# Benchmarking Prompt Optimization of Large Language Models With Chess

arXiv: https://arxiv.org/abs/2610.00416 · HTML: https://mlsanity.com/paper/2610.00416/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 42 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 30 of 32)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [How Can We Know What Language Models Know?](https://mlsanity.com/paper/1911.12543/) (2019)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [Evaluating Very Long-Term Conversational Memory of LLM Agents](https://mlsanity.com/paper/2402.17753/) (2024)
- [Automatic Prompt Optimization with "Gradient Descent" and Beam Search](https://mlsanity.com/paper/2305.03495/) (2023)
- [Terminal-Bench: Benchmarking Agents on Hard, Realistic Tasks in Command Line Interfaces](https://mlsanity.com/paper/2601.11868/) (2026)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [MLE-bench: Evaluating Machine Learning Agents on Machine Learning Engineering](https://mlsanity.com/paper/2410.07095/) (2024)
- [Dynabench: Rethinking Benchmarking in NLP](https://mlsanity.com/paper/2104.14337/) (2021)
- [RLPrompt: Optimizing Discrete Text Prompts with Reinforcement Learning](https://mlsanity.com/paper/2205.12548/) (2022)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [GrIPS: Gradient-free, Edit-based Instruction Search for Prompting Large Language Models](https://mlsanity.com/paper/2203.07281/) (2022)
- [Measuring what Matters: Construct Validity in Large Language Model Benchmarks](https://mlsanity.com/paper/2511.04703/) (2025)
- [AutoHarness: improving LLM agents by automatically synthesizing a code harness](https://mlsanity.com/paper/2603.03329/) (2026)
- [ChessGPT: Bridging Policy Learning and Language Modeling](https://mlsanity.com/paper/2306.09200/) (2023)
- [A Systematic Survey of Automatic Prompt Optimization Techniques](https://mlsanity.com/paper/2502.16923/) (2025)
- [Emergent World Models and Latent Variable Estimation in Chess-Playing Language Models](https://mlsanity.com/paper/2403.15498/) (2024)
- [The Chess Transformer: Mastering Play using Generative Language Models](https://mlsanity.com/paper/2008.04057/) (2020)
- [LLF-Bench: Benchmark for Interactive Learning from Language Feedback](https://mlsanity.com/paper/2312.06853/) (2023)
- [Evaluation data contamination in LLMs: how do we measure it and (when) does it matter?](https://mlsanity.com/paper/2411.03923/) (2024)
- [Complete Chess Games Enable LLM Become A Chess Master](https://mlsanity.com/paper/2501.17186/) (2025)
- [LLM CHESS: Benchmarking Reasoning and Instruction-Following in LLMs through Chess](https://mlsanity.com/paper/2512.01992/) (2025)
- [Can Large Language Models Develop Strategic Reasoning? Post-training Insights from Learning Chess](https://mlsanity.com/paper/2507.00726/) (2025)
- [Generating Creative Chess Puzzles](https://mlsanity.com/paper/2510.23881/) (2025)
- [A Comparative Study of DSPy Teleprompter Algorithms for Aligning Large Language Models Evaluation Metrics to Human Evaluation](https://mlsanity.com/paper/2412.15298/) (2024)

## Abstract (arXiv)

Evaluating large language models becomes increasingly challenging as their capabilities advance: benchmarks can saturate, public test sets risk contamination, and assessing harder tasks can require expensive grading or execution infrastructure. These challenges are amplified in automatic prompt optimization (APO), where evaluation is repeated throughout the search for better prompts. Studying APO therefore requires a benchmark that is cheap and deterministic to score, hard enough to leave room for improvement, and renewable as models evolve. We introduce a chess benchmark built from 1,118 Lichess puzzles to study APO for frozen LLMs: we optimize their prompts without updating their model weights. Chess combines inexpensive exact-match scoring, engine-based evaluation of alternative moves, and a renewable supply of problems with adjustable difficulty. Unlike evaluations that report only success on isolated test items, the benchmark also connects puzzle-solving gains to short game-play rollouts within the same domain. We use it to evaluate six APO algorithms on eight target models, measuring not only baseline strength but also how much each model responds to optimization and whether optimized prompts transfer across models and to game play. Chess is thus a well-suited benchmark for APO: it is (i) challenging, as even the strongest evaluated model, Gemini 3.5 Flash (used as the meta-model), solves only about 55% of puzzles; (ii) discriminative, revealing gains, unchanged performance, and regressions across methods and models; (iii) renewable, with fresh puzzles to reduce contamination risk and adjustable difficulty to maintain headroom as models improve; and (iv) affordable, as the complete study runs for around 800. We release the puzzles, optimization and evaluation code, and dataset-renewal scripts (https://github.com/imec-ailabs/Automatic-Prompt-Optimization-with-Chess).