Any position in the game can be described by a pair of integers ("n", "m") with "n" ≤ "m", describing the size of both piles in the position or the coordinates of the queen. The strategy of the game revolves around "cold positions" and "hot positions": in a cold position, the player whose turn it is to move will lose with best play, while in a hot position, the player whose turn it is to move will win with best play. The optimal strategy from a hot position is to move to any reachable cold position.