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The Magic Cafe Forum Index » » Magical equations » » Game of Nim. (0 Likes) Printer Friendly Version

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Profile of drkptrs1975
This is one of my most favorite math games. Pure math.

You have a number rows of markers, usually three, could be more, you can remove any number of markers you want, but they have to be from the same row. The winner is the one who takes or does not take the last marker.

Other Variations is, that you can only take upto a certian number of markers.

There is mathmatical strategy, I convert to binary digits.

Do it right, and you will win everytime.
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Profile of landmark
You can certainly use the binary strategy, but it's easier just to recognize certain ending patterns and work your way towards them Smile

Jack Shalom
Dennis Loomis
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1943 - 2013
2113 Posts

Profile of Dennis Loomis
Jack Shalom is right, if you only play the simple versions of the game. But, if you want to get exotic, and get into a large number of markers, the binary analysis will tell you the correct moves to make. Nim is a GREAT bar pastime and a way to win a lot of free drinks, if you're into that.

The game was prominently featured in the movie: "Last Year at Marienbad."

A complete analysis of the math behind Nim is in one of the Martin Gardner Books. Anyone recall which one?

It's not quite true that you can "win every time." For each different starting position, you can calculate whether it's advantageous to be the first player or not. If you take turns starting, sometimes your opponent with have the advantage. Then he can theoretically win, but only if he makes correct plays with every move. While that's not likely, it can happen.

Dennis Loomis
Itinerant Montebank
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