# Checkmating One, by Using Many: Combining Mixture of Experts with MCTS to Improve in Chess

arXiv: https://arxiv.org/abs/2401.16852 · HTML: https://mlsanity.com/paper/2401.16852/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in MoE in reinforcement learning and robotics, one of 12 directions in Mixture-of-experts.
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 30 Jan 2024.

## Placed in

- Mixture-of-experts / [MoE in reinforcement learning and robotics](https://mlsanity.com/moe/moe-in-reinforcement-learning-and-robotics/)

## Builds on (most cited first, 17 of 17)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [ECA-Net: Efficient Channel Attention for Deep Convolutional Neural Networks](https://mlsanity.com/paper/1910.03151/) (2019)
- [Modular Multitask Reinforcement Learning with Policy Sketches](https://mlsanity.com/paper/1611.01796/) (2016)
- [Efficient Large Scale Language Modeling with Mixtures of Experts](https://mlsanity.com/paper/2112.10684/) (2021)
- [Acquisition of Chess Knowledge in AlphaZero](https://mlsanity.com/paper/2111.09259/) (2021)
- [Aligning Superhuman AI with Human Behavior: Chess as a Model System](https://mlsanity.com/paper/2006.01855/) (2020)
- [Pommerman: A Multi-Agent Playground](https://mlsanity.com/paper/1809.07124/) (2018)
- [Learning Models of Individual Behavior in Chess](https://mlsanity.com/paper/2008.10086/) (2020)
- [One Network Fits All? Modular versus Monolithic Task Formulations in Neural Networks](https://mlsanity.com/paper/2103.15261/) (2021)
- [Representation Matters for Mastering Chess: Improved Feature Representation in AlphaZero Outperforms Switching to Transformers](https://mlsanity.com/paper/2304.14918/) (2023)
- [Learning to play the Chess Variant Crazyhouse above World Champion Level with Deep Neural Networks and Human Data](https://mlsanity.com/paper/1908.06660/) (2019)

## Built on by (most cited first, 4 of 4)

- [ToolTree: Efficient LLM Agent Tool Planning via Dual-Feedback Monte Carlo Tree Search and Bidirectional Pruning](https://mlsanity.com/paper/2603.12740/) (2026)
- [Beyond checkmate: exploring the creative chokepoints in AI text](https://mlsanity.com/paper/2501.19301/) (2025)
- [Mixture of Masters: Sparse Chess Language Models with Player Routing](https://mlsanity.com/paper/2602.04447/) (2026)
- [Policy Optimality Measurement for Multi-Vehicle Decision-Making: From Extrinsic Indicators to Intrinsic Quality](https://mlsanity.com/paper/2608.01133/) (2026)

## Abstract (arXiv)

In games like chess, strategy evolves dramatically across distinct phases - the opening, middlegame, and endgame each demand different forms of reasoning and decision-making. Yet, many modern chess engines rely on a single neural network to play the entire game uniformly, often missing opportunities to specialize. In this work, we introduce M2CTS, a modular framework that combines Mixture of Experts with Monte Carlo Tree Search to adapt strategy dynamically based on game phase. We explore three different methods for training the neural networks: Separated Learning, Staged Learning, and Weighted Learning. By routing decisions through specialized neural networks trained for each phase, M2CTS improves both computational efficiency and playing strength. In experiments on chess, M2CTS achieves up to +122 Elo over standard single-model baselines and shows promising generalization to multi-agent domains such as Pommerman. These results highlight how modular, phase-aware systems can better align with the structured nature of games and move us closer to human-like behavior in dividing a problem into many smaller units.