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

arXiv: https://arxiv.org/abs/2602.00528 · HTML: https://mlsanity.com/paper/2602.00528/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 31 of its 58 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 30 of 31)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025)
- [FreshLLMs: Refreshing Large Language Models with Search Engine Augmentation](https://mlsanity.com/paper/2310.03214/) (2023)
- [DeepResearcher: Scaling Deep Research via Reinforcement Learning in Real-world Environments](https://mlsanity.com/paper/2504.03160/) (2025)
- [WebAgent-R1: Training Web Agents via End-to-End Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2505.16421/) (2025)
- [Deep Reinforcement Learning from Self-Play in Imperfect-Information Games](https://mlsanity.com/paper/1603.01121/) (2016)
- [GameBench: Evaluating Strategic Reasoning Abilities of LLM Agents](https://mlsanity.com/paper/2406.06613/) (2024)
- [Solving Large Imperfect Information Games Using CFR+](https://mlsanity.com/paper/1407.5042/) (2014)
- [Suspicion-Agent: Playing Imperfect Information Games with Theory of Mind Aware GPT-4](https://mlsanity.com/paper/2309.17277/) (2023)
- [MATHSENSEI: A Tool-Augmented Large Language Model for Mathematical Reasoning](https://mlsanity.com/paper/2402.17231/) (2024)
- [A Survey on Self-play Methods in Reinforcement Learning](https://mlsanity.com/paper/2408.01072/) (2024)
- [SimPER: A Minimalist Approach to Preference Alignment without Hyperparameters](https://mlsanity.com/paper/2502.00883/) (2025)
- [Single Deep Counterfactual Regret Minimization](https://mlsanity.com/paper/1901.07621/) (2019)
- [Are ChatGPT and GPT-4 Good Poker Players? -- A Pre-Flop Analysis](https://mlsanity.com/paper/2308.12466/) (2023)
- [PokerGPT: An End-to-End Lightweight Solver for Multi-Player Texas Hold'em via Large Language Model](https://mlsanity.com/paper/2401.06781/) (2024)
- [R1-Code-Interpreter: LLMs Reason with Code via Supervised and Multi-stage Reinforcement Learning](https://mlsanity.com/paper/2505.21668/) (2025)
- [LLM4Causal: Democratized Causal Tools for Everyone via Large Language Model](https://mlsanity.com/paper/2312.17122/) (2023)
- [Beyond Correctness: Rewarding Faithful Reasoning in Retrieval-Augmented Generation](https://mlsanity.com/paper/2510.13272/) (2025)
- [Can Large Language Models Master Complex Card Games?](https://mlsanity.com/paper/2509.01328/) (2025)

## Built on by (most cited first, 7 of 7)

- [Harness Updating Is Not Harness Benefit: Disentangling Evolution Capabilities in Self-Evolving LLM Agents](https://mlsanity.com/paper/2605.30621/) (2026)
- [MemMA: Coordinating the Memory Cycle through Multi-Agent Reasoning and In-Situ Self-Evolution](https://mlsanity.com/paper/2603.18718/) (2026)
- [PokerSkill: LLMs Can Play Expert-Level Poker without Training or Solvers](https://mlsanity.com/paper/2605.30094/) (2026)
- [Solver-Guided Reasoning for Mixed-Equilibrium Strategies](https://mlsanity.com/paper/2608.06741/) (2026)
- [Abstraction Agent](https://mlsanity.com/paper/2609.04303/) (2026)
- [GENSTRAT: Toward a Science of Strategic Reasoning in Large Language Models](https://mlsanity.com/paper/2605.23238/) (2026)
- [Doing What They Say, Not What They Reason: Locating the Faithfulness Gap in LLM Agents](https://mlsanity.com/paper/2606.00476/) (2026)

## Abstract (arXiv)

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.