# A Novel Approach to Solving Goal-Achieving Problems for Board Games

arXiv: https://arxiv.org/abs/2112.02563 · HTML: https://mlsanity.com/paper/2112.02563/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 35 references that are in the map.
- First posted on arXiv 5 Dec 2021.

## Builds on (most cited first, 3 of 3)

- [ELF OpenGo: An Analysis and Open Reimplementation of AlphaZero](https://mlsanity.com/paper/1902.04522/) (2019)
- [Accelerating and Improving AlphaZero Using Population Based Training](https://mlsanity.com/paper/2003.06212/) (2020)
- [Multi-Labelled Value Networks for Computer Go](https://mlsanity.com/paper/1705.10701/) (2017)

## Built on by (most cited first, 7 of 7)

- [Are AlphaZero-like Agents Robust to Adversarial Perturbations?](https://mlsanity.com/paper/2211.03769/) (2022)
- [Impartial Games: A Challenge for Reinforcement Learning](https://mlsanity.com/paper/2205.12787/) (2022)
- [A Local-Pattern Related Look-Up Table](https://mlsanity.com/paper/2212.13922/) (2022)
- [Game Solving with Online Fine-Tuning](https://mlsanity.com/paper/2311.07178/) (2023)
- [Expected Work Search: Combining Win Rate and Proof Size Estimation](https://mlsanity.com/paper/2405.05594/) (2024)
- [Relevance-Zone Reduction in Game Solving](https://mlsanity.com/paper/2510.00689/) (2025)
- [A Study of Solving Life-and-Death Problems in Go Using Relevance-Zone Based Solvers](https://mlsanity.com/paper/2512.21365/) (2025)

## Abstract (arXiv)

Goal-achieving problems are puzzles that set up a specific situation with a clear objective. An example that is well-studied is the category of life-and-death (L&D) problems for Go, which helps players hone their skill of identifying region safety. Many previous methods like lambda search try null moves first, then derive so-called relevance zones (RZs), outside of which the opponent does not need to search. This paper first proposes a novel RZ-based approach, called the RZ-Based Search (RZS), to solving L&D problems for Go. RZS tries moves before determining whether they are null moves post-hoc. This means we do not need to rely on null move heuristics, resulting in a more elegant algorithm, so that it can also be seamlessly incorporated into AlphaZero's super-human level play in our solver. To repurpose AlphaZero for solving, we also propose a new training method called Faster to Life (FTL), which modifies AlphaZero to entice it to win more quickly. We use RZS and FTL to solve L&D problems on Go, namely solving 68 among 106 problems from a professional L&D book while a previous program solves 11 only. Finally, we discuss that the approach is generic in the sense that RZS is applicable to solving many other goal-achieving problems for board games.