Approximate Equilibrium Play in 4-Max Shove-or-Fold Poker

Abstract

We report validated shove/call ranges for 4-max all-in-or-fold poker at 8BB effective stacks, produced by a delayed-linear weighted-averaging MCCFR solver trained from iteration zero to 4,000,000 across two independent seeds and merged through the production adapter. The resulting policy (v2) passed a four-stage adoption protocol, including a fresh whole-game comparison against the prior production backend and an untouched structural holdout. These ranges are a validated best estimate, not a formal proof of Nash equilibrium; a frozen stress-cell regression returned a mixed result, retained here as adverse evidence rather than smoothed over. Corrections and feedback are welcome.

Keywords

• 4-max poker
• all-in-or-fold
• MCCFR
• weighted averaging
• Nash-equilibrium approximation