6-max push/fold at 18 bb

At 18 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 15.0% of hands from UTG, widening to 59.7% 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 15.0% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJo29%QJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

33+, A8s+, K9s+, Q9s+, J9s+, T9s, ATo+, KQo

HJ

shoves 18.8% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3s63%A2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8s23%T7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A3s+, K9s+, Q9s+, J9s+, T9s, 98s, ATo+, KJo+, QJo

CO

shoves 25.5% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKTo41%QTo56%JToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K9s+, Q9s+, J8s+, T8s+, 98s, 87s, A7o+, A5o, KJo+, QTo+, JTo

BTN

shoves 34.1% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s43%64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K5s+, Q8s+, J7s+, T7s+, 97s+, 86s+, 76s, A2o+, KTo+, QTo+, JTo, T9o

SB

shoves 59.7% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6o45%J6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K2s+, Q2s+, J3s+, T4s+, 95s+, 84s+, 74s+, 64s+, 53s+, 43s, A2o+, K2o+, Q7o+, 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 22.3% against a BTN shove of 34.1%

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTs33%J9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

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)
JTs	33%	−0.001
QJo	0%	−0.023
22	100%	+0.109
A4o	0%	−0.142
A5o	100%	+0.230
KTo	100%	+0.304
K8s	0%	−0.313
K9s	100%	+0.340
A6o	100%	+0.365
A3o	0%	−0.379

22+, A2s+, K9s+, QTs+, A5o+, KTo+

Every calling range at 18 bb

Spot	Calls	Range
HJ vs UTG	7.8%	77+, ATs+, AJo+
CO vs UTG	7.8%	77+, ATs+, AJo+
BTN vs UTG	7.8%	77+, ATs+, AJo+
SB vs UTG	8.3%	66+, ATs+, KQs, AJo+
BB vs UTG	8.3%	66+, ATs+, KQs, AJo+
CO vs HJ	10.0%	55+, A9s+, KQs, ATo+
BTN vs HJ	10.0%	55+, A9s+, KQs, ATo+
SB vs HJ	10.5%	55+, A9s+, KQs, ATo+, KQo
BB vs HJ	11.5%	55+, A8s+, KJs+, ATo+, KQo
BTN vs CO	13.1%	44+, A7s+, KJs+, A9o+, KQo
SB vs CO	14.1%	44+, A7s+, KJs+, A8o+, KQo
BB vs CO	15.9%	33+, A5s+, KTs+, QJs, A8o+, KQo
SB vs BTN	19.6%	33+, A2s+, KTs+, QTs+, A6o+, KJo+
BB vs BTN	22.3%	22+, A2s+, K9s+, QTs+, A5o+, KTo+
BB vs SB	36.4%	22+, A2s+, K2s+, Q7s+, J8s+, T9s, A2o+, K6o+, Q9o+, JTo

All 169 hands at 18 bb: shove EV by seat

Hand	UTG	HJ	CO	BTN	SB
AA	+5.608	+5.815	+5.967	+5.915	+5.913
KK	+4.665	+4.883	+5.042	+5.037	+5.159
QQ	+3.842	+4.146	+4.389	+4.532	+4.673
JJ	+3.023	+3.449	+3.795	+4.047	+4.273
TT	+2.386	+2.811	+3.281	+3.594	+3.900
99	+1.754	+2.181	+2.683	+3.110	+3.452
88	+1.263	+1.745	+2.213	+2.741	+3.103
77	+0.736	+1.314	+1.808	+2.379	+2.794
66	+0.315	+0.897	+1.454	+2.019	+2.503
55	+0.137	+0.481	+1.110	+1.693	+2.258
44	+0.077	+0.208	+0.722	+1.357	+1.982
33	+0.004	+0.136	+0.455	+1.034	+1.703
22	−0.068	+0.060	+0.328	+0.768	+1.422
AKs	+2.626	+2.934	+3.294	+3.597	+3.880
AQs	+1.776	+2.250	+2.749	+3.167	+3.569
AJs	+0.944	+1.523	+2.156	+2.774	+3.328
ATs	+0.434	+0.896	+1.645	+2.377	+3.110
A9s	+0.151	+0.386	+1.047	+1.843	+2.715
A8s	+0.076	+0.258	+0.694	+1.511	+2.465
A7s	−0.024	+0.170	+0.493	+1.223	+2.250
A6s	−0.134	+0.067	+0.373	+0.970	+2.048
A5s	−0.031	+0.138	+0.450	+0.966	+2.002
A4s	−0.071	+0.038	+0.346	+0.857	+1.896
A3s	−0.108	0.000	+0.260	+0.772	+1.823
A2s	−0.161	−0.053	+0.197	+0.684	+1.745
KQs	+0.623	+0.765	+0.994	+1.370	+2.442
KJs	+0.431	+0.487	+0.636	+1.019	+2.219
KTs	+0.411	+0.351	+0.461	+0.741	+2.012
K9s	+0.158	+0.149	+0.160	+0.386	+1.624
K8s	−0.042	−0.025	−0.024	+0.183	+1.282
K7s	−0.111	−0.073	−0.030	+0.141	+1.120
K6s	−0.191	−0.138	−0.070	+0.080	+0.981
K5s	−0.248	−0.233	−0.148	+0.027	+0.875
K4s	−0.298	−0.339	−0.258	−0.055	+0.791
K3s	−0.337	−0.379	−0.347	−0.146	+0.717
K2s	−0.388	−0.432	−0.410	−0.232	+0.638
QJs	+0.374	+0.451	+0.539	+0.745	+1.526
QTs	+0.367	+0.347	+0.455	+0.644	+1.344
Q9s	+0.114	+0.146	+0.175	+0.367	+0.952
Q8s	−0.089	−0.041	−0.020	+0.167	+0.689
Q7s	−0.317	−0.246	−0.191	−0.031	+0.484
Q6s	−0.369	−0.289	−0.203	−0.066	+0.451
Q5s	−0.428	−0.383	−0.281	−0.119	+0.408
Q4s	−0.471	−0.484	−0.389	−0.201	+0.332
Q3s	−0.517	−0.530	−0.481	−0.295	+0.252
Q2s	−0.561	−0.574	−0.537	−0.377	+0.177
JTs	+0.336	+0.368	+0.514	+0.661	+1.122
J9s	+0.078	+0.160	+0.231	+0.420	+0.797
J8s	−0.121	−0.022	+0.039	+0.218	+0.593
J7s	−0.362	−0.244	−0.149	+0.012	+0.400
J6s	−0.567	−0.450	−0.330	−0.189	+0.233
J5s	−0.597	−0.515	−0.377	−0.214	+0.218
J4s	−0.632	−0.604	−0.476	−0.290	+0.142
J3s	−0.683	−0.657	−0.565	−0.378	+0.069
J2s	−0.729	−0.705	−0.630	−0.467	−0.015
T9s	+0.157	+0.186	+0.288	+0.494	+0.809
T8s	−0.064	−0.001	+0.096	+0.297	+0.630
T7s	−0.299	−0.220	−0.090	+0.088	+0.449
T6s	−0.512	−0.432	−0.277	−0.113	+0.276
T5s	−0.702	−0.668	−0.503	−0.313	+0.103
T4s	−0.713	−0.736	−0.574	−0.357	+0.061
T3s	−0.757	−0.780	−0.661	−0.452	−0.016
T2s	−0.812	−0.836	−0.730	−0.541	−0.098
98s	−0.059	+0.047	+0.114	+0.348	+0.669
97s	−0.266	−0.150	−0.054	+0.156	+0.510
96s	−0.472	−0.357	−0.239	−0.050	+0.338
95s	−0.666	−0.596	−0.467	−0.255	+0.155
94s	−0.843	−0.832	−0.715	−0.479	−0.050
93s	−0.849	−0.838	−0.765	−0.528	−0.095
92s	−0.895	−0.885	−0.826	−0.611	−0.175
87s	−0.233	−0.090	+0.014	+0.238	+0.595
86s	−0.437	−0.289	−0.163	+0.038	+0.426
85s	−0.623	−0.523	−0.388	−0.159	+0.248
84s	−0.802	−0.766	−0.641	−0.385	+0.036
83s	−0.988	−0.956	−0.878	−0.623	−0.179
82s	−0.992	−0.963	−0.898	−0.671	−0.225
76s	−0.408	−0.236	−0.083	+0.106	+0.504
75s	−0.593	−0.468	−0.302	−0.085	+0.333
74s	−0.771	−0.713	−0.560	−0.318	+0.118
73s	−0.959	−0.902	−0.800	−0.557	−0.096
72s	−1.137	−1.086	−1.003	−0.788	−0.315
65s	−0.542	−0.394	−0.201	0.000	+0.420
64s	−0.702	−0.627	−0.445	−0.221	+0.217
63s	−0.901	−0.825	−0.696	−0.470	−0.003
62s	−1.090	−1.016	−0.904	−0.704	−0.225
54s	−0.610	−0.552	−0.351	−0.112	+0.328
53s	−0.793	−0.736	−0.586	−0.344	+0.120
52s	−0.978	−0.925	−0.796	−0.582	−0.101
43s	−0.840	−0.883	−0.715	−0.445	+0.033
42s	−1.019	−1.064	−0.916	−0.680	−0.187
32s	−1.078	−1.120	−1.040	−0.786	−0.275
AKo	+2.370	+2.686	+3.059	+3.385	+3.698
AQo	+1.472	+1.963	+2.481	+2.926	+3.354
AJo	+0.574	+1.175	+1.838	+2.500	+3.088
ATo	+0.023	+0.505	+1.289	+2.074	+2.853
A9o	−0.278	−0.044	+0.651	+1.499	+2.434
A8o	−0.370	−0.192	+0.266	+1.140	+2.156
A7o	−0.481	−0.294	+0.039	+0.824	+1.921
A6o	−0.598	−0.400	−0.086	+0.558	+1.707
A5o	−0.478	−0.316	+0.001	+0.551	+1.656
A4o	−0.521	−0.427	−0.113	+0.433	+1.541
A3o	−0.570	−0.472	−0.209	+0.342	+1.462
A2o	−0.625	−0.527	−0.276	+0.248	+1.382
KQo	+0.210	+0.344	+0.574	+0.977	+2.148
KJo	0.000	+0.037	+0.180	+0.594	+1.902
KTo	−0.031	−0.102	−0.001	+0.303	+1.683
K9o	−0.299	−0.324	−0.319	−0.081	+1.261
K8o	−0.511	−0.516	−0.522	−0.301	+0.900
K7o	−0.583	−0.557	−0.529	−0.343	+0.725
K6o	−0.670	−0.630	−0.573	−0.408	+0.571
K5o	−0.741	−0.737	−0.663	−0.475	+0.453
K4o	−0.782	−0.846	−0.773	−0.561	+0.366
K3o	−0.833	−0.899	−0.878	−0.663	+0.281
K2o	−0.882	−0.946	−0.939	−0.747	+0.206
QJo	−0.042	+0.018	+0.096	+0.317	+1.167
QTo	−0.071	−0.101	−0.001	+0.198	+0.961
Q9o	−0.349	−0.335	−0.309	−0.109	+0.541
Q8o	−0.561	−0.529	−0.517	−0.318	+0.256
Q7o	−0.802	−0.746	−0.706	−0.540	+0.029
Q6o	−0.850	−0.782	−0.710	−0.564	0.000
Q5o	−0.922	−0.891	−0.797	−0.626	−0.053
Q4o	−0.969	−1.000	−0.908	−0.712	−0.133
Q3o	−1.018	−1.051	−1.009	−0.814	−0.216
Q2o	−1.070	−1.102	−1.074	−0.904	−0.298
JTo	−0.098	−0.075	+0.061	+0.218	+0.728
J9o	−0.377	−0.314	−0.250	−0.048	+0.378
J8o	−0.584	−0.502	−0.453	−0.256	+0.159
J7o	−0.831	−0.730	−0.649	−0.477	−0.051
J6o	−1.059	−0.954	−0.849	−0.695	−0.228
J5o	−1.094	−1.022	−0.896	−0.719	−0.246
J4o	−1.140	−1.131	−1.007	−0.804	−0.324
J3o	−1.191	−1.182	−1.108	−0.906	−0.411
J2o	−1.245	−1.237	−1.180	−1.002	−0.502
T9o	−0.304	−0.288	−0.184	+0.034	+0.393
T8o	−0.528	−0.470	−0.378	−0.163	+0.202
T7o	−0.774	−0.702	−0.583	−0.390	+0.011
T6o	−1.006	−0.934	−0.790	−0.611	−0.173
T5o	−1.213	−1.185	−1.030	−0.831	−0.365
T4o	−1.223	−1.258	−1.102	−0.878	−0.413
T3o	−1.270	−1.307	−1.199	−0.977	−0.496
T2o	−1.323	−1.361	−1.268	−1.069	−0.583
98o	−0.520	−0.429	−0.362	−0.116	+0.239
97o	−0.738	−0.634	−0.546	−0.326	+0.067
96o	−0.954	−0.852	−0.739	−0.535	−0.111
95o	−1.168	−1.109	−0.988	−0.763	−0.310
94o	−1.360	−1.371	−1.257	−1.006	−0.533
93o	−1.361	−1.373	−1.310	−1.060	−0.580
92o	−1.417	−1.426	−1.376	−1.150	−0.668
87o	−0.706	−0.580	−0.484	−0.244	+0.152
86o	−0.922	−0.786	−0.664	−0.446	−0.022
85o	−1.129	−1.036	−0.902	−0.661	−0.214
84o	−1.317	−1.300	−1.174	−0.906	−0.440
83o	−1.516	−1.503	−1.435	−1.164	−0.670
82o	−1.525	−1.509	−1.457	−1.213	−0.721
76o	−0.889	−0.724	−0.580	−0.376	+0.061
75o	−1.096	−0.980	−0.825	−0.592	−0.125
74o	−1.283	−1.242	−1.090	−0.831	−0.352
73o	−1.481	−1.445	−1.354	−1.094	−0.585
72o	−1.680	−1.644	−1.574	−1.341	−0.819
65o	−1.034	−0.894	−0.709	−0.493	−0.033
64o	−1.212	−1.150	−0.971	−0.732	−0.250
63o	−1.409	−1.351	−1.231	−0.991	−0.482
62o	−1.618	−1.561	−1.460	−1.245	−0.719
54o	−1.112	−1.064	−0.862	−0.607	−0.127
53o	−1.295	−1.253	−1.115	−0.861	−0.353
52o	−1.501	−1.459	−1.339	−1.113	−0.587
43o	−1.344	−1.408	−1.247	−0.967	−0.445
42o	−1.545	−1.612	−1.471	−1.219	−0.677
32o	−1.600	−1.663	−1.595	−1.328	−0.769

Reading the chart is the easy half. The trainer deals you real hands at 18 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 6-max at 18 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 0.007 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.