The Dot Game That Breaks Your Brain

Published on September 10, 2019
21

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On Tuesday, February 21, 1967, in the math department common room of Sidney Sussex College, Cambridge, the world of pencil and paper math games changed. John Conway and Michael Paterson were trying to invent a brand new simple-to-play, hard-to-analyze game, and the result came to be known as Sprouts.

The basic setup of Sprouts is easy: start with any number of dots, then connect them with lines. When a dot has 3 lines coming to or from it, that dot can no longer be played. Lines are not allowed to cross, and the player to draw the last line wins. But the most important rule came from Paterson: every time a player draws a line, he or she gets to add a new dot anywhere on that line. As Conway put it, at that point “sprouts sprouted.”

Despite its simplicity, Sprouts is actually a game teeming with mathematical complexity and depth once it’s played with more than a few dots… and at a certain point, the human brain is overwhelmed by the possibilities. Not only is there no straightforward ‘perfect’ strategy for Sprouts, but the sheer number of ways the game can play out push the limits of microprocessors that attempt to map optimal approaches.

The complex world of Sproutology presents a delicate dance between making the most of surviving dots and engineering your opponent’s failure. Grab a pencil and paper and get ready to break your brain.

SOURCES:

Elwyn R. Berlekamp, John Conway and Richard K. Guy, “Winning Ways for your Mathematical Plays”: https://www.amazon.com/Winning-Ways-Your-Mathematical-Plays/dp/1568811306

Martin Gardner, “Mathematical Carnival”: https://www.amazon.com/Mathematical-Carnival-Martin-Gardner/dp/039472349X

World Game of Sprouts Association: http://www.wgosa.org

David Applegate, Guy Jacobson, Daniel Sleater: “Computer Analysis of Sprouts”: https://www.semanticscholar.org/paper/Computer-analysis-of-Sprouts-Applegate-Jacobson/286c54787d26231625cb6aedda9ef4b4e183c14e

Julien Lemoine and Simon Viennot, “A Further Computer Analysis of Sprouts”: https://compmath.files.wordpress.com/2008/08/a_further_computer_analysis_of_sprouts.pdf

Riccardo Focardi and Flaminia L. Luccio, “A new analysis technique for the Sprouts Game“: https://www.semanticscholar.org/paper/A-new-analysis-technique-for-the-Sprouts-Game-Focardi-Luccio/9ac27ad5a6fb4d094b306afaa08b30697939f7bc

Julien Lemoine and Simon Viennot, “Computer Analysis of Sprouts with Nimbers”: http://library.msri.org/books/Book63/files/131105-LeMoine.pdf

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