The Dot Game That Breaks Your Brain - monstrousmath.com

The Dot Game That Breaks Your Brain

Vsauce2
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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”:

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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500 Comments

  1. I can win this.

    Erase the dots, so you can't play, so you can't lose, so therefore you win.

  2. Can’t wait for 5d sprouts with time travel

  3. I found a method for winning
    When the dots number is even the first player always win accept if there is a blocked dot .. if so the second player win
    The oposet lead to the oposet

  4. Me who has 1 t friends which i dont even remenber there names sooooooo

  5. Doesn't that hurt ur throat to do that voice

  6. Why is tic tic toe a game if u don't tie then ur dumb

  7. Wait, I've watched this video before. But I just noticed this: at 8:34, shouldn't the beetle have another dot in the middle of the fully interior long line? Because these bugs must have exactly 3n dots with n dots being "alive", and this change would make the beetle match with the other 4 bugs.

  8. I am shur and you should listen and try at least

  9. hmm 3n-1 seems very simaler to anpther equation… 3n+1, the very cool and complex equation

  10. Finally found a use for all those old connect-the-dots books in the attic

  11. But in the demonstration couldn't Yoda have connected the dot to itself? It wasn't dead so am I just dumb?

  12. “Hey wanna play a game?” “Sure!” “You win.”

  13. So what if you draw a line around the second dot, that illustration wasn't on your diagram. Is it illegal in the rules?

  14. 5:50 bc of me listening to basic 2nd grading grade 7(im 12) i already understand what n(n+1)÷2 lol
    For example n=3, 3(3+1)÷2=3(4)÷2=12÷2=6
    old/"matured" people please dont roast im just a kid sharing what i got from listening to class, it's not that hard to attend to your class and listen to your teacher.

  15. Imagine creating a game a the scientist and mathematician goes berserk for it.

    Ahmmm. How can this evolve human kind again?

  16. Hmm.. Does the 3n + 1 rule work as a 4 2 1 loop? Or because the 3n – 1 doesn't loop.

  17. Basically this is headache i understand nothing but dots

  18. "…Surrounded by any number of lice." Hahaha, my favorite line from this!

  19. I have lost complete interest in these dramatic comedy….unsubscribing.

  20. It's so easy when they just go rage or shhh

  21. 6:30 Uoooooohhh!!!! It looks pretty cool!!! Like something came out of Kaiji.

  22. You didn't explain the game at all until you had already played it.

  23. I feel like this would mean that chess is also a game that “breaks your brain”. While chess may be easier to analyze and predict, there are many different combinations. By this logic most games would be impossible to comprehend especially if they have many choices. Although I do understand that this game is way more rooted in math than most other games and that a lot of games are able to be predicted by computers, but I am sure that there are other games out there that also are impossible to process

  24. It was actually a pretty darn good Yoda voice (the first thing Yoda says) not the others

  25. I like the fact how He making those noises of yoda by himself 😭

  26. 3:14 pad the run time, you must. 😂🤣 interesting video 😇

  27. Game not hurting my brain, you explaining it hurts.

  28. You don't hear of John Conway often, but when you do you know it's gonna be fun

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