# Combining Monte-Carlo Tree Search with Proof-Number Search

arXiv: https://arxiv.org/abs/2206.03965 · HTML: https://mlsanity.com/paper/2206.03965/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 41 references that are in the map.
- First posted on arXiv 8 Jun 2022.

## Builds on (most cited first, 2 of 2)

- [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)

## Built on by (most cited first, 2 of 2)

- [Proof Number Based Monte-Carlo Tree Search](https://mlsanity.com/paper/2303.09449/) (2023)
- [Generalized Proof-Number Monte-Carlo Tree Search](https://mlsanity.com/paper/2506.13249/) (2025)

## Abstract (arXiv)

Proof-Number Search (PNS) and Monte-Carlo Tree Search (MCTS) have been successfully applied for decision making in a range of games. This paper proposes a new approach called PN-MCTS that combines these two tree-search methods by incorporating the concept of proof and disproof numbers into the UCT formula of MCTS. Experimental results demonstrate that PN-MCTS outperforms basic MCTS in several games including Lines of Action, MiniShogi, Knightthrough, and Awari, achieving win rates up to 94.0%.