Real-Time Parallel Counterfactual Regret Minimization

TL;DR

This paper introduces Parallel CFR, a novel parallelization framework for real-time depth-limited CFR solving in large imperfect-information games, achieving significant speedups on a single desktop device.

Contribution

The paper presents the first parallelization framework for real-time CFR that integrates pruning, abstraction, and neural network inference, enabling faster decision-making in complex games.

Findings

Achieves 3.3-3.4x speedup over single-threaded CFR

Per-iteration time of approximately 47-54 ms on large game trees

Operates efficiently on a single desktop device, enabling hundreds of CFR iterations within real-time constraints

Abstract

Counterfactual Regret Minimization (CFR) is the dominant algorithmic family for solving large imperfect-information games, underpinning breakthroughs such as Libratus and Pluribus in No-Limit Texas Hold'em poker. In real-time game-playing systems, the solver must compute a near-equilibrium strategy within a strict time budget of only a few seconds per decision, and the number of CFR iterations completed in this window directly determines play strength. We present \textbf{Parallel CFR}, the first parallelization framework for real-time depth-limited CFR solving that seamlessly integrates pruning, abstraction, and advanced CFR variants. We decompose each CFR iteration into a pipeline of seven stages and identify two orthogonal dimensions of parallelism: \emph{by information set} and \emph{by tree node}. Leaf node evaluation is offloaded to GPUs via batched neural network inference, creating a heterogeneous CPU--GPU pipeline. Experiments on Heads-Up No-Limit Texas Hold'em demonstrate that Parallel CFR achieves $3.3$--$3.4\times$ speedup over the single-threaded baseline on postflop streets, with per-iteration time of ${\sim}47$--$54$~ms on a depth-limited game tree with over $1$ billion histories. All experiments run on a single desktop-class device (NVIDIA DGX Spark), enabling hundreds of CFR iterations within a typical real-time decision budget without requiring datacenter-scale infrastructure.