Mind the gap: A real-valued distance on combinatorial games

Kyle Burke; Michael Fisher; Craig Tennenhouse

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arXiv · 2601.10574

Mind the gap: A real-valued distance on combinatorial games

Kyle Burke·Michael Fisher·Craig Tennenhouse

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Abstract

We define a real-valued distance metric $wd$ on the space $\mathcal{C}$ of short combinatorial games in canonical form. We demonstrate the existence of Cauchy sequences informed by sidling sequences, find limit points, and investigate the closure $\overline{\mathcal{C}}$, which is shown to partition the set of loopy games in a non-trivial way. Stoppers, enders, and non-stopper-sided loopy games are explored, as well as the topological properties of $(\mathcal{C},wd)$.

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BibTeX RIS

Kyle Burke, Michael Fisher, Craig Tennenhouse. 2026-01-15. Mind the gap: A real-valued distance on combinatorial games. https://arxiv.org/abs/2601.10574

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