A puzzling Hex primer

Hayward, Ryan B.

doi:10.1017/cbo9780511807251.007

Cited by 2 publications

(5 citation statements)

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“…This section first defines relevance zones (RZs), and then reviews null moves and must-play regions (Hayward et al 2003;Hayward and Van Rijswijck 2006;Hayward 2009) with illustrations. Next, we define RZ-based solution trees (RZSTs) and present Consistent Replay Conditions, under which π can replay and therefore reuse previously searched solution trees to win.…”

Section: Our Approachmentioning

confidence: 99%

“…Relevance zones can be derived based on null moves, as in lambda search (Thomsen 2000;Wu and Lin 2010), and must-play regions (Hayward et al 2003;Hayward and Van Rijswijck 2006;Hayward 2009). For example, in Figure 1, if Black makes a null move on p a (in this case any move outside of z a , including passes), White simply plays at E2 to reach UCA, obtaining in the process an RZ, z b , like p b .…”

Section: Null Moves and Must-play Regionsmentioning

confidence: 99%

“…Actually, RZS can also be incorporated into depth-first search (e.g. alpha-beta search) as presented in (Shih et al 2021), which behaves similarly to the must-play-based Hex solver by Hayward (2009).…”

Section: Relevance Zone Based Searchmentioning

confidence: 99%

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

Chung-Chin¹,

Wu²,

Wei³

et al. 2022

AAAI

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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 state-of-the-art program TSUMEGO-EXPLORER 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.

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Section: Our Approachmentioning

confidence: 99%

Section: Null Moves and Must-play Regionsmentioning

confidence: 99%

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

Chung-Chin¹,

Wu²,

Wei³

et al. 2022

AAAI

View full text Add to dashboard Cite

show abstract

“…Actually, RZS can also be incorporated into depth-first search (e.g. alpha-beta search) as described in the Appendix, which behaves similarly to the must-play-based Hex solver by Hayward (2009).…”

Section: Relevance Zone Based Searchmentioning

confidence: 99%

“…In this subsection, we present a RZS solver implemented within a depth-first search algorithm, which we call AchieveGoal. It is similar to the must-play-based Hex solver by Hayward (2009). The algorithm AchieveGoal has inputs (p, G), where p is the given position and G the goal to achieve.…”

Section: Rzs Solver In Depth-first Searchmentioning

confidence: 99%

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

Chung-Chin¹,

Wu²,

Wei³

et al. 2021

Preprint

View full text Add to dashboard Cite

Goal-achieving problems are puzzles that set up a specific situation with a clear objective. An example that is wellstudied 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 superhuman 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.

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A puzzling Hex primer

Abstract: We explain some analytic methods that can be useful in solving Hex puzzles.

Cited by 2 publications

References 4 publications

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

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

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

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