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How Far Are LLMs from Professional Poker Players? Revisiting Game-Theoretic Reasoning with Agentic Tool Use

Minhua Lin, Enyan Dai, Hui Liu, Xianfeng Tang, Yuliang Yan, Zhenwei Dai, Jingying Zeng, Zhiwei Zhang, Fali Wang, Hongcheng Gao, Chen Luo, Xiang Zhang, Qi He, Suhang Wang

TL;DR

The paper systematically evaluates large language models (LLMs) in poker to assess their ability to perform game-theoretic reasoning under uncertainty. It reveals consistent gaps—heuristic biases, factual misunderstandings, and a gap between reasoning and action—and shows that internal fine-tuning (BC-RIRL) yields only modest gains. To address this, the authors introduce ToolPoker, a tool-integrated reasoning framework that centralizes solver calls to guarantee GTO actions while producing professional-style explanations. Empirical results demonstrate that ToolPoker achieves state-of-the-art gameplay among LLM-based methods and generates reasoning traces that closely reflect game-theoretic principles, highlighting the value of external tool use for high-stakes strategic tasks.

Abstract

As Large Language Models (LLMs) are increasingly applied in high-stakes domains, their ability to reason strategically under uncertainty becomes critical. Poker provides a rigorous testbed, requiring not only strong actions but also principled, game-theoretic reasoning. In this paper, we conduct a systematic study of LLMs in multiple realistic poker tasks, evaluating both gameplay outcomes and reasoning traces. Our analysis reveals LLMs fail to compete against traditional algorithms and identifies three recurring flaws: reliance on heuristics, factual misunderstandings, and a "knowing-doing" gap where actions diverge from reasoning. An initial attempt with behavior cloning and step-level reinforcement learning improves reasoning style but remains insufficient for accurate game-theoretic play. Motivated by these limitations, we propose ToolPoker, a tool-integrated reasoning framework that combines external solvers for GTO-consistent actions with more precise professional-style explanations. Experiments demonstrate that ToolPoker achieves state-of-the-art gameplay while producing reasoning traces that closely reflect game-theoretic principles.

How Far Are LLMs from Professional Poker Players? Revisiting Game-Theoretic Reasoning with Agentic Tool Use

TL;DR

The paper systematically evaluates large language models (LLMs) in poker to assess their ability to perform game-theoretic reasoning under uncertainty. It reveals consistent gaps—heuristic biases, factual misunderstandings, and a gap between reasoning and action—and shows that internal fine-tuning (BC-RIRL) yields only modest gains. To address this, the authors introduce ToolPoker, a tool-integrated reasoning framework that centralizes solver calls to guarantee GTO actions while producing professional-style explanations. Empirical results demonstrate that ToolPoker achieves state-of-the-art gameplay among LLM-based methods and generates reasoning traces that closely reflect game-theoretic principles, highlighting the value of external tool use for high-stakes strategic tasks.

Abstract

As Large Language Models (LLMs) are increasingly applied in high-stakes domains, their ability to reason strategically under uncertainty becomes critical. Poker provides a rigorous testbed, requiring not only strong actions but also principled, game-theoretic reasoning. In this paper, we conduct a systematic study of LLMs in multiple realistic poker tasks, evaluating both gameplay outcomes and reasoning traces. Our analysis reveals LLMs fail to compete against traditional algorithms and identifies three recurring flaws: reliance on heuristics, factual misunderstandings, and a "knowing-doing" gap where actions diverge from reasoning. An initial attempt with behavior cloning and step-level reinforcement learning improves reasoning style but remains insufficient for accurate game-theoretic play. Motivated by these limitations, we propose ToolPoker, a tool-integrated reasoning framework that combines external solvers for GTO-consistent actions with more precise professional-style explanations. Experiments demonstrate that ToolPoker achieves state-of-the-art gameplay while producing reasoning traces that closely reflect game-theoretic principles.
Paper Structure (63 sections, 11 equations, 3 figures, 22 tables, 1 algorithm)

This paper contains 63 sections, 11 equations, 3 figures, 22 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Backgrounds and Preliminaries
  3. Are LLMs Good at Poker? A Preliminary Analysis
  4. Experimental Setup
  5. Comparison with Traditional Method
  6. In-depth Analysis: Decomposing Reasoning Flaws of LLMs
  7. Can We Improve LLMs in Poker? Failures and Insights
  8. Behavior Cloning
  9. Regret-Inspired RL Fine-Tuning
  10. Experiment Analysis
  11. ToolPoker: Game-theoretic Reasoning with Agentic Tool Use
  12. Tool-Integrated Game-theoretic Reasoning in Poker
  13. Training Algorithm
  14. Experimental Results
  15. Related Work
  16. ...and 48 more sections

Figures (3)

  • Figure 1: Illustration of $\textnormal{ToolPoker}$ and its advantages over LLMs using internal policies.
  • Figure 2: Results for $\textnormal{ToolPoker}$: (a) and (b) present reasoning analysis in Leduc Hold’em and Limit Texas Hold’em; (c) and (d) show ablation studies on gameplay and reasoning in Leduc Hold’em.
  • Figure 3: Reward visualization of ToolPoker in Leduc Hold'em. Qwen2.5-7B-Instruct is the backbone model. (a) is the overall composite reward $R$, (b)-(d) shows the $R_{\text{answer}}$, $R_{\text{format}}$ and $R_{\text{tool}}$, respectively.

Theorems & Definitions (1)

  • Definition B.1: Nash Equilibrium nash1950equilibrium