Cold game Created 2026-10-20 Updated 2026-11-05
In combinatorial game theory, a cold game is a position with no gain from taking the next move, as illustrated by number games. For , Left can only lower the value to zero, while Right can only raise it to one; either player would prefer to leave the position untouched if another component offered a useful move.
This contrasts with a hot position such as , where either player benefits from moving first. The distinction matters when choosing which component of a disjunctive sum to play. Exact definitions at zero temperature depend on the adopted cooling convention; a cold numerical component need not be a losing position by itself.