The Game of Nim :

The Winning Strategy




Game Theory and Nim

Thursday January 27

1:00-2:00 PM

Room:  TBD

Light refreshments will be served at 12:45 PM 




Game Theory and  Nim



The game of Nim is a two player, in which the players takes turns picking up objects.  A Nim Board consists of piles (sometimes called heaps) of objects.  At each turn, players pick up objects from one pile.  They must pick up at least one object.  They could pick up the entire pile, or anything in between.

The game can be played as a “Normal Game” in which the person who picks up the last object wins, or as a “Misere Game” in which the person who moves last is the loser.   An interesting fact about this game is that the winning strategy is basically the same for each game.

The colloquium will  discuss some general aspects of Game Theory and present an analysis of the game, featuring the elegant theorems which completely characterize the winning strategy.   They will determine precisely which boards are winning positions, and to calculate all the winning moves.  This is done through a straightforward calculation involving binary numbers.

To learn more about the game,  download the computer game at .  This will allow you to play solitaire against the computer, which will deploy the winning strategy. 


Links:             For the Game

                                    For the Handouts from the Talk:

                                    For some Exercises:





Last Modified:  January 1/27/11