Plays of Nim

The plays of Nim are very current plays, of pure strategy, with two players (see Game theory). These plays, of which there exist innumerable alternatives, are played with seeds, balls, tokens, matches…

The origins are probably very old. They are announced in China under the name of fan-tan and are known in Africa under the name tiouk-tiouk . The current name (drawn from the German radical nim which means to take ) was given by the English mathematician Charles Leonard Bouton in 1901.

Each play is played two and it is with each one its turn to play. The chance does not intervene and of the precise rules the course of the play fixes. It is in general a question of moving or to take objects and that which takes (or does not take) the last object is victorious.

The plays of Nim are plays of duel to null sum (two players, a winner and a loser, not of possible equality). In all the cases, the number of cases of figures is finished and an optimal strategy of profit exists, based on the recognition of gaining intermediate positions.

A basic version of this play uses only one heap of objects. Each player in turn removes 1,2 or 3 objects. The winner is that which can play in the last. For this example, the strategy is to leave each time - if it can - a multiple number of objects of 4. It is noted whereas the adversary will not be able to do as much of it. In the alternative of this version where that which takes the last object loses, the strategy is then to leave an adequate number of objects with 1 modulo 4 (i.e.: 1,5,9,13…) It is then a good exercise of training of the Division S with remainder.

An alternative a little less immediate is the Jeu of Marienbad, made famous for a film of Alain Resnais of 1961, last year with Marienbad .

Simple: Nim

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