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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  • "Are you sweating?"


  • My brain already is broke

  • With the first game where the imitated character lost, why not just connect the remaining dot to itself?

  • The colorfull lights are so distracting.
    But still a reat video

  • LMFAO! Love the Yoda puppet and voice!

  • I honestly think that Yoda there is alive.

  • 3:28 6 year olds when they lose a game

  • Vsauce2: This is the hardest math equation ever!
    Also Vsauce2: 2+2! Are you sweating? You should be!

  • It strikes me that a form of topological analysis could be beneficial to understanding this game. That, or electrical circuit analysis…

  • Kevin *draw 2 dots * is your brain sweating yet?!?!

    Me: yep he's crazy.

  • Kevin *draw 2 dots * is your brain sweating yet?!?!

    Me: yep he's crazy.

  • 7:05 my man wrote a 47 page paper for $10

  • My brain protesting visciously trying to comprehend ftozom.

  • Don't know how he can keep a straight face drawing dots and lines while playing a crazed puppet in front of millions

  • kevin: *draws two dots
    me: sweats nervously

  • 3:29 is this cannon?

  • UwUUwU

    Author Reply

    I played the game with my friend… he has a hole in his head

    (Dark humor)

  • They are hiding this is in Area 51 as an IQ test for aliens

  • How does playing on other surfaces (e.g. sphere, torus, Klein bottle, projective plane) affect the game?

  • ah yes


  • him: (draws two dots)


    Author Reply

    Is this a kid show?

  • ash cash c

    Author Reply

    My gr8 teacher first showed my class this game

  • puts two dots
    my brain: KADNAOIDN[EW'PFNapf"mwa:foeF

  • 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 :

  • Dots dots more dots ok now stop 😀

  • 11:58
    What about my homework folder

  • 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!!

  • "You cant just play with yourself. You need an opponent!"

    Cirlce jerk time

  • 0:19 kiven:are you swettin yet
    Me:we have aircon and its very cold

  • This was better than Star Wars episode 8 and 9 combined.

  • i think yoda died

  • Ketamine, Yoda needs.

  • 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

  • yoda is a whole mood-

  • PC RPC R

    Author Reply

    Darth Reven plays this game

  • Vsuase is basically a video of math but actually fun

  • Teacher: Stop doodling
    Me: These aren't doodles
    Teacher: Then what are they? Complicated diagrams about unsolved fundamental theorems?
    Me: 8:46

  • 3:25 why cant you connect the remaining black dot to itself?

  • Yoda was the highlight of my day.

  • Yoda redo his death scene‼ LOL‼

  • 3:28 you’re welcome

  • 3:29 mmMmMMMmm

  • yoda goes on a katamine induced temper tantrum asmr

  • KadenKaden

    Author Reply


  • What about 3 players?

  • I just saw Yoda have a stroke for 22 seconds. Nice.

  • 3:28 when my brother finds out his parents lied about Santa

  • here's the answer:
    let D= dimensions of position
    let x= distance apart from dots
    let y= time per second of dots position