	+0.097	+0.222	+0.603	+1.986
K8s	−0.050	−0.044	+0.016	+0.360	+1.656
K7s	−0.095	−0.059	−0.032	+0.311	+1.488
K6s	−0.155	−0.106	−0.049	+0.260	+1.325
K5s	−0.246	−0.183	−0.124	+0.180	+1.203
K4s	−0.346	−0.296	−0.218	+0.087	+1.098
K3s	−0.395	−0.378	−0.308	+0.003	+1.017
K2s	−0.445	−0.437	−0.388	−0.074	+0.942
QJs	+0.420	+0.458	+0.577	+0.866	+1.742
QTs	+0.324	+0.387	+0.480	+0.669	+1.590
Q9s	+0.116	+0.113	+0.220	+0.371	+1.265
Q8s	−0.060	−0.041	+0.013	+0.193	+0.957
Q7s	−0.260	−0.213	−0.196	+0.015	+0.696
Q6s	−0.296	−0.233	−0.186	−0.002	+0.624
Q5s	−0.386	−0.310	−0.261	−0.079	+0.554
Q4s	−0.482	−0.421	−0.354	−0.173	+0.474
Q3s	−0.536	−0.506	−0.448	−0.261	+0.395
Q2s	−0.578	−0.558	−0.520	−0.335	+0.328
JTs	+0.345	+0.437	+0.531	+0.642	+1.276
J9s	+0.132	+0.162	+0.282	+0.398	+0.953
J8s	−0.039	+0.010	+0.074	+0.227	+0.693
J7s	−0.254	−0.177	−0.144	+0.038	+0.486
J6s	−0.450	−0.360	−0.300	−0.136	+0.329
J5s	−0.511	−0.407	−0.346	−0.184	+0.296
J4s	−0.595	−0.509	−0.434	−0.276	+0.219
J3s	−0.655	−0.593	−0.521	−0.359	+0.151
J2s	−0.702	−0.652	−0.602	−0.439	+0.075
T9s	+0.160	+0.217	+0.353	+0.474	+0.884
T8s	−0.015	+0.065	+0.148	+0.305	+0.661
T7s	−0.228	−0.123	−0.069	+0.116	+0.468
T6s	−0.430	−0.311	−0.229	−0.063	+0.316
T5s	−0.657	−0.531	−0.453	−0.281	+0.135
T4s	−0.720	−0.606	−0.507	−0.341	+0.091
T3s	−0.772	−0.686	−0.600	−0.428	+0.018
T2s	−0.825	−0.751	−0.681	−0.505	−0.058
98s	+0.027	+0.079	+0.191	+0.365	+0.669
97s	−0.164	−0.090	−0.009	+0.191	+0.506
96s	−0.361	−0.276	−0.172	+0.008	+0.356
95s	−0.591	−0.497	−0.399	−0.216	+0.170
94s	−0.816	−0.742	−0.632	−0.447	−0.029
93s	−0.832	−0.787	−0.680	−0.492	−0.071
92s	−0.878	−0.843	−0.756	−0.568	−0.145
87s	−0.103	−0.005	+0.064	+0.289	+0.574
86s	−0.293	−0.182	−0.095	+0.111	+0.431
85s	−0.518	−0.399	−0.315	−0.106	+0.246
84s	−0.751	−0.648	−0.550	−0.337	+0.040
83s	−0.943	−0.873	−0.787	−0.566	−0.164
82s	−0.950	−0.889	−0.826	−0.605	−0.205
76s	−0.241	−0.110	−0.036	+0.184	+0.504
75s	−0.464	−0.321	−0.249	−0.021	+0.327
74s	−0.698	−0.574	−0.493	−0.261	+0.115
73s	−0.891	−0.801	−0.731	−0.487	−0.088
72s	−1.068	−0.992	−0.951	−0.707	−0.296
65s	−0.391	−0.230	−0.135	+0.070	+0.416
64s	−0.613	−0.469	−0.365	−0.154	+0.217
63s	−0.814	−0.707	−0.614	−0.389	+0.008
62s	−0.999	−0.903	−0.839	−0.612	−0.200
54s	−0.539	−0.382	−0.271	−0.062	+0.319
53s	−0.727	−0.604	−0.503	−0.282	+0.123
52s	−0.909	−0.801	−0.730	−0.506	−0.086
43s	−0.862	−0.732	−0.614	−0.386	+0.038
42s	−1.036	−0.922	−0.836	−0.609	−0.169
32s	−1.106	−1.041	−0.945	−0.708	−0.252
AKo	+2.610	+2.896	+3.203	+3.409	+3.619
AQo	+1.919	+2.308	+2.711	+3.029	+3.309
AJo	+1.174	+1.671	+2.229	+2.684	+3.069
ATo	+0.532	+1.110	+1.765	+2.326	+2.884
A9o	−0.021	+0.483	+1.182	+1.801	+2.538
A8o	−0.196	+0.158	+0.802	+1.462	+2.297
A7o	−0.306	+0.003	+0.473	+1.179	+2.092
A6o	−0.414	−0.103	+0.241	+0.921	+1.891
A5o	−0.330	−0.020	+0.276	+0.890	+1.878
A4o	−0.436	−0.134	+0.156	+0.752	+1.772
A3o	−0.492	−0.228	+0.058	+0.657	+1.688
A2o	−0.544	−0.290	−0.035	+0.562	+1.607
KQo	+0.313	+0.543	+0.742	+1.215	+2.431
KJo	+0.021	+0.126	+0.376	+0.915	+2.201
KTo	−0.118	−0.067	+0.112	+0.613	+2.017
K9o	−0.344	−0.366	−0.247	+0.162	+1.670
K8o	−0.526	−0.525	−0.471	−0.096	+1.319
K7o	−0.565	−0.538	−0.519	−0.144	+1.136
K6o	−0.632	−0.591	−0.541	−0.204	+0.957
K5o	−0.734	−0.678	−0.630	−0.297	+0.823
K4o	−0.836	−0.791	−0.724	−0.393	+0.714
K3o	−0.898	−0.890	−0.827	−0.487	+0.623
K2o	−0.944	−0.946	−0.904	−0.561	+0.547
QJo	0.000	+0.030	+0.144	+0.461	+1.415
QTo	−0.111	−0.054	+0.032	+0.240	+1.244
Q9o	−0.349	−0.354	−0.256	−0.084	+0.897
Q8o	−0.533	−0.520	−0.474	−0.275	+0.563
Q7o	−0.744	−0.707	−0.703	−0.475	+0.279
Q6o	−0.775	−0.721	−0.684	−0.482	+0.205
Q5o	−0.878	−0.807	−0.768	−0.568	+0.127
Q4o	−0.980	−0.922	−0.866	−0.666	+0.041
Q3o	−1.040	−1.016	−0.965	−0.762	−0.041
Q2o	−1.089	−1.076	−1.048	−0.845	−0.117
JTo	−0.084	0.000	+0.086	+0.216	+0.912
J9o	−0.326	−0.301	−0.188	−0.052	+0.564
J8o	−0.505	−0.466	−0.402	−0.232	+0.287
J7o	−0.724	−0.657	−0.634	−0.436	+0.061
J6o	−0.938	−0.858	−0.809	−0.623	−0.111
J5o	−1.002	−0.906	−0.854	−0.673	−0.144
J4o	−1.103	−1.020	−0.949	−0.769	−0.224
J3o	−1.163	−1.114	−1.050	−0.867	−0.305
J2o	−1.217	−1.181	−1.138	−0.955	−0.388
T9o	−0.296	−0.240	−0.108	+0.029	+0.492
T8o	−0.469	−0.394	−0.314	−0.142	+0.256
T7o	−0.694	−0.597	−0.548	−0.347	+0.046
T6o	−0.915	−0.805	−0.729	−0.542	−0.117
T5o	−1.157	−1.037	−0.970	−0.779	−0.312
T4o	−1.223	−1.115	−1.027	−0.842	−0.361
T3o	−1.280	−1.204	−1.124	−0.934	−0.442
T2o	−1.333	−1.267	−1.206	−1.018	−0.522
98o	−0.432	−0.382	−0.273	−0.085	+0.263
97o	−0.631	−0.563	−0.491	−0.275	+0.085
96o	−0.839	−0.758	−0.659	−0.463	−0.073
95o	−1.086	−0.997	−0.908	−0.705	−0.274
94o	−1.335	−1.263	−1.160	−0.955	−0.490
93o	−1.348	−1.310	−1.213	−1.006	−0.534
92o	−1.400	−1.372	−1.294	−1.089	−0.615
87o	−0.575	−0.485	−0.420	−0.175	+0.151
86o	−0.772	−0.666	−0.582	−0.357	0.000
85o	−1.013	−0.896	−0.816	−0.589	−0.196
84o	−1.264	−1.163	−1.070	−0.840	−0.417
83o	−1.471	−1.411	−1.328	−1.086	−0.636
82o	−1.477	−1.428	−1.368	−1.128	−0.683
76o	−0.712	−0.586	−0.520	−0.283	+0.078
75o	−0.959	−0.821	−0.758	−0.507	−0.114
74o	−1.207	−1.083	−1.006	−0.752	−0.333
73o	−1.415	−1.333	−1.268	−1.002	−0.557
72o	−1.607	−1.539	−1.505	−1.239	−0.779
65o	−0.873	−0.718	−0.630	−0.404	−0.018
64o	−1.116	−0.976	−0.878	−0.645	−0.230
63o	−1.322	−1.222	−1.135	−0.894	−0.451
62o	−1.525	−1.438	−1.380	−1.133	−0.675
54o	−1.032	−0.874	−0.768	−0.537	−0.116
53o	−1.226	−1.112	−1.019	−0.780	−0.329
52o	−1.425	−1.323	−1.261	−1.015	−0.551
43o	−1.367	−1.243	−1.134	−0.887	−0.419
42o	−1.563	−1.454	−1.376	−1.124	−0.639
32o	−1.629	−1.573	−1.485	−1.229	−0.726

Reading the chart is the easy half. The trainer deals you real hands at 14 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 6-max at 14 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 0.009 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.