boardgames.zone
Nim
Mathematical strategy - take the last object
- 2 players
- 3–10 min
- DifficultyMedium
Lobby
No open tables right now
Open one and anyone browsing can join.
Top players
Full leaderboardHow to play
- Remove any number of tokens from one row
- Must remove at least one token
- Player who takes the last token loses
- Mathematical strategy determines the winner
Questions
Take the last object(s) to win (normal play), or avoid taking the last object (misere variant).
Objects (traditionally matchsticks or stones) are arranged in several piles. Classic setup: rows of 1, 3, 5, and 7 objects (16 total). Many variations exist with different starting configurations.
Win by taking the last object (normal) or forcing your opponent to take it (misere). The winning strategy involves binary XOR calculations of pile sizes.
Players alternate turns. On your turn, remove any number of objects from a single pile (at least one, up to all of them). You can only take from one pile per turn.
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.
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).