# Generalized Proof-Number Monte-Carlo Tree Search

arXiv: https://arxiv.org/abs/2506.13249 · HTML: https://mlsanity.com/paper/2506.13249/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 6 of 6)

- [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)
- [Proof Number Based Monte-Carlo Tree Search](https://mlsanity.com/paper/2303.09449/) (2023)
- [Combining Monte-Carlo Tree Search with Proof-Number Search](https://mlsanity.com/paper/2206.03965/) (2022)
- [Expected Work Search: Combining Win Rate and Proof Size Estimation](https://mlsanity.com/paper/2405.05594/) (2024)

## Abstract (arXiv)

This paper presents Generalized Proof-Number Monte-Carlo Tree Search: a generalization of recently proposed combinations of Proof-Number Search (PNS) with Monte-Carlo Tree Search (MCTS), which use (dis)proof numbers to bias UCB1-based Selection strategies towards parts of the search that are expected to be easily (dis)proven. We propose three core modifications of prior combinations of PNS with MCTS. First, we track proof numbers per player. This reduces code complexity in the sense that we no longer need disproof numbers, and generalizes the technique to be applicable to games with more than two players. Second, we propose and extensively evaluate different methods of using proof numbers to bias the selection strategy, achieving strong performance with strategies that are simpler to implement and compute. Third, we merge our technique with Score Bounded MCTS, enabling the algorithm to prove and leverage upper and lower bounds on scores - as opposed to only proving wins or not-wins. Experiments demonstrate substantial performance increases, reaching the range of 80% for 8 out of the 11 tested board games.