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@BenCrowell Dear Ben, I thought you might interested in this recent work tackling the structure of the state space of chess: arxiv.org/abs/1609.04648 given your interest towards chess and physics.
@Nathaniel Although this is a year old post, but since then, have you finally come across relevant bits of the graph theory literature in regard to study of random digraphs? I am very much interested as well.
