6-max push/fold at 24 bb

At 24 big blinds with a 1 bb big-blind ante, the equilibrium open-shoves 11.7% of hands from UTG, widening to 49.3% 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 11.7% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3332sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

55+, A9s+, K9s+, QTs+, JTs, AJo+, KQo

HJ

shoves 14.3% first in

AAAKsAQsAJsATsA9sA8sA7sA6sA5s41%A4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJo46%QJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7oK7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3372%32sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

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

CO

shoves 19.5% first in

22+, A3s+, K9s+, Q9s+, J8s+, T8s+, 98s, ATo+, KJo+, QJo

BTN

shoves 29.8% first in

22+, A2s+, K7s+, Q8s+, J8s+, T8s+, 97s+, 87s, 76s, A4o+, KTo+, QTo+, JTo

SB

shoves 49.3% first in

22+, A2s+, K2s+, Q4s+, J5s+, T6s+, 95s+, 85s+, 74s+, 64s+, 54s, A2o+, K5o+, Q9o+, J8o+, T8o+, 98o, 87o

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 16.7% against a BTN shove of 29.8%

AAAKsAQsAJsATsA9sA8sA7sA6sA5sA4sA3sA2sAKoKKKQsKJsKTsK9sK8sK7sK6sK5sK4sK3sK2sAQoKQoQQQJsQTsQ9sQ8sQ7sQ6sQ5sQ4sQ3sQ2sAJoKJoQJoJJJTsJ9sJ8sJ7sJ6sJ5sJ4sJ3sJ2sAToKToQToJToTTT9sT8sT7sT6sT5sT4sT3sT2sA9oK9oQ9oJ9oT9o9998s97s96s95s94s93s92sA8oK8oQ8oJ8oT8o98o8887s86s85s84s83s82sA7o40%K7oQ7oJ7oT7o97o87o7776s75s74s73s72sA6oK6oQ6oJ6oT6o96o86o76o6665s64s63s62sA5oK5oQ5oJ5oT5o95o85o75o65o5554s53s52sA4oK4oQ4oJ4oT4o94o84o74o64o54o4443s42sA3oK3oQ3oJ3oT3o93o83o73o63o53o43o3351%32sA2oK2oQ2oJ2oT2o92o82o72o62o52o42o32o22

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)
33	51%	+0.001
A4s	6%	−0.001
A7o	40%	+0.001
KJo	100%	+0.085
QJs	100%	+0.141
A3s	0%	−0.249
A5s	100%	+0.405
A6s	100%	+0.493
A2s	0%	−0.518
KTs	100%	+0.521

33+, A5s+, KTs+, QJs, A8o+, KJo+

Every calling range at 24 bb

Spot	Calls	Range
HJ vs UTG	5.8%	88+, AJs+, AQo+
CO vs UTG	5.8%	88+, AJs+, AQo+
BTN vs UTG	5.8%	88+, AJs+, AQo+
SB vs UTG	5.9%	88+, AJs+, AQo+
BB vs UTG	5.9%	88+, AJs+, AQo+
CO vs HJ	6.9%	77+, AJs+, AJo+
BTN vs HJ	6.9%	77+, AJs+, AJo+
SB vs HJ	7.7%	77+, ATs+, KQs, AJo+
BB vs HJ	8.3%	66+, ATs+, KQs, AJo+
BTN vs CO	10.0%	55+, A9s+, KQs, ATo+
SB vs CO	10.0%	55+, A9s+, KQs, ATo+
BB vs CO	11.4%	55+, A8s+, KJs+, ATo+, KQo
SB vs BTN	14.9%	44+, A5s+, KTs+, A8o+, KQo
BB vs BTN	16.7%	33+, A5s+, KTs+, QJs, A8o+, KJo+
BB vs SB	29.7%	22+, A2s+, K6s+, Q9s+, JTs, A2o+, K8o+, QTo+

All 169 hands at 24 bb: shove EV by seat

Hand	UTG	HJ	CO	BTN	SB
AA	+5.653	+5.731	+5.953	+6.083	+6.176
KK	+4.535	+4.761	+5.049	+5.176	+5.397
QQ	+3.421	+3.853	+4.298	+4.563	+4.875
JJ	+2.549	+2.989	+3.586	+3.982	+4.460
TT	+1.850	+2.336	+2.927	+3.478	+4.034
99	+1.061	+1.661	+2.281	+2.903	+3.555
88	+0.388	+1.117	+1.829	+2.428	+3.195
77	+0.025	+0.540	+1.380	+2.021	+2.882
66	+0.028	+0.205	+0.948	+1.662	+2.587
55	+0.022	+0.142	+0.517	+1.309	+2.313
44	−0.034	+0.080	+0.234	+0.927	+1.990
33	−0.114	+0.003	+0.161	+0.668	+1.661
22	−0.191	−0.073	+0.082	+0.545	+1.332
AKs	+2.374	+2.652	+3.031	+3.529	+4.029
AQs	+1.217	+1.721	+2.329	+3.001	+3.676
AJs	+0.505	+0.875	+1.591	+2.472	+3.368
ATs	+0.285	+0.418	+0.946	+1.973	+3.081
A9s	+0.037	+0.154	+0.422	+1.385	+2.605
A8s	−0.067	+0.071	+0.286	+1.000	+2.305
A7s	−0.165	−0.039	+0.191	+0.750	+2.030
A6s	−0.178	−0.142	+0.085	+0.598	+1.796
A5s	−0.025	−0.001	+0.158	+0.654	+1.753
A4s	−0.069	−0.044	+0.055	+0.551	+1.624
A3s	−0.107	−0.081	+0.017	+0.468	+1.541
A2s	−0.157	−0.135	−0.038	+0.410	+1.447
KQs	+0.448	+0.619	+0.811	+1.201	+2.104
KJs	+0.416	+0.440	+0.536	+0.815	+1.832
KTs	+0.312	+0.416	+0.393	+0.567	+1.575
K9s	0.000	+0.140	+0.183	+0.247	+1.112
K8s	−0.226	−0.070	0.000	+0.033	+0.777
K7s	−0.291	−0.148	−0.048	+0.037	+0.676
K6s	−0.277	−0.221	−0.115	−0.008	+0.609
K5s	−0.289	−0.247	−0.214	−0.085	+0.522
K4s	−0.343	−0.299	−0.324	−0.183	+0.432
K3s	−0.382	−0.339	−0.365	−0.272	+0.342
K2s	−0.432	−0.392	−0.420	−0.331	+0.249
QJs	+0.284	+0.367	+0.496	+0.624	+1.253
QTs	+0.187	+0.355	+0.390	+0.545	+1.020
Q9s	−0.119	+0.081	+0.180	+0.273	+0.638
Q8s	−0.344	−0.132	−0.015	+0.046	+0.433
Q7s	−0.567	−0.374	−0.226	−0.119	+0.266
Q6s	−0.524	−0.418	−0.270	−0.135	+0.251
Q5s	−0.541	−0.447	−0.367	−0.212	+0.180
Q4s	−0.584	−0.491	−0.472	−0.310	+0.089
Q3s	−0.634	−0.539	−0.520	−0.401	−0.006
Q2s	−0.678	−0.584	−0.565	−0.454	−0.096
JTs	+0.229	+0.331	+0.408	+0.598	+0.936
J9s	−0.079	+0.051	+0.193	+0.325	+0.672
J8s	−0.328	−0.162	+0.003	+0.100	+0.486
J7s	−0.556	−0.415	−0.226	−0.077	+0.305
J6s	−0.670	−0.614	−0.438	−0.265	+0.121
J5s	−0.645	−0.611	−0.505	−0.313	+0.082
J4s	−0.686	−0.650	−0.599	−0.403	−0.008
J3s	−0.737	−0.703	−0.653	−0.488	−0.095
J2s	−0.783	−0.750	−0.703	−0.550	−0.193
T9s	−0.058	+0.128	+0.219	+0.391	+0.747
T8s	−0.323	−0.108	+0.024	+0.167	+0.565
T7s	−0.541	−0.354	−0.201	−0.010	+0.383
T6s	−0.658	−0.562	−0.420	−0.205	+0.198
T5s	−0.809	−0.726	−0.664	−0.436	−0.018
T4s	−0.821	−0.739	−0.735	−0.494	−0.074
T3s	−0.871	−0.785	−0.781	−0.581	−0.167
T2s	−0.926	−0.843	−0.838	−0.647	−0.262
98s	−0.372	−0.117	+0.072	+0.198	+0.619
97s	−0.563	−0.335	−0.130	+0.038	+0.457
96s	−0.663	−0.535	−0.344	−0.156	+0.266
95s	−0.811	−0.700	−0.591	−0.389	+0.042
94s	−0.997	−0.884	−0.837	−0.631	−0.193
93s	−1.008	−0.891	−0.843	−0.677	−0.245
92s	−1.050	−0.937	−0.891	−0.734	−0.339
87s	−0.565	−0.307	−0.070	+0.096	+0.557
86s	−0.660	−0.506	−0.277	−0.092	+0.370
85s	−0.796	−0.662	−0.518	−0.319	+0.150
84s	−0.986	−0.848	−0.772	−0.566	−0.086
83s	−1.182	−1.041	−0.967	−0.804	−0.329
82s	−1.188	−1.046	−0.975	−0.821	−0.384
76s	−0.663	−0.482	−0.221	+0.001	+0.459
75s	−0.793	−0.634	−0.461	−0.222	+0.251
74s	−0.985	−0.822	−0.716	−0.475	+0.006
73s	−1.178	−1.016	−0.912	−0.717	−0.233
72s	−1.372	−1.203	−1.102	−0.922	−0.480
65s	−0.604	−0.587	−0.385	−0.120	+0.350
64s	−0.778	−0.754	−0.627	−0.358	+0.120
63s	−0.991	−0.962	−0.832	−0.612	−0.129
62s	−1.195	−1.158	−1.030	−0.821	−0.377
54s	−0.598	−0.601	−0.550	−0.259	+0.225
53s	−0.804	−0.794	−0.740	−0.497	−0.010
52s	−1.003	−0.988	−0.935	−0.709	−0.261
43s	−0.854	−0.843	−0.895	−0.618	−0.113
42s	−1.050	−1.031	−1.082	−0.822	−0.361
32s	−1.109	−1.093	−1.140	−0.943	−0.466
AKo	+2.102	+2.389	+2.778	+3.300	+3.829
AQo	+0.875	+1.404	+2.035	+2.736	+3.447
AJo	+0.092	+0.489	+1.235	+2.165	+3.109
ATo	−0.142	−0.007	+0.545	+1.628	+2.802
A9o	−0.398	−0.285	−0.019	+0.999	+2.291
A8o	−0.525	−0.386	−0.175	+0.582	+1.961
A7o	−0.641	−0.507	−0.285	+0.301	+1.661
A6o	−0.651	−0.621	−0.395	+0.144	+1.414
A5o	−0.475	−0.458	−0.307	+0.208	+1.367
A4o	−0.522	−0.504	−0.423	+0.091	+1.229
A3o	−0.570	−0.554	−0.469	−0.002	+1.135
A2o	−0.622	−0.609	−0.526	−0.064	+1.039
KQo	+0.025	+0.195	+0.377	+0.781	+1.748
KJo	−0.024	−0.002	+0.072	+0.359	+1.445
KTo	−0.136	−0.038	−0.073	+0.100	+1.178
K9o	−0.465	−0.332	−0.305	−0.240	+0.672
K8o	−0.700	−0.553	−0.506	−0.472	+0.318
K7o	−0.782	−0.635	−0.547	−0.470	+0.212
K6o	−0.765	−0.718	−0.622	−0.520	+0.135
K5o	−0.787	−0.754	−0.733	−0.610	+0.032
K4o	−0.830	−0.796	−0.847	−0.707	−0.061
K3o	−0.879	−0.848	−0.901	−0.812	−0.160
K2o	−0.927	−0.899	−0.950	−0.868	−0.250
QJo	−0.146	−0.063	+0.051	+0.174	+0.837
QTo	−0.255	−0.095	−0.072	+0.080	+0.579
Q9o	−0.593	−0.398	−0.315	−0.222	+0.167
Q8o	−0.830	−0.620	−0.518	−0.460	−0.055
Q7o	−1.076	−0.876	−0.741	−0.645	−0.246
Q6o	−1.023	−0.918	−0.778	−0.653	−0.252
Q5o	−1.041	−0.955	−0.890	−0.739	−0.330
Q4o	−1.091	−1.004	−1.005	−0.838	−0.427
Q3o	−1.137	−1.054	−1.057	−0.940	−0.528
Q2o	−1.190	−1.108	−1.110	−1.000	−0.628
JTo	−0.223	−0.117	−0.047	+0.136	+0.493
J9o	−0.554	−0.421	−0.295	−0.164	+0.202
J8o	−0.812	−0.642	−0.492	−0.398	+0.005
J7o	−1.058	−0.902	−0.726	−0.586	−0.194
J6o	−1.184	−1.127	−0.957	−0.796	−0.389
J5o	−1.160	−1.125	−1.027	−0.843	−0.429
J4o	−1.208	−1.174	−1.142	−0.941	−0.522
J3o	−1.262	−1.227	−1.194	−1.041	−0.626
J2o	−1.319	−1.283	−1.251	−1.110	−0.733
T9o	−0.536	−0.348	−0.268	−0.092	+0.284
T8o	−0.797	−0.587	−0.459	−0.316	+0.099
T7o	−1.047	−0.847	−0.698	−0.514	−0.101
T6o	−1.169	−1.077	−0.936	−0.730	−0.301
T5o	−1.322	−1.252	−1.196	−0.976	−0.537
T4o	−1.335	−1.263	−1.274	−1.034	−0.596
T3o	−1.387	−1.313	−1.324	−1.132	−0.695
T2o	−1.442	−1.368	−1.380	−1.196	−0.795
98o	−0.845	−0.593	−0.419	−0.286	+0.148
97o	−1.056	−0.823	−0.630	−0.465	−0.032
96o	−1.164	−1.037	−0.855	−0.666	−0.228
95o	−1.329	−1.219	−1.121	−0.922	−0.470
94o	−1.527	−1.417	−1.394	−1.181	−0.725
93o	−1.527	−1.419	−1.396	−1.234	−0.782
92o	−1.583	−1.477	−1.451	−1.296	−0.884
87o	−1.062	−0.797	−0.575	−0.412	+0.069
86o	−1.160	−1.011	−0.789	−0.601	−0.122
85o	−1.311	−1.182	−1.048	−0.844	−0.356
84o	−1.515	−1.379	−1.323	−1.108	−0.611
83o	−1.728	−1.587	−1.533	−1.371	−0.871
82o	−1.730	−1.595	−1.539	−1.390	−0.930
76o	−1.171	−0.984	−0.725	−0.509	−0.031
75o	−1.313	−1.155	−0.990	−0.756	−0.257
74o	−1.513	−1.349	−1.263	−1.013	−0.510
73o	−1.724	−1.556	−1.473	−1.283	−0.773
72o	−1.937	−1.763	−1.678	−1.504	−1.036
65o	−1.114	−1.101	−0.901	−0.639	−0.149
64o	−1.305	−1.285	−1.168	−0.895	−0.394
63o	−1.517	−1.490	−1.376	−1.160	−0.657
62o	−1.739	−1.707	−1.593	−1.389	−0.922
54o	−1.113	−1.119	−1.079	−0.780	−0.274
53o	−1.312	−1.311	−1.274	−1.039	−0.532
52o	−1.535	−1.526	−1.488	−1.264	−0.793
43o	−1.368	−1.364	−1.438	−1.162	−0.637
42o	−1.584	−1.574	−1.648	−1.387	−0.899
32o	−1.640	−1.632	−1.702	−1.511	−1.010

Reading the chart is the easy half. The trainer deals you real hands at 24 bb in a seat you choose and prices every wrong shove or call in big blinds.

Drill 6-max at 24 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 0.017 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.