# Proof Number Based Monte-Carlo Tree Search

arXiv: https://arxiv.org/abs/2303.09449 · HTML: https://mlsanity.com/paper/2303.09449/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 52 references that are in the map.
- First posted on arXiv 16 Mar 2023.

## Builds on (most cited first, 5 of 5)

- [Monte Carlo Tree Search: A Review of Recent Modifications and Applications](https://mlsanity.com/paper/2103.04931/) (2021)
- [Ludii -- The Ludemic General Game System](https://mlsanity.com/paper/1905.05013/) (2019)
- [Monte Carlo Tree Search with Heuristic Evaluations using Implicit Minimax Backups](https://mlsanity.com/paper/1406.0486/) (2014)
- [Split Moves for Monte-Carlo Tree Search](https://mlsanity.com/paper/2112.07761/) (2021)
- [Combining Monte-Carlo Tree Search with Proof-Number Search](https://mlsanity.com/paper/2206.03965/) (2022)

## Built on by (most cited first, 3 of 3)

- [Expected Work Search: Combining Win Rate and Proof Size Estimation](https://mlsanity.com/paper/2405.05594/) (2024)
- [Towards Explaining Monte-Carlo Tree Search by Using Its Enhancements](https://mlsanity.com/paper/2506.13223/) (2025)
- [Generalized Proof-Number Monte-Carlo Tree Search](https://mlsanity.com/paper/2506.13249/) (2025)

## Abstract (arXiv)

This paper proposes a new game-search algorithm, PN-MCTS, which combines Monte-Carlo Tree Search (MCTS) and Proof-Number Search (PNS). These two algorithms have been successfully applied for decision making in a range of domains. We define three areas where the additional knowledge provided by the proof and disproof numbers gathered in MCTS trees might be used: final move selection, solving subtrees, and the UCB1 selection mechanism. We test all possible combinations on different time settings, playing against vanilla UCT on several games: Lines of Action (7×7 and 8×8 board sizes), MiniShogi, Knightthrough, and Awari. Furthermore, we extend this new algorithm to properly address games with draws, like Awari, by adding an additional layer of PNS on top of the MCTS tree. The experiments show that PN-MCTS is able to outperform MCTS in all tested game domains, achieving win rates up to 96.2% for Lines of Action.