The Dot Game That Breaks Your Brain

June 16, 2020



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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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All Comments

  • My gr8 teacher first showed my class this game
    .
    .
    MY GR 8 TEACHER

    ash c June 16, 2020 7:45 am Reply
  • puts two dots
    my brain: KADNAOIDN[EW'PFNapf"mwa:foeF

    HyDragon Gaming June 16, 2020 7:45 am Reply
  • He says we're far off from being able to compute the outcomes of larger dot games, yet in the next 50 years we might have proper functioning quantum computer… Which will be able to compute more dot games :

    GGsolokid June 16, 2020 7:45 am Reply
  • Dots dots more dots ok now stop 😀

    xenchowlee June 16, 2020 7:45 am Reply
  • 11:58
    What about my homework folder

    stormcloud June 16, 2020 7:45 am Reply
  • I love how he just casually says crazy things and keeps going! Really reminds me of college. At least he goes back and addresses it. Simulates us all simultaneously saying “hold on a second, go back” to our professors. I swear one of mine did it on purpose because she loved hearing the immediate proof that the class was still with her. Great professor! Easily the smartest person I’ve ever met. She also baked for us! Shout out to Dr. Browning!!

    nicksurfs1 June 16, 2020 7:45 am Reply
  • "You cant just play with yourself. You need an opponent!"

    Cirlce jerk time

    Larry The Cable Guy June 16, 2020 7:45 am Reply
  • 0:19 kiven:are you swettin yet
    Me:we have aircon and its very cold

    Prince Quiñones June 16, 2020 7:45 am Reply
  • This was better than Star Wars episode 8 and 9 combined.

    Robert Tomkinson June 16, 2020 7:45 am Reply
  • i think yoda died

    Brian Ock June 16, 2020 7:45 am Reply
  • Ketamine, Yoda needs.

    Anon Ymous June 16, 2020 7:45 am Reply
  • V s a u s e
    N o t
    M i c h l e
    H e r e
    B u t
    K e v i n
    I s

    Ash Draws Stuff June 16, 2020 7:45 am Reply
  • yoda is a whole mood-

    Insanely Sane June 16, 2020 7:45 am Reply
  • Darth Reven plays this game

    PC R June 16, 2020 7:45 am Reply
  • Vsuase is basically a video of math but actually fun

    snipclip_ djninja June 16, 2020 7:45 am Reply
  • Teacher: Stop doodling
    Me: These aren't doodles
    Teacher: Then what are they? Complicated diagrams about unsolved fundamental theorems?
    Me: 8:46

    Smash fan Zhao June 16, 2020 7:45 am Reply
  • 3:25 why cant you connect the remaining black dot to itself?

    Carmen June 16, 2020 7:45 am Reply
  • Yoda was the highlight of my day.

    General 666 June 16, 2020 7:45 am Reply
  • Yoda redo his death scene‼ LOL‼

    Cookie Monster June 16, 2020 7:45 am Reply
  • 3:28 you’re welcome

    Watermelon The Rainwing June 16, 2020 7:45 am Reply
  • 3:29 mmMmMMMmm

    TheSpikeDevice June 16, 2020 7:45 am Reply
  • yoda goes on a katamine induced temper tantrum asmr

    SolarCipher June 16, 2020 7:45 am Reply
  • 3:31

    Kaden June 16, 2020 7:45 am Reply
  • What about 3 players?

    DarthXalex June 16, 2020 7:45 am Reply
  • I just saw Yoda have a stroke for 22 seconds. Nice.

    Jadon Andemichael June 16, 2020 7:45 am Reply
  • 3:28 when my brother finds out his parents lied about Santa

    Jim The spider June 16, 2020 7:45 am Reply
  • here's the answer:
    ((2pi)^(x!))D^y!
    let D= dimensions of position
    let x= distance apart from dots
    let y= time per second of dots position

    Dan -Horsenwelles- Williams June 16, 2020 7:45 am Reply
  • My first thought:
    Tree(3)

    Diamond Wolf June 16, 2020 7:45 am Reply
  • WhTs the song at around 6 minute mark?!

    rapacca June 16, 2020 7:45 am Reply
  • 3:28 why did he dont draw a line to himself

    Nikola Vukcevic June 16, 2020 7:45 am Reply
  • Yay, a new game to torture my friends with

    Labratondarun Is back June 16, 2020 7:45 am Reply
  • 3:28 For some reason, I wish that there was 5 more minutes ofthis, followed by it just ending,

    Michael Antonio June 16, 2020 7:45 am Reply
  • 1:40

    Michael Antonio June 16, 2020 7:45 am Reply
  • visible confusion

    Gilbert TheRegular June 16, 2020 7:45 am Reply
  • visible confusion

    Gilbert TheRegular June 16, 2020 7:45 am Reply
  • Me playing with 0 dots to end the game in -1 turns.

    Le Child June 16, 2020 7:45 am Reply

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