6-max push/fold at 15 bb

At 15 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 17.1% of hands from UTG, widening to 64.2% 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 17.1% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJo21%JJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o2264%

22+, A7s+, A5s, K9s+, Q9s+, J9s+, T9s, 98s, ATo+, KJo+

HJ

shoves 21.7% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K9s+, Q9s+, J8s+, T8s+, 98s, A8o+, KJo+, QJo

CO

shoves 29.4% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8s65%Q7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3o74%K3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

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

BTN

shoves 36.1% first in

22+, A2s+, K4s+, Q7s+, J7s+, T7s+, 96s+, 86s+, 76s, 65s, A2o+, K9o+, QTo+, JTo, T9o

SB

shoves 64.2% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o44%5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K2s+, Q2s+, J2s+, T3s+, 95s+, 84s+, 74s+, 63s+, 53s+, 43s, A2o+, K2o+, Q5o+, 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 26.4% against a BTN shove of 36.1%

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)
Q9s	0%	−0.004
A2o	100%	+0.028
K7s	0%	−0.041
K9o	0%	−0.124
QTo	0%	−0.126
K8s	100%	+0.137
A3o	100%	+0.221
J9s	0%	−0.251
K6s	0%	−0.256
QJo	100%	+0.367

22+, A2s+, K8s+, QTs+, JTs, A2o+, KTo+, QJo

Every calling range at 15 bb

Spot	Calls	Range
HJ vs UTG	9.5%	55+, ATs+, KQs, ATo+
CO vs UTG	9.5%	55+, ATs+, KQs, ATo+
BTN vs UTG	9.5%	55+, ATs+, KQs, ATo+
SB vs UTG	10.0%	55+, A9s+, KQs, ATo+
BB vs UTG	11.5%	55+, A8s+, KJs+, ATo+, KQo
CO vs HJ	12.6%	44+, A8s+, KJs+, A9o+, KQo
BTN vs HJ	12.6%	44+, A8s+, KJs+, A9o+, KQo
SB vs HJ	12.8%	44+, A8s+, KJs+, A9o+, KQo
BB vs HJ	14.2%	33+, A7s+, A5s, KTs+, A9o+, KQo
BTN vs CO	15.7%	33+, A5s+, KTs+, QJs, A8o+, KQo
SB vs CO	18.1%	33+, A3s+, KTs+, QJs, A7o+, KJo+
BB vs CO	19.2%	22+, A2s+, KTs+, QTs+, A7o+, KJo+
SB vs BTN	24.0%	22+, A2s+, K9s+, QTs+, JTs, A4o+, KTo+, QJo
BB vs BTN	26.4%	22+, A2s+, K8s+, QTs+, JTs, A2o+, KTo+, QJo
BB vs SB	42.3%	22+, A2s+, K2s+, Q5s+, J7s+, T8s+, A2o+, K3o+, Q8o+, J9o+

All 169 hands at 15 bb: shove EV by seat

Hand	UTG	HJ	CO	BTN	SB
AA	+5.663	+5.867	+5.927	+5.828	+5.816
KK	+4.733	+4.913	+4.997	+4.980	+5.073
QQ	+4.009	+4.242	+4.419	+4.492	+4.592
JJ	+3.311	+3.624	+3.872	+4.028	+4.200
TT	+2.662	+3.086	+3.400	+3.588	+3.866
99	+2.048	+2.458	+2.878	+3.136	+3.445
88	+1.627	+2.016	+2.455	+2.809	+3.091
77	+1.190	+1.643	+2.060	+2.497	+2.795
66	+0.770	+1.290	+1.723	+2.194	+2.529
55	+0.383	+0.939	+1.408	+1.901	+2.282
44	+0.145	+0.538	+1.054	+1.550	+1.995
33	+0.077	+0.279	+0.707	+1.220	+1.709
22	+0.003	+0.169	+0.457	+0.908	+1.440
AKs	+2.799	+3.093	+3.377	+3.625	+3.815
AQs	+2.102	+2.514	+2.901	+3.250	+3.520
AJs	+1.380	+1.888	+2.426	+2.924	+3.308
ATs	+0.742	+1.355	+1.958	+2.569	+3.115
A9s	+0.270	+0.740	+1.405	+2.056	+2.772
A8s	+0.181	+0.456	+1.050	+1.754	+2.559
A7s	+0.093	+0.348	+0.777	+1.478	+2.353
A6s	−0.011	+0.252	+0.596	+1.230	+2.176
A5s	+0.060	+0.330	+0.648	+1.199	+2.159
A4s	−0.030	+0.221	+0.544	+1.067	+2.053
A3s	−0.067	+0.134	+0.449	+0.979	+1.977
A2s	−0.119	+0.072	+0.360	+0.886	+1.887
KQs	+0.699	+0.887	+1.128	+1.488	+2.620
KJs	+0.459	+0.538	+0.765	+1.208	+2.417
KTs	+0.323	+0.378	+0.523	+0.900	+2.226
K9s	+0.145	+0.086	+0.216	+0.509	+1.888
K8s	−0.037	−0.046	+0.014	+0.294	+1.565
K7s	−0.088	−0.066	−0.008	+0.251	+1.384
K6s	−0.156	−0.116	−0.035	+0.201	+1.241
K5s	−0.247	−0.199	−0.107	+0.117	+1.118
K4s	−0.342	−0.316	−0.205	+0.019	+1.008
K3s	−0.381	−0.402	−0.305	−0.053	+0.931
K2s	−0.433	−0.463	−0.388	−0.143	+0.856
QJs	+0.422	+0.466	+0.572	+0.815	+1.666
QTs	+0.314	+0.392	+0.481	+0.645	+1.503
Q9s	+0.138	+0.107	+0.212	+0.385	+1.162
Q8s	−0.055	−0.036	0.000	+0.199	+0.862
Q7s	−0.262	−0.217	−0.184	+0.018	+0.631
Q6s	−0.306	−0.240	−0.182	−0.005	+0.585
Q5s	−0.396	−0.324	−0.255	−0.087	+0.515
Q4s	−0.487	−0.437	−0.352	−0.185	+0.434
Q3s	−0.532	−0.527	−0.456	−0.262	+0.353
Q2s	−0.575	−0.580	−0.532	−0.349	+0.301
JTs	+0.324	+0.441	+0.523	+0.656	+1.238
J9s	+0.143	+0.154	+0.267	+0.418	+0.900
J8s	−0.046	+0.013	+0.054	+0.231	+0.650
J7s	−0.268	−0.184	−0.140	+0.040	+0.465
J6s	−0.470	−0.373	−0.305	−0.141	+0.297
J5s	−0.532	−0.426	−0.348	−0.194	+0.261
J4s	−0.611	−0.529	−0.440	−0.290	+0.186
J3s	−0.662	−0.619	−0.537	−0.361	+0.113
J2s	−0.709	−0.681	−0.622	−0.455	+0.052
T9s	+0.161	+0.205	+0.339	+0.492	+0.852
T8s	−0.033	+0.064	+0.130	+0.308	+0.653
T7s	−0.251	−0.133	−0.067	+0.117	+0.481
T6s	−0.461	−0.326	−0.236	−0.070	+0.315
T5s	−0.688	−0.555	−0.458	−0.295	+0.129
T4s	−0.746	−0.632	−0.516	−0.359	+0.087
T3s	−0.789	−0.718	−0.617	−0.434	+0.009
T2s	−0.843	−0.784	−0.704	−0.526	−0.052
98s	+0.025	+0.070	+0.168	+0.376	+0.676
97s	−0.170	−0.107	−0.010	+0.198	+0.536
96s	−0.375	−0.299	−0.181	+0.006	+0.372
95s	−0.604	−0.528	−0.406	−0.225	+0.181
94s	−0.826	−0.777	−0.643	−0.463	−0.021
93s	−0.832	−0.828	−0.702	−0.494	−0.067
92s	−0.877	−0.885	−0.781	−0.584	−0.125
87s	−0.119	−0.017	+0.058	+0.290	+0.606
86s	−0.318	−0.199	−0.109	+0.104	+0.449
85s	−0.542	−0.425	−0.328	−0.118	+0.260
84s	−0.770	−0.680	−0.568	−0.356	+0.054
83s	−0.954	−0.913	−0.814	−0.575	−0.157
82s	−0.960	−0.929	−0.856	−0.627	−0.182
76s	−0.270	−0.129	−0.034	+0.178	+0.530
75s	−0.492	−0.349	−0.247	−0.034	+0.350
74s	−0.722	−0.607	−0.493	−0.280	+0.139
73s	−0.905	−0.842	−0.741	−0.497	−0.069
72s	−1.083	−1.036	−0.965	−0.733	−0.263
65s	−0.426	−0.260	−0.138	+0.057	+0.435
64s	−0.641	−0.504	−0.372	−0.174	+0.237
63s	−0.834	−0.750	−0.631	−0.401	+0.023
62s	−1.021	−0.949	−0.859	−0.640	−0.172
54s	−0.572	−0.419	−0.274	−0.086	+0.336
53s	−0.751	−0.649	−0.516	−0.294	+0.132
52s	−0.934	−0.849	−0.748	−0.536	−0.063
43s	−0.880	−0.782	−0.631	−0.403	+0.046
42s	−1.055	−0.975	−0.856	−0.643	−0.147
32s	−1.111	−1.101	−0.973	−0.735	−0.234
AKo	+2.553	+2.856	+3.151	+3.421	+3.639
AQo	+1.817	+2.240	+2.644	+3.021	+3.312
AJo	+1.035	+1.562	+2.131	+2.669	+3.078
ATo	+0.354	+0.990	+1.626	+2.286	+2.869
A9o	−0.155	+0.335	+1.035	+1.733	+2.506
A8o	−0.261	+0.020	+0.650	+1.404	+2.269
A7o	−0.362	−0.108	+0.348	+1.102	+2.041
A6o	−0.470	−0.205	+0.157	+0.841	+1.856
A5o	−0.385	−0.116	+0.215	+0.807	+1.839
A4o	−0.485	−0.236	+0.101	+0.665	+1.721
A3o	−0.529	−0.333	0.000	+0.569	+1.641
A2o	−0.584	−0.397	−0.098	+0.473	+1.543
KQo	+0.286	+0.476	+0.722	+1.112	+2.356
KJo	+0.019	+0.088	+0.326	+0.806	+2.130
KTo	−0.119	−0.076	+0.072	+0.482	+1.928
K9o	−0.315	−0.386	−0.256	+0.052	+1.561
K8o	−0.516	−0.536	−0.476	−0.174	+1.220
K7o	−0.561	−0.553	−0.498	−0.218	+1.022
K6o	−0.636	−0.608	−0.530	−0.275	+0.865
K5o	−0.740	−0.702	−0.615	−0.371	+0.731
K4o	−0.836	−0.819	−0.713	−0.472	+0.614
K3o	−0.887	−0.924	−0.825	−0.556	+0.528
K2o	−0.933	−0.982	−0.907	−0.643	+0.452
QJo	0.000	+0.030	+0.138	+0.399	+1.332
QTo	−0.124	−0.055	+0.030	+0.207	+1.146
Q9o	−0.330	−0.366	−0.266	−0.081	+0.781
Q8o	−0.532	−0.523	−0.490	−0.276	+0.457
Q7o	−0.749	−0.717	−0.693	−0.480	+0.204
Q6o	−0.787	−0.734	−0.683	−0.493	+0.159
Q5o	−0.893	−0.829	−0.764	−0.584	+0.080
Q4o	−0.990	−0.946	−0.865	−0.686	−0.008
Q3o	−1.039	−1.045	−0.975	−0.771	−0.090
Q2o	−1.089	−1.108	−1.061	−0.867	−0.152
JTo	−0.107	−0.002	+0.076	+0.224	+0.868
J9o	−0.318	−0.317	−0.205	−0.040	+0.504
J8o	−0.513	−0.471	−0.426	−0.234	+0.237
J7o	−0.739	−0.672	−0.632	−0.440	+0.035
J6o	−0.961	−0.878	−0.817	−0.636	−0.147
J5o	−1.026	−0.933	−0.860	−0.690	−0.181
J4o	−1.123	−1.049	−0.958	−0.791	−0.260
J3o	−1.174	−1.150	−1.068	−0.877	−0.348
J2o	−1.227	−1.218	−1.161	−0.979	−0.416
T9o	−0.299	−0.257	−0.126	+0.041	+0.456
T8o	−0.490	−0.402	−0.336	−0.145	+0.245
T7o	−0.720	−0.613	−0.550	−0.353	+0.055
T6o	−0.949	−0.828	−0.741	−0.558	−0.120
T5o	−1.192	−1.068	−0.979	−0.802	−0.321
T4o	−1.254	−1.149	−1.037	−0.869	−0.368
T3o	−1.301	−1.243	−1.146	−0.949	−0.454
T2o	−1.354	−1.308	−1.233	−1.047	−0.520
98o	−0.437	−0.398	−0.299	−0.081	+0.265
97o	−0.641	−0.587	−0.494	−0.276	+0.111
96o	−0.855	−0.788	−0.672	−0.472	−0.059
95o	−1.103	−1.036	−0.919	−0.722	−0.265
94o	−1.349	−1.307	−1.173	−0.980	−0.483
93o	−1.350	−1.359	−1.236	−1.018	−0.533
92o	−1.402	−1.422	−1.322	−1.114	−0.599
87o	−0.595	−0.504	−0.429	−0.180	+0.181
86o	−0.800	−0.692	−0.599	−0.370	+0.019
85o	−1.042	−0.932	−0.831	−0.608	−0.183
84o	−1.288	−1.204	−1.089	−0.867	−0.402
83o	−1.485	−1.461	−1.358	−1.104	−0.628
82o	−1.491	−1.478	−1.402	−1.157	−0.661
76o	−0.745	−0.612	−0.523	−0.295	+0.103
75o	−0.992	−0.857	−0.759	−0.527	−0.093
74o	−1.236	−1.125	−1.008	−0.779	−0.312
73o	−1.433	−1.382	−1.281	−1.021	−0.541
72o	−1.627	−1.593	−1.522	−1.274	−0.749
65o	−0.912	−0.756	−0.637	−0.426	0.000
64o	−1.150	−1.019	−0.888	−0.674	−0.212
63o	−1.346	−1.273	−1.154	−0.914	−0.439
62o	−1.550	−1.493	−1.405	−1.169	−0.650
54o	−1.070	−0.920	−0.774	−0.568	−0.099
53o	−1.253	−1.166	−1.036	−0.801	−0.321
52o	−1.454	−1.382	−1.282	−1.053	−0.529
43o	−1.390	−1.302	−1.153	−0.913	−0.411
42o	−1.587	−1.517	−1.399	−1.167	−0.620
32o	−1.638	−1.643	−1.516	−1.266	−0.710

Reading the chart is the easy half. The trainer deals you real hands at 15 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 6-max at 15 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 0.016 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.