A strategy game in which players take turns to reduce the number of objects in some sets, the aim being either to remove the last object or _not_ to do so.
Nim is a two-player zero-sum game with $n$ piles of pebbles. Players may take any number of pebbles from a single pile. The aim is either to win by taking all the pebbles in the last remaining pile (normal play) or alternatively to force that move upon your opponent (misere play).
Many variations of Nim exist, such as Wythoff's game. Most if not all of these have been completely solved, an optimal strategy discovered and proved.