In competitive two-player games, the killer heuristic is a move-ordering method based on the observation that a strong move or small set of such moves in a particular position may be equally strong in similar positions at the same move (ply) in the game tree.
Retaining such moves obviates the effort of rediscovering them in sibling nodes.
The killer heuristic attempts to produce a cutoff by assuming that a move that produced a cutoff in another branch of the game tree at the same depth is likely to produce a cutoff in the present position, that is to say that a move that was a very good move from a different (but possibly similar) position might also be a good move in the present position.
In practical implementation, game-playing programs frequently keep track of two killer moves for each depth of the game tree (greater than depth of 1) and see if either of these moves, if legal, produces a cutoff before the program generates and considers the rest of the possible moves.
When there is a cutoff, the appropriate entry in the table is incremented, such as by adding d or d² where d is the current search depth.