6-max push/fold at 17 bb

At 17 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 15.6% of hands from UTG, widening to 60.6% 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 15.6% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJo47%QJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3362%32sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

33+, A7s+, A5s, K9s+, Q9s+, J9s+, T9s, ATo+, KQo

HJ

shoves 20.1% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A3s+, K9s+, Q9s+, J9s+, T8s+, 98s, A9o+, KJo+, QJo

CO

shoves 26.2% first in

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

BTN

shoves 34.0% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4s62%K3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o53%9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K4s+, Q8s+, J7s+, T7s+, 97s+, 86s+, 76s, 65s, A2o+, KTo+, QTo+, JTo, T9o

SB

shoves 60.6% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3s23%T2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

22+, A2s+, K2s+, Q2s+, J3s+, T4s+, 95s+, 84s+, 74s+, 63s+, 53s+, 43s, A2o+, K2o+, Q6o+, 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 23.3% against a BTN shove of 34.0%

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)
QJo	95%	+0.002
A4o	0%	−0.024
JTs	100%	+0.034
K8s	0%	−0.200
22	100%	+0.204
A3o	0%	−0.264
A5o	100%	+0.333
KTo	100%	+0.355
Q9s	0%	−0.358
K9s	100%	+0.392

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

Every calling range at 17 bb

Spot	Calls	Range
HJ vs UTG	8.2%	66+, ATs+, KQs, AJo+
CO vs UTG	8.2%	66+, ATs+, KQs, AJo+
BTN vs UTG	8.2%	66+, ATs+, KQs, AJo+
SB vs UTG	8.3%	66+, ATs+, KQs, AJo+
BB vs UTG	9.8%	55+, A9s+, KQs, ATo+
CO vs HJ	10.0%	55+, A9s+, KQs, ATo+
BTN vs HJ	10.0%	55+, A9s+, KQs, ATo+
SB vs HJ	11.5%	55+, A8s+, KJs+, ATo+, KQo
BB vs HJ	12.8%	44+, A8s+, KJs+, A9o+, KQo
BTN vs CO	13.8%	44+, A7s+, KJs+, A8o+, KQo
SB vs CO	15.0%	44+, A5s+, KTs+, A8o+, KQo
BB vs CO	17.2%	33+, A3s+, KTs+, QJs, A8o+, KJo+
SB vs BTN	20.7%	33+, A2s+, K9s+, QTs+, A6o+, KTo+
BB vs BTN	23.3%	22+, A2s+, K9s+, QTs+, JTs, A5o+, KTo+, QJo
BB vs SB	38.2%	22+, A2s+, K2s+, Q7s+, J8s+, T9s, A2o+, K5o+, Q8o+, JTo

All 169 hands at 17 bb: shove EV by seat

Hand	UTG	HJ	CO	BTN	SB
AA	+5.624	+5.775	+5.944	+5.906	+5.903
KK	+4.691	+4.847	+5.002	+5.028	+5.146
QQ	+3.888	+4.135	+4.380	+4.503	+4.635
JJ	+3.104	+3.462	+3.803	+4.011	+4.252
TT	+2.482	+2.853	+3.305	+3.538	+3.902
99	+1.865	+2.232	+2.731	+3.046	+3.474
88	+1.396	+1.795	+2.259	+2.684	+3.111
77	+0.900	+1.381	+1.864	+2.339	+2.798
66	+0.422	+0.983	+1.520	+1.995	+2.522
55	+0.156	+0.588	+1.182	+1.686	+2.260
44	+0.072	+0.293	+0.800	+1.365	+1.977
33	0.000	+0.183	+0.531	+1.057	+1.706
22	−0.071	+0.107	+0.400	+0.802	+1.436
AKs	+2.658	+2.958	+3.348	+3.601	+3.873
AQs	+1.861	+2.305	+2.818	+3.179	+3.568
AJs	+1.058	+1.613	+2.267	+2.811	+3.325
ATs	+0.541	+1.011	+1.766	+2.433	+3.123
A9s	+0.217	+0.485	+1.183	+1.896	+2.740
A8s	+0.135	+0.316	+0.806	+1.572	+2.523
A7s	+0.041	+0.223	+0.580	+1.300	+2.292
A6s	−0.075	+0.125	+0.450	+1.060	+2.102
A5s	+0.009	+0.197	+0.514	+1.058	+2.075
A4s	−0.039	+0.099	+0.408	+0.956	+1.950
A3s	−0.075	+0.049	+0.322	+0.876	+1.878
A2s	−0.128	−0.003	+0.260	+0.791	+1.803
KQs	+0.654	+0.805	+1.032	+1.508	+2.519
KJs	+0.434	+0.510	+0.667	+1.177	+2.291
KTs	+0.397	+0.368	+0.461	+0.843	+2.095
K9s	+0.156	+0.152	+0.158	+0.438	+1.719
K8s	−0.037	−0.015	−0.047	+0.226	+1.402
K7s	−0.101	−0.054	−0.035	+0.186	+1.215
K6s	−0.186	−0.115	−0.079	+0.128	+1.076
K5s	−0.263	−0.206	−0.157	+0.079	+0.956
K4s	−0.319	−0.310	−0.263	+0.001	+0.860
K3s	−0.358	−0.362	−0.352	−0.086	+0.789
K2s	−0.409	−0.414	−0.411	−0.169	+0.715
QJs	+0.386	+0.465	+0.530	+0.777	+1.576
QTs	+0.363	+0.370	+0.455	+0.616	+1.404
Q9s	+0.121	+0.154	+0.182	+0.352	+1.023
Q8s	−0.077	−0.024	−0.035	+0.163	+0.726
Q7s	−0.297	−0.221	−0.188	−0.027	+0.488
Q6s	−0.356	−0.258	−0.204	−0.058	+0.458
Q5s	−0.433	−0.348	−0.282	−0.107	+0.393
Q4s	−0.484	−0.447	−0.387	−0.185	+0.334
Q3s	−0.530	−0.505	−0.478	−0.276	+0.257
Q2s	−0.573	−0.549	−0.531	−0.355	+0.185
JTs	+0.348	+0.395	+0.511	+0.627	+1.127
J9s	+0.101	+0.174	+0.237	+0.394	+0.809
J8s	−0.093	0.000	+0.023	+0.203	+0.585
J7s	−0.329	−0.213	−0.144	+0.004	+0.408
J6s	−0.543	−0.413	−0.329	−0.189	+0.244
J5s	−0.590	−0.473	−0.376	−0.209	+0.208
J4s	−0.633	−0.562	−0.473	−0.283	+0.148
J3s	−0.683	−0.624	−0.560	−0.368	+0.078
J2s	−0.729	−0.673	−0.622	−0.453	−0.002
T9s	+0.172	+0.205	+0.299	+0.457	+0.828
T8s	−0.041	+0.027	+0.086	+0.270	+0.627
T7s	−0.270	−0.184	−0.081	+0.070	+0.464
T6s	−0.491	−0.389	−0.271	−0.126	+0.294
T5s	−0.698	−0.620	−0.497	−0.319	+0.099
T4s	−0.717	−0.686	−0.564	−0.362	+0.074
T3s	−0.761	−0.741	−0.651	−0.454	0.000
T2s	−0.815	−0.797	−0.717	−0.539	−0.080
98s	−0.027	+0.068	+0.111	+0.329	+0.669
97s	−0.229	−0.121	−0.038	+0.144	+0.525
96s	−0.444	−0.322	−0.227	−0.057	+0.357
95s	−0.657	−0.555	−0.456	−0.257	+0.154
94s	−0.841	−0.788	−0.701	−0.475	−0.034
93s	−0.846	−0.807	−0.749	−0.522	−0.076
92s	−0.891	−0.853	−0.806	−0.603	−0.152
87s	−0.193	−0.058	+0.019	+0.230	+0.596
86s	−0.403	−0.252	−0.164	+0.036	+0.433
85s	−0.609	−0.480	−0.388	−0.155	+0.236
84s	−0.795	−0.720	−0.638	−0.376	+0.041
83s	−0.979	−0.920	−0.872	−0.609	−0.170
82s	−0.985	−0.926	−0.890	−0.655	−0.212
76s	−0.367	−0.195	−0.070	+0.106	+0.517
75s	−0.575	−0.420	−0.290	−0.077	+0.327
74s	−0.759	−0.663	−0.544	−0.306	+0.127
73s	−0.945	−0.863	−0.782	−0.540	−0.082
72s	−1.122	−1.044	−0.983	−0.766	−0.297
65s	−0.521	−0.344	−0.190	+0.009	+0.414
64s	−0.690	−0.573	−0.430	−0.206	+0.227
63s	−0.887	−0.783	−0.680	−0.449	+0.012
62s	−1.074	−0.971	−0.884	−0.678	−0.206
54s	−0.628	−0.497	−0.336	−0.094	+0.327
53s	−0.808	−0.691	−0.569	−0.321	+0.122
52s	−0.992	−0.878	−0.776	−0.554	−0.095
43s	−0.867	−0.831	−0.694	−0.417	+0.042
42s	−1.044	−1.009	−0.892	−0.648	−0.173
32s	−1.101	−1.084	−1.013	−0.750	−0.257
AKo	+2.406	+2.717	+3.119	+3.393	+3.694
AQo	+1.562	+2.025	+2.555	+2.941	+3.358
AJo	+0.694	+1.274	+1.959	+2.543	+3.088
ATo	+0.137	+0.630	+1.421	+2.137	+2.869
A9o	−0.209	+0.065	+0.798	+1.557	+2.464
A8o	−0.309	−0.124	+0.390	+1.205	+2.223
A7o	−0.415	−0.234	+0.134	+0.906	+1.969
A6o	−0.535	−0.335	0.000	+0.654	+1.767
A5o	−0.438	−0.249	+0.073	+0.650	+1.740
A4o	−0.490	−0.358	−0.044	+0.539	+1.602
A3o	−0.537	−0.417	−0.140	+0.452	+1.524
A2o	−0.592	−0.470	−0.207	+0.364	+1.447
KQo	+0.243	+0.391	+0.617	+1.132	+2.236
KJo	+0.001	+0.066	+0.215	+0.771	+1.984
KTo	−0.043	−0.081	+0.001	+0.421	+1.776
K9o	−0.301	−0.315	−0.319	−0.020	+1.369
K8o	−0.507	−0.499	−0.542	−0.249	+1.035
K7o	−0.571	−0.533	−0.532	−0.289	+0.831
K6o	−0.664	−0.601	−0.580	−0.351	+0.678
K5o	−0.755	−0.703	−0.670	−0.415	+0.545
K4o	−0.805	−0.809	−0.776	−0.495	+0.445
K3o	−0.856	−0.876	−0.880	−0.593	+0.364
K2o	−0.904	−0.922	−0.936	−0.673	+0.292
QJo	−0.031	+0.036	+0.089	+0.356	+1.224
QTo	−0.074	−0.072	0.000	+0.176	+1.029
Q9o	−0.341	−0.319	−0.302	−0.120	+0.622
Q8o	−0.548	−0.507	−0.530	−0.316	+0.303
Q7o	−0.781	−0.714	−0.702	−0.530	+0.040
Q6o	−0.835	−0.746	−0.710	−0.550	+0.013
Q5o	−0.927	−0.849	−0.796	−0.608	−0.060
Q4o	−0.982	−0.955	−0.904	−0.690	−0.127
Q3o	−1.031	−1.019	−1.004	−0.788	−0.206
Q2o	−1.083	−1.070	−1.065	−0.875	−0.285
JTo	−0.083	−0.043	+0.061	+0.190	+0.735
J9o	−0.353	−0.293	−0.241	−0.069	+0.393
J8o	−0.555	−0.476	−0.465	−0.266	+0.155
J7o	−0.796	−0.693	−0.642	−0.480	−0.040
J6o	−1.031	−0.911	−0.846	−0.688	−0.215
J5o	−1.085	−0.974	−0.893	−0.709	−0.250
J4o	−1.139	−1.080	−0.999	−0.790	−0.315
J3o	−1.190	−1.145	−1.099	−0.890	−0.400
J2o	−1.243	−1.199	−1.168	−0.983	−0.485
T9o	−0.287	−0.260	−0.172	+0.001	+0.416
T8o	−0.500	−0.436	−0.386	−0.187	+0.206
T7o	−0.740	−0.659	−0.572	−0.404	+0.027
T6o	−0.980	−0.884	−0.783	−0.619	−0.153
T5o	−1.206	−1.130	−1.023	−0.832	−0.364
T4o	−1.224	−1.200	−1.090	−0.877	−0.397
T3o	−1.271	−1.262	−1.188	−0.972	−0.478
T2o	−1.324	−1.315	−1.252	−1.062	−0.561
98o	−0.486	−0.401	−0.362	−0.133	+0.244
97o	−0.700	−0.598	−0.530	−0.335	+0.086
96o	−0.923	−0.810	−0.725	−0.539	−0.088
95o	−1.157	−1.061	−0.976	−0.761	−0.305
94o	−1.356	−1.317	−1.239	−0.998	−0.514
93o	−1.357	−1.334	−1.291	−1.050	−0.558
92o	−1.412	−1.386	−1.353	−1.137	−0.641
87o	−0.664	−0.542	−0.477	−0.247	+0.157
86o	−0.883	−0.741	−0.661	−0.444	−0.009
85o	−1.112	−0.986	−0.899	−0.652	−0.219
84o	−1.309	−1.245	−1.167	−0.893	−0.430
83o	−1.506	−1.460	−1.425	−1.145	−0.654
82o	−1.514	−1.466	−1.446	−1.191	−0.704
76o	−0.844	−0.676	−0.567	−0.372	+0.077
75o	−1.075	−0.926	−0.810	−0.579	−0.127
74o	−1.270	−1.182	−1.071	−0.813	−0.339
73o	−1.466	−1.399	−1.334	−1.070	−0.568
72o	−1.663	−1.595	−1.551	−1.313	−0.797
65o	−1.009	−0.837	−0.696	−0.479	−0.033
64o	−1.196	−1.088	−0.954	−0.711	−0.236
63o	−1.392	−1.302	−1.212	−0.965	−0.464
62o	−1.599	−1.509	−1.437	−1.213	−0.697
54o	−1.128	−1.000	−0.844	−0.584	−0.124
53o	−1.310	−1.202	−1.096	−0.833	−0.347
52o	−1.513	−1.405	−1.315	−1.079	−0.576
43o	−1.371	−1.348	−1.224	−0.934	−0.432
42o	−1.569	−1.548	−1.443	−1.180	−0.660
32o	−1.623	−1.620	−1.564	−1.286	−0.749

Reading the chart is the easy half. The trainer deals you real hands at 17 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 6-max at 17 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.