Combinatorial Game Theory
who wins, and by how much
Series

Colouring — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Col and Snort on a path of four. One graph, two games, and one word of difference between the rules. Col forbids painting next to your own colour, which makes every move a small self-harm and drives the values towards numbers. Snort forbids painting next to your opponent's, which makes every move a land grab and drives them towards fights. Both values are computed from the same recursion.

    One board, two rules

    Col forbids painting next to your own colour. Snort forbids painting next to your opponent's. One word differs, the boards are identical, and the values that come out are not the same kind of object.

    part 1 · positions
  2. Every position of both games, and where the fights are. Every colouring of every graph in the library, under both rules, with the temperature of each computed. A position with a positive temperature is one both players want to move in. Col has none anywhere; Snort has them on every graph, and the hottest grows with the graph.

    One rule makes it cold, the other hot

    Col forbids painting next to your own colour and Snort forbids painting next to your opponent's. Over all 540 colourings of six graphs, not one Col position has anything at stake and 61 Snort positions do — the difference between a game that is a count and a game that is a series of fights, produced by one word.

    part 2 · positions

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