# GameSmith: Scaling Zero-Sum Self-Play with Synthesised Games

arXiv: https://arxiv.org/abs/2610.13995 · HTML: https://mlsanity.com/paper/2610.13995/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Self-play RL for reasoning, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 52 of its 64 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-play RL for reasoning](https://mlsanity.com/synth/self-play-rl-for-reasoning/)

## Builds on (most cited first, 30 of 52)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Quantifying Generalization in Reinforcement Learning](https://mlsanity.com/paper/1812.02341/) (2018)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [Emergent Tool Use From Multi-Agent Autocurricula](https://mlsanity.com/paper/1909.07528/) (2019)
- [Emergent Complexity and Zero-shot Transfer via Unsupervised Environment Design](https://mlsanity.com/paper/2012.02096/) (2020)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Paired Open-Ended Trailblazer (POET): Endlessly Generating Increasingly Complex and Diverse Learning Environments and Their Solutions](https://mlsanity.com/paper/1901.01753/) (2019)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.24760/) (2025)
- [GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations](https://mlsanity.com/paper/2402.12348/) (2024)
- [How Well Can LLMs Negotiate? NegotiationArena Platform and Analysis](https://mlsanity.com/paper/2402.05863/) (2024)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [GameBench: Evaluating Strategic Reasoning Abilities of LLM Agents](https://mlsanity.com/paper/2406.06613/) (2024)
- [Provably Strict Generalisation Benefit for Equivariant Models](https://mlsanity.com/paper/2102.10333/) (2021)

## Abstract (arXiv)

Post-training large language models (LLMs) on two-player zero-sum games provides a verifiable reward, and the gains have been shown to transfer to general reasoning. Existing pipelines, however, rely on a handful of hand-written games and on advantage estimators tied to them, so both the supply of games and the advantage estimate on a large corpus limit scaling. We present GameSmith, which scales both. An LLM synthesises games inside templates whose reward, observation, and hidden-information code is fixed. Each game is verified by seed-paired replay and by an independent re-implementation of its specification, then expanded into encoding, rule, and size variants, giving 26 new games in 29 families and 336 verified variants from the three SPIRAL templates. The model is distilled from the self-play of a larger teacher (Qwen3-32B) on these games and then trained by self-play reinforcement learning with CRAB, an advantage estimator that credits each decision against a shrinkage estimate of the expected return of its position and is defined on every variant. On Qwen3-4B-Base, distillation raises the 13-benchmark mean pass@1 from 45.5 to 62.5, above the three SPIRAL games at the same budget, and self-play with CRAB reaches 64.9. The ordering holds across models, and transfer grows with the number of game families.