The Dot Game That Breaks Your Brain -

The Dot Game That Breaks Your Brain

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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.


Elwyn R. Berlekamp, John Conway and Richard K. Guy, “Winning Ways for your Mathematical Plays”:

Martin Gardner, “Mathematical Carnival”:

World Game of Sprouts Association:

David Applegate, Guy Jacobson, Daniel Sleater: “Computer Analysis of Sprouts”:

Julien Lemoine and Simon Viennot, “A Further Computer Analysis of Sprouts”:

Riccardo Focardi and Flaminia L. Luccio, “A new analysis technique for the Sprouts Game“:

Julien Lemoine and Simon Viennot, “Computer Analysis of Sprouts with Nimbers”:

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Research And Writing by Matthew Tabor

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  1. 7:48 After I heard this part, I basically stopped the video and roared with laughter for an hour.

  2. Why play a game when the winner is always known? Like Joshua said in Wargames. The only way to win is to not play…

  3. But why are we trying to compute all possible results of games for all the number of dots?

  4. I just realized that vsauce is left handed

  5. Turns out this game isn’t that hard… I literally played it in maths (year 7)

  6. He's having way too much fun with his puppet.

  7. You know it is funny how I had just watched the meme where the guy hits the yoda puppet and he has the exact same one.

  8. Did you know that Yoda is worth like $300?

  9. Of course you can play with yourself, I do it all the time

  10. I wish this was on coolmathgames it’s a more of a math game than half the stuff and is perfect for vector graphics

  11. vsauce:r u sweat yet

    me:*forgets to on the fan

  12. I love this i played it with my uncle for hoirs on end but he called it "flees" and not sprouts

  13. Can sprouts be classified as an undecidable problem like Conway's game of life?

  14. Jesse Pinkman thought he was to do a meth video.. but forced to do a math video instead..

  15. imagine the connect the dots thing at bonefish grill actually hides a secret to the sprouts game

  16. A game starting with 500 dots would probably brick my computer.

  17. So unless we use quantum computers we will probably never reach more than 200 dots

  18. My idea: make it a 3d game! Surely there is a way to make it fun and complicated

  19. he is unknowingly drawing disfigured baymax faces lol

  20. Yoda is me after a losing streak of 10 in ANY gaming session

  21. 2 dots appear

  22. If you can draw a line from a dot back to itself, then how does Yoda lose?

  23. i had played this game with my friend at i lost a few braincells every round

  24. His first Yoda impression sounded more like Scooby Doo, lol

  25. I must say thanks for the new game for me to play It's pretty nice.

  26. When switching back and forth with ‘Yoda’ it looks like you’re ambidextrous.

  27. Why did I laugh so much at the breakdown Yoda had.

  28. first time noticed that kevin is left-handed


    accepts fate*

  30. I love it when his face collapses in on itself

  31. 3:14 went one much much much much longer than I would have expected. wow.

  32. teacher: the homework isn't that hard
    the homework: memorize this game's tactics

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