概述
Nim is a mathematical strategy game of perfect information. Players take turns removing objects from distinct piles. The player who takes the last object wins (normal play) or loses (misere play). Despite simple rules, Nim has deep mathematical structure.
历史
Nim was comprehensively analyzed by Charles Bouton in 1901, who proved the winning strategy. The name may come from German 'nimm' (take) or archaic English 'nim' (steal).
策略
Learn the Nim-sum
XOR all pile sizes in binary. If Nim-sum is 0 before your move, you're in a losing position (with perfect opponent play).
Always aim to leave a Nim-sum of 0 after your move.
With two equal piles, mirror your opponent's moves in the other pile.
In misere play, the strategy differs only at the endgame - aim for an odd number of 1-piles.
Recognize losing positions and play to maximize opponent mistakes.
Practice calculating Nim-sums quickly to find winning moves.
常见问题
Take the last object(s) to win (normal play), or avoid taking the last object (misere variant).