Nash Push/Fold Chart

Also known as: Nash chart, Nash push/fold ranges, ICM Nash chart

Precomputed equilibrium shove and call ranges for heads-up and short-stacked spots, by stack depth and position.

The Nash push/fold chart is the Nash equilibrium solution to the shove-or-call game at short stacks. For a given stack-to-blind ratio it gives the exact range each position can profitably open-jam and the exact range the blinds can call — neither player can deviate and gain, by definition of equilibrium.

The charts are solved in Chip EV (cEV), so they are the correct baseline only when ICM pressure is low. Near a bubble or pay jump you must tighten calls by the risk premium — covered stacks call far tighter than Nash, and short stacks shove slightly tighter against likely callers. Tools like HoldemResources and ICMIZER produce ICM-adjusted versions on demand.

Treat Nash as the chip-EV reference frame for push/fold, then layer pool reads and ICM on top — pure Nash assumes a perfectly balanced opponent, which the live and online pools rarely are.

Example

At 10bb on the button, the Nash open-jam range is roughly 50-55% of hands; the big blind's Nash calling range is around 27%. On a satellite bubble, the BB's correct call collapses to maybe 8-10% of hands — the risk premium overrides the chip-EV Nash number entirely.