# The Dot Game That Breaks Your Brain

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”:

*** LINKS ***

Vsauce2 Links

Twitter:

Facebook:

Hosted and Produced by Kevin Lieber

Instagram:

Twitter:

Podcast:

Research And Writing by Matthew Tabor

Editing by AspectScience

Huge Thanks To Paula Lieber

Get Vsauce’s favorite science and math toys delivered to your door!

Select Music By Jake Chudnow:

#education #vsauce2

I can win this.

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

amo ngu s

Can’t wait for 5d sprouts with time travel

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

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

3:46 to skip the 3:14 Yoda spasm.

hey that rhymes

If you can zigzag the 1 turn win

Doesn't that hurt ur throat to do that voice

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

3:15 – 3:45

I choked on my oxygen while laughing

3:20 You’re welcome.

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.

I am shur and you should listen and try at least

All this over 2 dots

I played this with my friend before

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

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

Here comes Tree(3)

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

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

3:10 the dots aren’t the only things dying

No not 3n-1 it’s haunting me help

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

Watching Yoda rage is the best thing ever

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.

Who else realised that Kevin is left-handed.

Who else realised that Kevin is left-handed.

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

Ahmmm. How can this evolve human kind again?

hes just talking about osu

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

Tantrum Yoda had

Basically this is headache i understand nothing but dots

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

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

Congratulations. You broke me

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

0:44 Daaaaang, that looks beautiful and super cool!

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

6:50–7:06

*DAB INTENSIFIES!!!!!*You didn't explain the game at all until you had already played it.

Yoda is the ultimate abstract math teacher

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

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

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

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

yoda just had a stroke

Game not hurting my brain, you explaining it hurts.

Are you on crack?

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