# Grounded Chess Reasoning in Language Models via Master Distillation

arXiv: https://arxiv.org/abs/2603.20510 · HTML: https://mlsanity.com/paper/2603.20510/

## Key facts

- Cited by 5 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 19 of its 51 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 19 of 19)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [WebSailor: Navigating Super-human Reasoning for Web Agent](https://mlsanity.com/paper/2507.02592/) (2025)
- [Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs](https://mlsanity.com/paper/2402.14740/) (2024)
- [The Chess Transformer: Mastering Play using Generative Language Models](https://mlsanity.com/paper/2008.04057/) (2020)
- [Mastering Chess with a Transformer Model](https://mlsanity.com/paper/2409.12272/) (2024)
- [Can Large Language Models Develop Strategic Reasoning? Post-training Insights from Learning Chess](https://mlsanity.com/paper/2507.00726/) (2025)
- [ChessQA: Evaluating Large Language Models for Chess Understanding](https://mlsanity.com/paper/2510.23948/) (2025)

## Built on by (most cited first, 5 of 5)

- [SafeGEO: Understanding Generative Engine Optimization Risks in Recommendation Agents](https://mlsanity.com/paper/2606.28356/) (2026)
- [GAMBIT: A Three-Mode Benchmark for Adversarial Robustness in Multi-Agent LLM Collectives](https://mlsanity.com/paper/2605.09027/) (2026)
- [MicroVerse: An Instrument for Measuring Self-Authored Identity Drift in Long-Horizon Multi-Agent Language-Model Simulations](https://mlsanity.com/paper/2608.15844/) (2026)
- [Generalization or Memorization? Brittleness Testing for Chess-Trained Language Models](https://mlsanity.com/paper/2605.17565/) (2026)
- [Do Chess Explanations Reflect Model Decisions? Behavioral and Token-Level Tests of LLM Reasoning Faithfulness](https://mlsanity.com/paper/2609.22245/) (2026)

## Abstract (arXiv)

Language models often lack grounded reasoning capabilities in specialized domains where training data is scarce but bespoke systems excel. We introduce a general framework for distilling expert system reasoning into natural language chain-of-thought explanations, enabling compact models to acquire domain expertise and the ability to generate faithful, grounded explanations. Rather than distilling only final outputs, we capture the full reasoning process, transforming opaque expert computations into transparent, step-by-step explanations. We demonstrate this approach in chess, a canonical reasoning domain where language models continue to underperform. Our 4B parameter model, C1, advances from a near-zero baseline to 48.1% accuracy, outperforming all open-source models and most frontier proprietary systems. Notably, C1 surpasses its distillation teacher and generates solutions in two orders of magnitude fewer tokens than baselines. Unlike prior neural chess approaches that predict only best moves, C1 generates explainable solutions revealing strategic reasoning. Our pipeline combines supervised fine-tuning and reinforcement learning with theme-balanced data sampling for comprehensive tactical coverage. Master Distillation demonstrates how to inject expert-level knowledge into compact models for under-optimized domains, offering a recipe for unlocking RLVR where LLMs lack sufficient base capabilities.