Nim

Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps. On each turn, a player must remove at least one object, and no more than a set maximum number from the heap.

Variants of Nim have been played since ancient times. The game is said to have originated in China (it closely resembles the Chinese game of "Jianshizi", or "picking stones"), but the origin is uncertain; the earliest European references to Nim are from the beginning of the 16th century. Its current name was coined by Charles L. Bouton of Harvard University, who also developed the complete theory of the game in 1901, but the origins of the name were never fully explained. The name is probably derived from German nimm meaning "take ", or the obsolete English verb nim of the same meaning. It should also be noted that rotating the word NIM by 180 degrees results in WIN (see Ambigram).

Nim can be played as a misère game, in which the player to take the last object loses. Nim can also be played as a normal play game, which means that the person who makes the last move (i.e., who takes the last object) wins. This is called normal play because most games follow this convention, even though Nim usually does not.

Normal play Nim (or more precisely the system of nimbers) is fundamental to the Sprague-Grundy theorem, which essentially says that in normal play every impartial game is equivalent to a Nim heap that yields the same outcome when played in parallel with other normal play impartial games (see disjunctive sum).

While all normal play impartial games can be assigned a nim value, that is not the case under the misère convention. Only tame games can be played using the same strategy as misère nim.

A version of Nim is played—and has symbolic importance—in the French New Wave film Last Year at Marienbad (1961).

It was one of the first ever electronic computerized games (1952). Herbert Koppel, Eugene Grant and Howard Bailer, engineers from the W.L. Maxon Corporation, developed a 50-pound machine which played Nim against a human opponent and regularly won.

Nim is a special case of a Poset Game where the Poset consists of disjoint Chains (the heaps).

Read more about Nim:  Game Play and Illustration, Mathematical Theory, Proof of The Winning Formula

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