Combinatorial Game Theory
who wins, and by how much
Series

Equality — the series

One essay so far on this idea, and more questions about it than one essay answers.
  1. The context that tells them apart. Two positions put into the same company, one context at a time. Each column is a game X; each cell is the outcome class of that side added to X. Equality means every column agrees, for every X there is — so a single disagreeing column is a disproof, and agreement across a bounded list of contexts is evidence rather than proof. The proof is that the difference is zero.

    Equal in every company

    Two games are equal when no third game can tell them apart — a quantifier over every position there is, discharged by one finite test. A search over 184 contexts separates all 5,790 unequal pairs it is handed and still calls two different games the same, which is exactly why G − H = 0 is a theorem and an exhaustive search is not.

    part 1 · sums

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