6-max push/fold at 16 bb

At 16 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 16.6% of hands from UTG, widening to 61.6% 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 16.6% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

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

HJ

shoves 20.8% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8s23%K7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K9s+, Q9s+, J8s+, T8s+, 98s, A9o+, KJo+, QJo

CO

shoves 28.2% first in

22+, A2s+, K9s+, Q9s+, J8s+, T8s+, 98s, 87s, A4o+, KTo+, QTo+, JTo

BTN

shoves 35.1% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4s50%K3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9o49%Q9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K5s+, Q7s+, J7s+, T7s+, 97s+, 86s+, 76s, 65s, A2o+, KTo+, QTo+, JTo, T9o

SB

shoves 61.6% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s70%62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K2s+, Q2s+, J2s+, T4s+, 95s+, 84s+, 74s+, 63s+, 53s+, 43s, A2o+, K2o+, Q5o+, J8o+, T7o+, 97o+, 87o, 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 24.7% against a BTN shove of 35.1%

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3o43%K3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

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)
A3o	43%	+0.002
K8s	0%	−0.006
Q9s	0%	−0.133
K7s	0%	−0.200
A2o	0%	−0.208
A4o	100%	+0.219
JTs	100%	+0.238
QJo	100%	+0.239
QTo	0%	−0.301
22	100%	+0.344

22+, A2s+, K9s+, QTs+, JTs, A4o+, KTo+, QJo

Every calling range at 16 bb

Spot	Calls	Range
HJ vs UTG	8.3%	66+, ATs+, KQs, AJo+
CO vs UTG	8.3%	66+, ATs+, KQs, AJo+
BTN vs UTG	8.3%	66+, ATs+, KQs, AJo+
SB vs UTG	10.0%	55+, A9s+, KQs, ATo+
BB vs UTG	10.8%	55+, A9s+, KQs, ATo+, KQo
CO vs HJ	10.6%	55+, A8s+, KJs+, ATo+
BTN vs HJ	10.6%	55+, A8s+, KJs+, ATo+
SB vs HJ	12.2%	44+, A8s+, KJs+, ATo+, KQo
BB vs HJ	13.4%	44+, A7s+, A5s, KJs+, A9o+, KQo
BTN vs CO	14.9%	44+, A5s+, KTs+, A8o+, KQo
SB vs CO	16.0%	33+, A5s+, KTs+, QJs, A8o+, KQo
BB vs CO	18.4%	33+, A2s+, KTs+, QJs, A7o+, KJo+
SB vs BTN	21.7%	33+, A2s+, K9s+, QTs+, A5o+, KTo+
BB vs BTN	24.7%	22+, A2s+, K9s+, QTs+, JTs, A4o+, KTo+, QJo
BB vs SB	40.5%	22+, A2s+, K2s+, Q6s+, J8s+, T8s+, A2o+, K4o+, Q8o+, J9o+

All 169 hands at 16 bb: shove EV by seat

Hand	UTG	HJ	CO	BTN	SB
AA	+5.622	+5.720	+5.934	+5.818	+5.902
KK	+4.683	+4.800	+4.993	+4.951	+5.151
QQ	+3.898	+4.122	+4.396	+4.455	+4.656
JJ	+3.144	+3.476	+3.839	+3.993	+4.252
TT	+2.533	+2.897	+3.354	+3.544	+3.910
99	+1.925	+2.304	+2.805	+3.075	+3.471
88	+1.474	+1.872	+2.354	+2.732	+3.101
77	+1.007	+1.468	+1.959	+2.407	+2.797
66	+0.555	+1.088	+1.613	+2.085	+2.523
55	+0.253	+0.712	+1.279	+1.766	+2.269
44	+0.112	+0.388	+0.911	+1.426	+1.972
33	+0.042	+0.236	+0.612	+1.107	+1.694
22	−0.029	+0.161	+0.433	+0.855	+1.433
AKs	+2.706	+2.980	+3.379	+3.609	+3.863
AQs	+1.955	+2.359	+2.872	+3.206	+3.562
AJs	+1.174	+1.712	+2.360	+2.856	+3.338
ATs	+0.645	+1.135	+1.878	+2.498	+3.133
A9s	+0.280	+0.620	+1.308	+1.976	+2.776
A8s	+0.191	+0.422	+0.934	+1.660	+2.552
A7s	+0.103	+0.302	+0.681	+1.389	+2.328
A6s	−0.007	+0.200	+0.522	+1.143	+2.150
A5s	+0.074	+0.270	+0.574	+1.118	+2.123
A4s	+0.008	+0.171	+0.469	+0.999	+2.017
A3s	−0.028	+0.108	+0.381	+0.915	+1.923
A2s	−0.079	+0.059	+0.306	+0.830	+1.852
KQs	+0.685	+0.852	+1.071	+1.476	+2.588
KJs	+0.433	+0.545	+0.714	+1.170	+2.376
KTs	+0.379	+0.390	+0.485	+0.852	+2.177
K9s	+0.151	+0.173	+0.173	+0.455	+1.826
K8s	−0.032	−0.002	−0.035	+0.247	+1.493
K7s	−0.091	−0.032	−0.035	+0.209	+1.304
K6s	−0.170	−0.088	−0.076	+0.157	+1.167
K5s	−0.247	−0.177	−0.152	+0.076	+1.039
K4s	−0.320	−0.280	−0.249	0.000	+0.936
K3s	−0.359	−0.344	−0.341	−0.082	+0.860
K2s	−0.409	−0.393	−0.415	−0.156	+0.789
QJs	+0.393	+0.484	+0.540	+0.790	+1.639
QTs	+0.353	+0.402	+0.457	+0.636	+1.467
Q9s	+0.125	+0.184	+0.193	+0.379	+1.111
Q8s	−0.067	−0.003	−0.027	+0.194	+0.802
Q7s	−0.279	−0.188	−0.192	+0.009	+0.560
Q6s	−0.332	−0.220	−0.204	−0.018	+0.521
Q5s	−0.410	−0.308	−0.281	−0.098	+0.454
Q4s	−0.478	−0.407	−0.377	−0.174	+0.373
Q3s	−0.523	−0.476	−0.471	−0.260	+0.311
Q2s	−0.566	−0.517	−0.539	−0.330	+0.244
JTs	+0.350	+0.428	+0.514	+0.655	+1.199
J9s	+0.116	+0.206	+0.250	+0.428	+0.847
J8s	−0.072	+0.023	+0.032	+0.241	+0.591
J7s	−0.301	−0.177	−0.144	+0.045	+0.412
J6s	−0.509	−0.368	−0.325	−0.141	+0.247
J5s	−0.557	−0.429	−0.372	−0.193	+0.214
J4s	−0.616	−0.517	−0.461	−0.264	+0.134
J3s	−0.666	−0.589	−0.550	−0.344	+0.080
J2s	−0.712	−0.636	−0.627	−0.421	+0.003
T9s	+0.179	+0.244	+0.315	+0.495	+0.820
T8s	−0.024	+0.059	+0.099	+0.311	+0.624
T7s	−0.247	−0.140	−0.078	+0.115	+0.454
T6s	−0.461	−0.338	−0.264	−0.074	+0.281
T5s	−0.670	−0.567	−0.490	−0.298	+0.093
T4s	−0.706	−0.632	−0.547	−0.338	+0.047
T3s	−0.749	−0.697	−0.638	−0.424	−0.012
T2s	−0.803	−0.751	−0.717	−0.500	−0.088
98s	−0.002	+0.099	+0.131	+0.372	+0.649
97s	−0.200	−0.079	−0.028	+0.190	+0.510
96s	−0.408	−0.272	−0.214	−0.004	+0.339
95s	−0.621	−0.502	−0.442	−0.233	+0.146
94s	−0.820	−0.732	−0.679	−0.447	−0.065
93s	−0.826	−0.762	−0.729	−0.488	−0.091
92s	−0.870	−0.807	−0.800	−0.561	−0.165
87s	−0.159	−0.022	+0.032	+0.278	+0.581
86s	−0.361	−0.208	−0.148	+0.090	+0.416
85s	−0.568	−0.433	−0.371	−0.130	+0.226
84s	−0.770	−0.671	−0.612	−0.345	+0.011
83s	−0.952	−0.878	−0.850	−0.572	−0.185
82s	−0.959	−0.884	−0.883	−0.609	−0.224
76s	−0.320	−0.146	−0.060	+0.159	+0.502
75s	−0.527	−0.368	−0.278	−0.050	+0.319
74s	−0.730	−0.608	−0.524	−0.274	+0.099
73s	−0.913	−0.817	−0.764	−0.501	−0.095
72s	−1.089	−0.995	−0.980	−0.718	−0.307
65s	−0.469	−0.289	−0.177	+0.037	+0.406
64s	−0.657	−0.516	−0.410	−0.173	+0.199
63s	−0.851	−0.735	−0.662	−0.408	0.000
62s	−1.036	−0.920	−0.882	−0.630	−0.214
54s	−0.588	−0.439	−0.314	−0.085	+0.302
53s	−0.765	−0.644	−0.550	−0.303	+0.113
52s	−0.948	−0.827	−0.774	−0.527	−0.101
43s	−0.853	−0.776	−0.667	−0.397	+0.021
42s	−1.028	−0.951	−0.883	−0.619	−0.189
32s	−1.083	−1.045	−0.998	−0.717	−0.267
AKo	+2.458	+2.744	+3.152	+3.406	+3.682
AQo	+1.664	+2.085	+2.612	+2.976	+3.350
AJo	+0.818	+1.385	+2.058	+2.597	+3.103
ATo	+0.250	+0.765	+1.540	+2.212	+2.881
A9o	−0.140	+0.213	+0.930	+1.650	+2.503
A8o	−0.248	−0.007	+0.527	+1.305	+2.254
A7o	−0.347	−0.144	+0.243	+1.009	+2.006
A6o	−0.462	−0.250	+0.077	+0.750	+1.820
A5o	−0.367	−0.166	+0.137	+0.723	+1.790
A4o	−0.439	−0.278	+0.020	+0.593	+1.674
A3o	−0.484	−0.350	−0.075	+0.501	+1.573
A2o	−0.538	−0.401	−0.157	+0.414	+1.498
KQo	+0.278	+0.447	+0.659	+1.103	+2.314
KJo	+0.001	+0.109	+0.268	+0.767	+2.077
KTo	−0.058	−0.053	+0.028	+0.433	+1.866
K9o	−0.303	−0.286	−0.302	0.000	+1.485
K8o	−0.500	−0.480	−0.529	−0.222	+1.135
K7o	−0.558	−0.504	−0.529	−0.260	+0.927
K6o	−0.644	−0.565	−0.575	−0.318	+0.778
K5o	−0.734	−0.666	−0.664	−0.412	+0.636
K4o	−0.804	−0.770	−0.761	−0.491	+0.529
K3o	−0.854	−0.850	−0.866	−0.585	+0.442
K2o	−0.902	−0.895	−0.939	−0.656	+0.372
QJo	−0.023	+0.061	+0.101	+0.373	+1.295
QTo	−0.081	−0.032	+0.003	+0.200	+1.099
Q9o	−0.336	−0.279	−0.290	−0.085	+0.719
Q8o	−0.536	−0.477	−0.520	−0.278	+0.384
Q7o	−0.760	−0.673	−0.704	−0.488	+0.118
Q6o	−0.809	−0.699	−0.708	−0.505	+0.083
Q5o	−0.899	−0.799	−0.794	−0.594	+0.005
Q4o	−0.973	−0.904	−0.892	−0.672	−0.081
Q3o	−1.022	−0.981	−0.994	−0.766	−0.145
Q2o	−1.072	−1.029	−1.071	−0.846	−0.221
JTo	−0.078	−0.003	+0.065	+0.224	+0.816
J9o	−0.337	−0.253	−0.226	−0.029	+0.437
J8o	−0.532	−0.446	−0.453	−0.222	+0.165
J7o	−0.766	−0.649	−0.640	−0.432	−0.033
J6o	−0.995	−0.857	−0.841	−0.633	−0.209
J5o	−1.048	−0.920	−0.888	−0.686	−0.240
J4o	−1.120	−1.024	−0.984	−0.764	−0.325
J3o	−1.170	−1.101	−1.086	−0.859	−0.395
J2o	−1.224	−1.155	−1.171	−0.944	−0.478
T9o	−0.277	−0.211	−0.154	+0.045	+0.412
T8o	−0.478	−0.396	−0.371	−0.140	+0.205
T7o	−0.713	−0.608	−0.566	−0.352	+0.018
T6o	−0.946	−0.823	−0.774	−0.561	−0.165
T5o	−1.172	−1.066	−1.015	−0.803	−0.368
T4o	−1.209	−1.135	−1.072	−0.847	−0.422
T3o	−1.255	−1.208	−1.172	−0.937	−0.489
T2o	−1.308	−1.261	−1.251	−1.017	−0.568
98o	−0.459	−0.360	−0.339	−0.083	+0.227
97o	−0.667	−0.546	−0.517	−0.282	+0.073
96o	−0.884	−0.749	−0.709	−0.481	−0.104
95o	−1.116	−0.997	−0.960	−0.729	−0.310
94o	−1.334	−1.250	−1.213	−0.963	−0.539
93o	−1.335	−1.280	−1.268	−1.010	−0.570
92o	−1.389	−1.330	−1.346	−1.090	−0.651
87o	−0.627	−0.496	−0.460	−0.192	+0.144
86o	−0.838	−0.688	−0.643	−0.384	−0.025
85o	−1.065	−0.928	−0.880	−0.619	−0.229
84o	−1.281	−1.183	−1.138	−0.855	−0.458
83o	−1.477	−1.409	−1.399	−1.100	−0.669
82o	−1.484	−1.415	−1.435	−1.138	−0.714
76o	−0.792	−0.617	−0.554	−0.312	+0.063
75o	−1.023	−0.863	−0.795	−0.544	−0.135
74o	−1.237	−1.116	−1.046	−0.774	−0.365
73o	−1.432	−1.342	−1.310	−1.025	−0.580
72o	−1.626	−1.535	−1.544	−1.259	−0.804
65o	−0.952	−0.772	−0.681	−0.444	−0.041
64o	−1.159	−1.019	−0.930	−0.671	−0.261
63o	−1.353	−1.244	−1.190	−0.919	−0.476
62o	−1.557	−1.448	−1.433	−1.158	−0.704
54o	−1.083	−0.929	−0.819	−0.566	−0.145
53o	−1.263	−1.145	−1.074	−0.808	−0.354
52o	−1.464	−1.344	−1.312	−1.044	−0.579
43o	−1.355	−1.282	−1.193	−0.906	−0.449
42o	−1.551	−1.478	−1.431	−1.143	−0.674
32o	−1.603	−1.571	−1.546	−1.247	−0.756

Reading the chart is the easy half. The trainer deals you real hands at 16 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 6-max at 16 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 0.011 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.