If a move causes a cut-off, it is likely that it will also be good enough to cause a cut-off if tried at the same depth in the search when another continuation of moves is under consideration. Such moves have become known as Killer Moves.

Early chess programs implemented this idea by keeping track of the best killer at each depth in the tree. Rival implements the idea used in CHESS 4.5, Slate & Atkin (1977). Slate and Atkin noted that killer heuristics become more useful when a transposition table is being used because trying the same move early in the search at each depth will result in more repeated positions and thus more successful retrievals from the transposition table. In order that a popular killer move not be forgotten if it is temporarily overshadowed by a move that is useful for refuting a different line of play, Rival maintains the best two killers at each depth.