Vsauce! Kevin here, with a game you can’t possibly
comprehend. Really, it’s too hard for you. Your brain can’t take it. Look, I’ll show you: That’s it. Are you sweating yet? You should be. Real quick, huge thanks to ExpressVPN for
sponsoring this video and supporting Vsauce2. If your device is unsecured you’re gonna want
to get ExpressVPN to take care of that. I’ll explain more later but first let’s explain
our dots. Alright, as you stare into these dots your
brain starts to short circuit, doesn’t it? No. Why would it? I mean… it’s just two dots! I can draw out all the possible moves for
a game this simple. Look, I’ll show you. Okay, my award-winning handwriting aside,
this was a lot more complicated than I thought it was gonna be. And the thing is… as it scales, analyzing
what appears to be the simplest game in the world doesn’t just break your brain, computers
can’t even crunch the possibilities. Here’s how it works. The game of Sprouts starts with any number
of dots placed… anywhere. The boundaries of the game board are limitless,
so put the dots wherever you want. We’ll play with two dots. But ya can’t just play with yourself, you
need an opponent. Yes, yes. A worthy adversary, you need. Let’s go over the three rules of Sprouts. First, a player draws a line from one dot
to another, or from one dot back to itself. Lines can be curved or they can be straight…
they just can’t cross another line or themselves. When you draw a line, you get to place a new
dot anywhere on that new line. And in Sprouts, no dot can have more than
3 lines coming from it or going to it. Once a dot has 3 lines — it’s an unplayable,
dead dot. The winner of Sprouts is the last person to
draw a line. Or to put it another way, the player who can’t
draw another line loses. Okay, now my friend and I will play a two-dot
game of Sprouts. Go first, I will! Alright, Yoda. Dude. Okay Hang on! Alright fine. Just go. Alright, alright. Great job. You gotta make sure you draw a new dot on
the line. Yes, yes, yes. Invented this game, I did! Sprouts trained many Jedi minds, hundreds
of years! Hundreds of years? No, No, No. Sprouts was created in 1967 by Cambridge mathematicians
John Conway and Michael Paterson. My turn it is! Dots lead to lines. Lines lead to dots. Sprouts is the path to the light side of the… And I just won. Alive this dot still is! Yeah but you can’t connect it to anything. Look. Dead, dead, dead, dead and you can’t draw
a line to get to this one. *angry noises* Explain why I lost you must! Alright, the first player can always lose
a two dot game against a perfect opponent because, even though it’s complex — your
brain can analyze two dot Sprouts. I mean, you could literally just memorize
this whole game tree chart to make exactly the right moves as player two, rendering player
one helpless. Player 2 can engineer the two-dot game so
that it ends on a 4th move win for them — but Conway and Paterson figured out when the game
has to end. Check it out. They discovered that a game of Sprouts must
be completed by 3n – 1 moves, where n=the number of starting dots. So that means a two-dot game is concluded
in no more than 5 moves because (3*2) – 1=5. So problem solved, right? No. Why? Because the game can play out in many different
ways. What’s interesting is that player 1 actually
has 11 ways of winning compared to player 2 having only 6. It’s just that if player 2 knows exactly
what they’re doing they can always facilitate one of their 6 winning outcomes. What’s amazing to me about Sprouts is…
this is all with just two dots! As soon as we add a third dot to the game… Become more difficult to analyze than Tic-Tac-Toe
it does! Adding a third dot at the beginning means
that we could have up to 8 moves to determine a winner since (3*3) – 1=8, but we have
more possible moves to start. It isn’t hard to figure out how many possibilities
we begin with — it’s just [n(n + 1)] / 2. So here we have our number of dots at start
and number of initial possible moves. [n(n + 1)] / 2. And number of moves to determine a winner
that’s 3n -1. So if we have 2 dots to start the game, the
initial possible moves would be 3. With 3 dots to start that jumps to 6. For 4, it’s 10. For 5 it’s 15. And so on. Now that we know this, what’s the guaranteed
strategy for winning every time? There isn’t one. Because since the game can develop in so many
different ways, especially once you start playing with 4 or 5 dots, players will have
to constantly re-analyze and adapt their moves to force their opponent into a loss. You need to factor in which dots are still
— and eventually no moves at all. There’s just no formula for this. Adapt and overcome, you must! What we do know — kind of — is who can win. The first real glimpse into dominant Sproutology
came from Denis Mollison, a Professor of Applied Probability at Heriot-Watt University. Conway bet Mollison 10 shillings — before
the 1971 decimalization of the British monetary system and equivalent to a little under \$10
today — that he couldn’t complete a full analysis of a 6-dot Sprouts game within a
month. Well, he did. And it only took 47 pages. I’m not looking forward to picking those up. Mollison’s analysis led to the conclusion
that Sprouts games with 0, 1, or 2 dots could always be
won by the second player. Games with 3, 4, and 5 dots could always be
won by the first player. The second player can always win with 6 dots,
but that’s where the computational power of the human mind started to strain under
the weight of the Sprout. There were just too many scenarios to compute. WAIT — how can you have a game with 0 dots? Well, if there are zero dots, the first player
wouldn’t be able to draw a line, so the second player wins. One thing that’s really weird about Sprouts
is… you’d think that playing the game would visually result in nothing but near-random
lines and patterns but Conway and Mollison unearthed something: bugs. They call this.. FTOZOM! The Fundamental Theorem of Zeroth Order Moribundity,
which states that any Sprouts game of n dots must last at least 2n moves, and if it lasts
exactly 2n moves, the final board will consist of one of five insect patterns: louse, beetle,
cockroach, earwig, and scorpion, surrounded by any number of lice. Scorpions are arachnids, not insects, but
these guys don’t have time for biology. And that’s the FTOZOM for you. But this was all 50 years ago. How has Sproutology progressed since? Well, it lay dormant for decades until Carnegie
Mellon University fired up its computers in 1990. Using some of the most advanced processors
of the era, computer scientists David Applegate, Guy Jacobson, and Daniel Sleator were able
to map Sprouts conclusively up to 11 dots. They found the same pattern: 6, 7 and 8 favored
the second player. 9, 10 and 11 favored the first player. There appears to be an endless 3-loss-3-win
pattern with a cycle length of 6 dots. In 2001, Focardi and Luccio published “A
New Analysis Technique for the Sprouts Game” that showed a simpler proof of Sprouts to
7 dots by hand. Now we’re up to 11. So, we’re making progress on the pencil
and paper front. But what about…1,272 dots? Or a billion dots? We’re not even close. Like really… not close. Julien Lemoine and Simon Viennot created a
computer program called GLOP that could calculate Sprouts results more efficiently, and in 2011
they were only able to process up to 44 dots consecutively. Their results were in line with Carnegie Mellon’s
cycle of 6, but the computational power — and time — required to get us to proving results
with, say, a million dots, is way beyond our reach. It’s been over half a century since Conway
and Paterson were drinking tea in the Cambridge math department’s common room and playing
around with inventing a simple pencil and paper-based game. They noticed that the game was spreading throughout
the department and then the campus, seeing students hunched over tables and spotting
the discarded remnants of epic Sprouts battles. They stumbled on something so big and so complex
that the human mind can’t fully fathom it beyond a very limited point — and it all
started by just connecting a couple of dots. And as always — thanks for watching. Mmm, mmm. Perfect! What are you doing to my phone? Oh, great! Listen! If you use unsecured public wifi like at a
coffee shop or airport then your phone is vulnerable to attackers seeing your bank info,
with ExpressVPN because it’s consistently faster than other VPNs and it’s ridiculously
easy to use. You literally just hit this giant button,
it connects to a local server and that’s it. I love that it works in different countries
and how it works is ExpressVPN creates a secure, encrypted tunnel between your device and the
internet to make sure any hackers on the same network can’t snoop on or steal any of your
data. To get 3-months free with a 1-year package
and a 30-day money-back guarantee go to expressvpn.com/Vsauce2. I have it on my phone and you can too. How do I change the wallpaper back? Yoda…

• ### samsamsammy2013

Does anybody know what the outro music is? At 11:29

• ### Brandon Caudell

Kevin, Conway, and Yoda. Yes, yes, and yes.

• ### Game Stuff

Three year olds when mom doesn’t buy them stuff

Insert Yoda in a tantrum here

• ### NineNineSevenTurbo

The slightly offsync audio in this video broke my brain…

• ### Newby Ton

This isnt just a normal game
This is angry baymax with a nose

• ### Red Fox

I am glad that I haven't done that much of Math .
My mind is safe.

• ### Newby Ton

Imagine spending a month, 47 papers and ink for less than \$10

• ### Mohamed Shakib

What's the name of the track that starts @ 5:40

• ### Charlie

anyone else get the dot vs snake app ad before the video ?

• ### D0nsies

This was a more realistic Yoda death scene than in Star Wars ep 4

• ### Josh Garcia

Explain naughts and crosses now…

• ### Nolan Turek

Another game. Alright, lets how I can have another siezure trying to understand it

I do enjoy these videos pls dont stop

• ### pauldzim

The dude does a pretty good Yoda

• ### Poppin' It

Assuming we make some big leaps forward, wouldn’t Quantum Computing be perfect for analyzing scenarios starting with a high number of sprouts?

• ### Grand Flex Johnson: John Jhon Jon Jonathan IV

yoda gaming doesnt look so good

• ### Filip Petrovski

did anyone notice that he is left handed

• ### Psybandit -

3:29 when you lose a game of sprouts against Kevin from VSauce and you are yoda.

• ### The Laynz

wtf happened to vsauce o.o

• ### Smellfish

Challenge accepted.

• ### Captain zac

I don't think they let Kevin out between videos

• ### Yagami Raito

Is Kevin the man behind the Pimp Master Broda twitter account?

• ### B P

A "like" for the Yoda voice.

• ### Juan Bernal

This is the best video you have ever made.

• ### blimp boi

kevin is howtobasic

• ### SteelBreeze021

For book fans: The Sprouts game is a component of a science fiction story written by Piers Anthony in 1970 titled "Macroscope".

• ### Hyenphea

If any hacker wants to hack my phone, it's their loss tbh. The horrors within will scar them far longer than a hack will scar me.

• ### lokolo lok

Yes, I am sweating. But probably it is because of the heat

Nerd

• ### Matthew Boyd

I used a method like this to creat maps for this game I had in my head.

It was replayable maps and the dots where rooms, the lines where the doors and paths to other rooms, and the idea was entering a room you have two choices to leave and progress (3 or more was to complex)

I wash blown away to see the exact same paths I used for my maps in this video, but I guess there is a limit to how many different designs there are.

• ### Charles Birkner

BTW, this video looks rather funky when viewed with some red+blue 3D glasses.

• ### Jesus Christ

3:33 when yoda has a seizure.

• ### Angel R

Bring Yoda back on the next video, this was so funny

• ### Tania L. Williamson

The decimalization started in 1969. I was living there at the time. Where did you get 1971 from?

• ### Nomekop 777

9:25 why did it only take the computer 8 seconds to calculate a 9 dot game?

• ### El Bichote

1:49 Next time try a Scooby-Doo puppet

• ### George Higgins

Kevin> Frank Oz: change my mjnd

• ### RDX CC

Why I play with myself everyday

• ### Educated Drilla

How would this game work in 3 dimensions?

• ### Will lopez

Yodas a boomer

• ### Karan Gupta

I have a conjecture, if a dot dies in n branches, then the win-loose cycle will have a 2n dots period.

• ### The Illusionist

I can’t help but think I would be more able to focus on the subject without the over the top theatrical acting, but that’s just, like, my opinion, man.

• ### Karina ilsøe

1:13 my brain hurts

• ### Atlas

Dots are vertices, edges are drawn between them.
A new vertex is added anywhere on the a newly drawn edge.

A curved plane is created whenever a newly drawn edge makes a closed shape in 3D space (any loop of vertices and edges).

New edges cannot pass through planes.

Vertices which have 3 edges connected to them are dead.

• ### Dustin Hoeppner

I LOVE the pink and blue and 80s music

• ### VidkunQL

You are left-handed, Why, why did you draw the left dot first?

• ### Michael G

That's The basics of Evolution……

• ### K0DeX

0:55 You guys forgot to credit Julian Emery for the sample of Synthetic Life you used. Love you guys <3 Don't want you getting in to trouble!

• ### Edgar Perez Ochoa

less yoda please, great video though

• ### Sapphire High Noon Yasuo

The Yoda segment is even more horrifying with red/blue 3D glasses. I do not know if this video was made with that intention, but it does have a 3D effect to it.

• ### Angelita Tavares

3:32 yoda.exe has stopped working

• ### Joe Mills

Sprouts? Completed it, mate.

• ### Nuki YT

These numbers are inconclusive because you forgot that spacially dots cannot go through eachother which means you have to factor in people's handwriting, marker thickness, especially in the 400 dot range. Just a thought

• ### The Major

Well it's easy, to figure out 1 billion dots… at least the number of starting moves is 500000000500000000 so it's not that hard to compute…

• ### FluffySquidGamer

3:35The face you make when someone around you farts

• ### Bugbears and Wormwood

Jokes on you, my brokes already brain

Well we came to a conclusion that i9s, xeons and threadrippers cant handle a bag of dots!!!

• ### Toster Cx

Where is the phone's wallpaper from?

• ### Bip901

I wonder about variations of the game where a dot is dead after K lines, not 3.

• ### shakur

me: wakes up
also me: 3:28

3*2-1=5
yup

• ### Clark Potter

You look like that douche in Avatar that wants all the unobtainium.

Great vid that was.

• ### 〈Clex〉

Player 3 has joined the game

• ### Kinryko

Yoda off a perc

• ### Alan Burggren

But why is it 3n-1?????

Vsauce: This game physically cannot he comprehended

Also Vsauce: 6:27–6:48

Me: So… so it’s just chess…? Chess can’t be comprehended…?

• ### Jack Hill

Kevin's like the last guy in a group chat trying to keep it alive

• ### Doc Brown

the next obvious evolution of this game is to make it 3 dimensional

advanced version of dots and boxes?

• ### Ryūjin Jakka

I'm going to remember every single pattern and how to 100% win. That way when I have a son or a daughter I could say "let's play a game. If I win, you have to go to bed. If you win, you stay up."

My parenting level is over 9,000 and I don't even have a child.

Yoda got me

• ### Brontar

1:41 just leaving this here

NO!
WHY?
))

• ### Lily Lavelle

YODA WHATS WRONG

• ### Commander Boreal

“Invented by John Conway and..”
Damnit! There he is again!

• ### Michael Baker

lol… lol

this guy has to wipe his board clean with spray everytime he erases something

• ### me3333

In my best Peewee Herman voice "Connect the dots La, La, La"

• ### _ jaybird _

3:30 Leaked audio from Angry Birds 3, work in progress

haha GLOP

• ### Luka Hrvatic

Number one is written like this: ( 1 ), NOT like this ( I ). Please learn this and apply it. What you are writing is incorrect.

• ### Twop

What if we did this with lines?

• ### Ανδρέας Στέλλας

sorry brain for these 12' and 50" of awkardness

• ### Catherine Juan

is his shirt grey?

Tree 3.

• ### Michael Jordan

Wait, aren't arachnids insects?

What. 3:29

• ### DJack Klingler

Ok how about a line like this then //////////// it confines it's self to what the rules say and if the rules don't exclude it then….

• ### Eli Egbert

Why do I feel like this guy isn't wearing pants

• ### James Bond

3:30 my last 2 brain cells

• ### Renee Krueger

Damn, you and Matt weren’t joking about giving that vintage yoda the airtime it needs to pay itself off ?

• ### Emily Rose Lacy-Nichols

Oooh fun!!! Must try this lol!
Fascinating video!

• ### MrCrazyhack3r

So mind blown died and no one ever said anything????

• ### john bailey

The moment I get back to school I'm challenging my math teacher to a 5 sprout game

• ### Runn

Knot theory: The game.

3:28 the number of memes that can be created exceeds the number of possible moves for 1000000000 dots.

• ### Draven Petroski

Can we make dying puppet Yoda a new meme? Anyone?

• ### Nick G.

Now how much harder will it be to compute if there are more than two players?

• ### Steven Utter

sprouts?
Hey if Vsause 1 could make a video once every decade that would be cool too.