Solving Pasur Using GPU-Accelerated Counterfactual Regret Minimization

TL;DR

This paper presents a GPU-accelerated framework for simulating the complex card game Pasur, enabling the computation of near-Nash equilibria using CFR and facilitating strategy prediction and game value estimation.

Contribution

It introduces a novel CUDA-based approach for efficiently handling Pasur's large game tree and rule complexity, advancing equilibrium computation in imperfect-information games.

Findings

Constructed a game tree with over 10^9 nodes.

Successfully computed near-Nash equilibria for Pasur.

Demonstrated scalable GPU-based simulation and strategy prediction.

Abstract

Pasur is a fishing card game played over six rounds and is played similarly to games such as Cassino and Scopa, and Bastra. This paper introduces a CUDA-accelerated computational framework for simulating Pasur, emphasizing efficient memory management. We use our framework to compute near-Nash equilibria via Counterfactual Regret Minimization (CFR), a well-known algorithm for solving large imperfect-information games. Solving Pasur presents unique challenges due to its intricate rules and the large size of its game tree. We handle rule complexity using PyTorch CUDA tensors and to address the memory-intensive nature of the game, we decompose the game tree into two key components: (1) actual game states, and (2) inherited scores from previous rounds. We construct the Full Game Tree by pairing card states with accumulated scores in the Unfolding Process. This design reduces memory overhead by storing only essential strategy values and node connections. To further manage computational complexity, we apply a round-by-round backward training strategy, starting from the final round and recursively propagating average utilities to earlier stages. Our approach constructs the complete game tree, which on average consists of over $10^9$ nodes. We provide detailed implementation snippets. After computing a near-Nash equilibrium strategy, we train a tree-based model to predict these strategies for use during gameplay. We then estimate the fair value of each deck through large-scale self-play between equilibrium strategies by simulating, for instance, 10,000 games per matchup, executed in parallel using GPU acceleration. Similar frameworks can be extended to other reinforcement learning algorithms where the action tree naturally decomposes into multiple rounds such as turn-based strategy games or sequential trading decisions in financial markets.