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.
and a (surreal) number
is cooled is known as the temperature; the minimum
Heating is the inverse of cooling and is defined as the "integral"[6]
Norton multiplication is an extension of multiplication to a game
and a positive game
(the "unit") defined by[7] The incentives
Overheating is an extension of heating used in Berlekamp's solution of Blockbusting, where
is defined for arbitrary games
as[8] Winning Ways also defines overheating of a game
by a positive game
, as[9] Chilling is a variant of cooling by
used to analyse the Go endgame of Go and is defined by[10] This is equivalent to cooling by
is an "even elementary Go position in canonical form".
[11] Warming is a special case of overheating, namely
is an "even elementary Go position in canonical form".
In this case the previous definition simplifies to the form[12]
This combinatorics-related article is a stub.