Cooling and heating (combinatorial game theory)

In combinatorial game theory, cooling, heating, and overheating are operations on hot games to make them more amenable to the traditional methods of the theory, which was originally devised for cold games in which the winner is the last player to have a legal move.[1] Overheating was generalised by Elwyn Berlekamp for the analysis of Blockbusting.[2] Chilling (or unheating) and warming are variants used in the analysis of the endgame of Go.[3][4]

Cooling and chilling may be thought of as a tax on the player who moves, making them pay for the privilege of doing so, while heating, warming and overheating are operations that more or less reverse cooling and chilling.

  1. ^ Berlekamp, Elwyn R.; Conway, John H.; Guy, Richard K. (1982). Winning Ways for Your Mathematical Plays. Academic Press. pp. 147, 163, 170. ISBN 978-0-12-091101-1.
  2. ^ Berlekamp, Elwyn (January 13, 1987). "Blockbusting and Domineering". Journal of Combinatorial Theory. 49 (1) (published September 1988): 67–116. doi:10.1016/0097-3165(88)90028-3.[permanent dead link]
  3. ^ Berlekamp, Elwyn; Wolfe, David (1997). Mathematical Go: Chilling Gets the Last Point. A K Peters Ltd. ISBN 978-1-56881-032-4.
  4. ^ Berlekamp, Elwyn; Wolfe, David (1994). Mathematical Go Endgames. Ishi Press. pp. 50–55. ISBN 978-0-923891-36-7. (paperback version of Mathematical Go: Chilling Gets the Last Point)