Mind the gap: A real-valued distance on combinatorial games
Abstract
We define a real-valued distance metric wd on the space 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 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 (C,wd).
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