Combinatorial Game Theory
who wins, and by how much
Series

Gift horse — the series

One essay so far on this idea, and more questions about it than one essay answers.
  1. Options handed to Left in 1 | −1. A position, and one candidate option after another added to it. Where the gift is one the player would never take the value does not move at all; where it is one they would, it does. The last column is the value of the enlarged form, computed by the same recursion as the original.

    An option nobody would take

    Every reduction of a form deletes. The gift horse principle adds: a move may be handed to a player for nothing, provided it is one they would never choose. Over all 484 additions to the values born by day two, 283 leave the value exactly where it was and the 201 that move it are precisely the ones the condition forbids — with the boundary at *not better*, which is a weaker demand than *worse*.

    part 1 · values

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