Push/fold charts (heads-up Nash)

Heads-up jam-or-fold Nash across 10 stacks (2-20bb): at 10bb the SB jams 52.9% and the BB calls 34.2%. Every number is solved on our exhaustive matrix with per-stack convergence gap ≤0.033bb.

SB jam range (first in)

Jam / Call（702 combos, 52.9%） Fold

BB call range (facing jam)

Jam / Call（454 combos, 34.2%） Fold

Per-stack data (text version)

2bb — SB jam 89.4% / BB call 100.0%

SB jam	1186 / 1,326 combos（89.4%）
BB call	1326 / 1,326 combos（100.0%）
Convergence gap	0 bb

3bb — SB jam 76.8% / BB call 91.9%

SB jam	1018 / 1,326 combos（76.8%）
BB call	1218 / 1,326 combos（91.9%）
Convergence gap	0.00003 bb

4bb — SB jam 73.8% / BB call 74.1%

SB jam	978 / 1,326 combos（73.8%）
BB call	982 / 1,326 combos（74.1%）
Convergence gap	0 bb

5bb — SB jam 71.9% / BB call 62.0%

SB jam	954 / 1,326 combos（71.9%）
BB call	822 / 1,326 combos（62.0%）
Convergence gap	0.00005 bb

6bb — SB jam 65.9% / BB call 50.8%

SB jam	874 / 1,326 combos（65.9%）
BB call	674 / 1,326 combos（50.8%）
Convergence gap	0.00684 bb

8bb — SB jam 57.2% / BB call 40.3%

SB jam	758 / 1,326 combos（57.2%）
BB call	534 / 1,326 combos（40.3%）
Convergence gap	0.02073 bb

10bb — SB jam 52.9% / BB call 34.2%

SB jam	702 / 1,326 combos（52.9%）
BB call	454 / 1,326 combos（34.2%）
Convergence gap	0.01925 bb

12bb — SB jam 47.8% / BB call 30.0%

SB jam	634 / 1,326 combos（47.8%）
BB call	398 / 1,326 combos（30.0%）
Convergence gap	0.02159 bb

15bb — SB jam 41.2% / BB call 25.2%

SB jam	546 / 1,326 combos（41.2%）
BB call	334 / 1,326 combos（25.2%）
Convergence gap	0.03222 bb

20bb — SB jam 36.3% / BB call 19.9%

SB jam	482 / 1,326 combos（36.3%）
BB call	264 / 1,326 combos（19.9%）
Convergence gap	0.01989 bb

Methodology

Scenario: heads-up SB vs BB where actions are restricted to jam-or-fold (SB) and call-or-fold (BB); ChipEV, no ICM, no rake. Solved by best-response iteration on our exhaustive 169×169 class-average equity matrix with card-removal conditional combo weights; cycles are resolved for boundary hands against the averaged opponent strategy. Each stack records its exploitability (best-response gain in bb/hand) as convergence evidence — all ≤0.033bb. Reproduce with scripts/gen-push-fold.mjs.

Educational use: post-session study tool, not real-time assistance (RTA); not betting advice. Beyond ~20bb, jam-or-fold stops being a reasonable simplification.

Data version 2026-07-04; source: app/data/push-fold.json

Cite this page: Pailiku, “Push/fold charts (heads-up Nash)”, pailiku.com/push-fold (2026-07-04).

FAQ

How wide should the SB jam at 10bb heads-up?

Nash solution here: at 10bb the SB jams 52.9% (702/1,326 combos) and the BB calls 34.2%. At 5bb the jam widens to 71.9%; at 20bb it narrows to 36.3%.

Do these match SnapShove/HoldemResources?

Same jam-or-fold model family with matching magnitudes; boundary hands may differ by a few tenths of a percent due to class-average equities and tie-breaking. Our methodology and re-computation script are fully published, with per-stack convergence gaps.

Can I use this table multiway?

Not directly. This is heads-up ChipEV Nash; multiway and final tables need ICM and positional adjustments — pair it with the ICM calculator; a multiway approximation is planned.