The Game of Nim :
The Winning Strategy
Colloquium: Game Theory and Nim
Thursday
January 27 1:00-2:00
PM Room: TBD Light refreshments will be served at 12:45 PM |
Abstract
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 http://canjarrm.faculty.udmercy.edu/Nim-Beta2.zip
. This will allow you to play solitaire against
the computer, which will deploy the winning strategy.
Links: For the Game http://canjarrm.faculty.udmercy.edu/Nim-Beta2.zip
For the
Handouts from the Talk: http://canjarrm.faculty.udmercy.edu/NimTalk.pdf
For some Exercises: http://canjarrm.faculty.udmercy.edu/Nim%20%20Exercises.pdf
Last Modified: January 1/27/11