Misère

Misère, derived from the French word for "misery," generally refers to a variant of a game where the objective is to lose rather than win. In a misère game, the player who is forced to make the last move, or takes the last piece, is the winner (or avoids the misery of losing).

The term is most commonly applied to combinatorial games, such as Nim, but can be applied to other game types as well. When a game is played under misère rules, the optimal strategies can differ significantly from those used in the standard (normal play) version of the game.

The primary difference between normal play and misère play lies in the goal:

• Normal Play: The player who makes the last move (i.e., takes the last piece or performs the last action) wins.
• Misère Play: The player who makes the last move loses (i.e., is forced to take the last piece or perform the last action).

Analyzing a game under misère rules often requires different mathematical approaches and can lead to unexpected complexities. Strategies that are advantageous in normal play may be detrimental in misère play. Some games have a simple strategy under normal rules but become significantly more challenging under misère rules. The difference between the two modes of play creates distinct mathematical structures.

The strategy for winning a misère game often involves forcing your opponent into positions where they are compelled to make the final move, thus ensuring your victory (avoiding misery). Careful planning and an understanding of the game's end states are critical for successful misère play.