Combinatorial Game Theory
who wins, and by how much
Series

Additivity — the series

One essay so far on this idea, and more questions about it than one essay answers.
  1. Knowing who wins is not enough. Three pairs of positions, every one of which is in outcome class N on its own. Their sums are not all the same, and not all in the same outcome class — so the outcome of a sum cannot be worked out from the outcomes of its parts, and that is why the theory needs values.

    Outcomes do not add

    Knowing who wins each part of a position tells almost nothing about who wins the whole. Counted over every sum of two values born by day two, six of the outcome table's ten entries are settled and four are not — and every settled one is settled by the order rather than by anything about outcomes. Two first-player wins reach all four classes between them.

    part 1 · sums

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