Evaluating Model-Free Policy Optimization in Masked-Action Environments via an Exact Blackjack Oracle

TL;DR

This paper evaluates model-free policy optimization methods in a rigorously defined blackjack environment with dynamic action masking, comparing their sample efficiency and policy accuracy against an exact dynamic programming oracle.

Contribution

It introduces a benchmark for discrete stochastic control with dynamic masking and compares the effectiveness of three model-free optimizers against an exact oracle.

Findings

REINFORCE outperformed other methods in sample efficiency.

All methods showed significant cell-conditional regret.

Optimal bet sizing collapses to minimum without counting, increasing volatility.

Abstract

Infinite-shoe casino blackjack provides a rigorous, exactly verifiable benchmark for discrete stochastic control under dynamically masked actions. Under a fixed Vegas-style ruleset (S17, 3:2 payout, dealer peek, double on any two, double after split, resplit to four), an exact dynamic programming (DP) oracle was derived over 4,600 canonical decision cells. This oracle yielded ground-truth action values, optimal policy labels, and a theoretical expected value (EV) of -0.00161 per hand. To evaluate sample-efficient policy recovery, three model-free optimizers were trained via simulated interaction: masked REINFORCE with a per-cell exponential moving average baseline, simultaneous perturbation stochastic approximation (SPSA), and the cross-entropy method (CEM). REINFORCE was the most sample-efficient, achieving a 46.37% action-match rate and an EV of -0.04688 after 10^6 hands, outperforming CEM (39.46%, 7.5x10^6 evaluations) and SPSA (38.63%, 4.8x10^6 evaluations). However, all methods exhibited substantial cell-conditional regret, indicating persistent policy-level errors despite smooth reward convergence. This gap shows that tabular environments with severe state-visitation sparsity and dynamic action masking remain challenging, while aggregate reward curves can obscure critical local failures. As a negative control, it was proven and empirically confirmed that under i.i.d. draws without counting, optimal bet sizing collapses to the table minimum. In addition, larger wagers strictly increased volatility and ruin without improving expectation. These results highlight the need for exact oracles and negative controls to avoid mistaking stochastic variability for genuine algorithmic performance.