Set Matching: An Enhancement of the Hales-Jewett Pairing Strategy
Jos Uiterwijk

TL;DR
The paper introduces Set Matching, a new strategy for k-in-a-Row games that uses fewer markers than the traditional Hales-Jewett pairing, enabling the proof of draws in positions previously unprovable.
Contribution
It presents Set Matching, a novel strategy that reduces marker usage and proves more positions as draws in k-in-a-Row games compared to existing methods.
Findings
Set Matching requires less than two markers per group.
It can prove certain positions as draws that Hales-Jewett cannot.
The strategy is effective in configurations like Cycle, BiCycle, and PolyCycle.
Abstract
When solving k-in-a-Row games, the Hales-Jewett pairing strategy [4] is a well-known strategy to prove that specific positions are (at most) a draw. It requires two empty squares per possible winning line (group) to be marked, i.e., with a coverage ratio of 2.0. In this paper we present a new strategy, called Set Matching. A matching set consists of a set of nodes (the markers), a set of possible winning lines (the groups), and a coverage set indicating how all groups are covered after every first initial move. This strategy needs less than two markers per group. As such it is able to prove positions in k-in-a-Row games to be draws, which cannot be proven using the Hales-Jewett pairing strategy. We show several efficient configurations with their matching sets. These include Cycle Configurations, BiCycle Configurations, and PolyCycle Configurations involving more than two cycles.…
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Taxonomy
TopicsArtificial Intelligence in Games · Sports Analytics and Performance
