Nim

Players: Two

Players take turns in removing dots from one of several rows. The first player unable to move loses.

Description

The players start by drawing several rows of dots on a piece of paper. A good start is three rows of 5, 7, and 9 dots:

Description

The players now take turns in crossing out (or erasing) one or more dots from a single row. They must remove at least one dot, and they can remove any number up to the entire row.

The last player able to move wins.

Once you know the simple strategy for winning at Nim (see below) it's not a very challenging game, but it's important because its forms the foundation for analysing many more complex and interesting games.

Example

Here's an example game. The first player, Blue, chooses to remove two dots from the third row:

Example

Red then removes the entire first row:

Example2

It's clear that Blue's opening move was foolish, because from now on Red can copy whatever Blue does and win the game.

Other topics

Strategy

Variations

History

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