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Ben Reiniger wrote on 2013-06-25 UTC
In regard to dimensionality of chess variants, I think of it as the most convenient way to describe the rules. Any (most?) variants can be thought of purely combinatorially, with a set of locations and pieces occupying those locations, with a set of transitions between states. But often the transition rules are easiest to describe using some extra geometry. (Do FIDE rooks move orthogonally in 2d, or as in Eeeeeeeex as a 1 or 9 rider in 1d, or as some set of at most 14 locations that depend on the current locations of itself and the other pieces?)

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