The Secret of Nim
Explore the mathematical background of the game of Nim and learn how to play the optimal strategy.
The crucial factor for an optimal (winning) strategy is the nim-value. For details of how to calculate it, see Nim-Value (Wolfram MathWorld). The circle-plus symbol used in this Demonstration indicates the operation of calculating the nim-value.
Snapshot 1: if at any point in the game, the nim-value is zero for a given player, the position is safe, which means that player can win with correct play
Snapshot 2: otherwise, the position is unsafe and the player will always lose if the other player plays correctly
Snapshot 3: to achieve a safe position, find a heap whose size is less than the min-value of with the nim-value of all the heaps; reduce that heap to , resulting in a nim-value of zero