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

live and which ones are dead. You need to force your opponent into bad moves

— 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,

your logins, your secret collection of… memes. You’re gonna want to protect your meme folder

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…

The lighting gives me dad flashbacks

n1

I have not watched Star Wars and now I never want to watch it.

SO CAN WE PLAY THIS IN SCHOOL OR NOT!?!?

But… At the beginning, have you forgotten the case where a line is drawn around the other point ?

I'll tell Brandine it smells like slurry.

How did you get Fozzie Bear to voice-act the Yoda part?

rip yoda, pls dont bring him back…

How can he write with his left hand?

Video, I watched.

A like, I dropped.

Why does your voice sounds like Aaron Paul's?

Can’t you just draw a circle on that last dot?

6:48 – improvise…

Kill i must

3:32 when anything tries to figure this game out

Isn't this exactly the math question from Good Will Hunting?

3:28 when you run out of pizza rolls

That John Conway came up with a lot. I've only ever known him for his famous Conway's Game of Life, but lately his name's been cropping up in some other equally interesting things.

I thought that the entire topic of sprouts had already been covered by Robert Rankin.

I'd be interested to see how this game's complexity scales with extra dimensions. I mean, imagine how much more complexity there would be if it were 3 dimensional. Or 4!

Wtf. This is just awful.

Yoda as voiced by Marge Simpson

When you wake up happy to play something on your console,but your parents took it away 3:28

This is easy to understand I'm reading it like it's chess it all depends on who you play with

I came up with 46 different possible moves within the first 3 moves and I may have stumbled upon the way to win every single time

3:28 me when my sister said that D&D is just a board game

Use The Force, Yoda.

3:29 me when someone eats the last dorito

u cant play with urselfMe: watches Yoda spasming.

Me: alright that's enough internet for today

memes3:35 me when school starts

I vote Yoda for the new host.

I imagine that the reason the cycle comes in 3's is because it takes three lines to kill a dot, if you played a modified version where it took 4 lines to kill a dot and then analyzed the games you might find that the cycle comes in patterns of 4 (0 – 1 – 2 – 3 always being P2 winnable, and 4 – 5 – 6 – 7 alway be being P1 winnable) just a guess though

3:28

Kevin= HTB confirmed XD

This isn’t how I remember playing this game on a napkin with my dad at restaurants…there were dots all over and you could only draw one line IIRC.

With quantum computing this will likely become easier

Can you make a change reaction that start from multiple areas let me explain A reacts to B but E stops B but the a and b reaction make reaction that make C then C makes a new change reaction

Yoda:

loses[Angry Yoda noises]

If you draw two dots instead of one, when connecting the dots, and keep the other rules the same, the game becomes infinite

In the intro it's sounded like he said HEY FEETOSS

3:27 to 4:00

Why? Get the duck on with it

Clickbaity title :/

Nothing brain breaking except for the exponentially growing complexity found in all kinds of things.

Also, there is no upper limit of how many dots you can start with, so of course we can't brute force an exhaustive plotting, ever

0:27 of course that's his wallpaper

1:40 hehe you have no idea how often I do that

… what about higher dimensions and other kinds of space like hyperbolic and spherical?

Title: brain can’t handle this dot

My brain:

starts teleporting my eyes left to rightSubtitles

angry noisesThink I'll lookup sprouts without the stupidity and childishness….

No like from me

Explain how it breaks the brain, replacing each dot with a number to represent how many lines can sprout makes the pattern/formula extremely easy to see. Endlessly drawing more and more dots to "prove" a simple pattern isn't "breaking the brain" nor is it really proving anything, if anything broke my brain it's a breakdown in language. 3 simple rules can explain it easily. Every line drawn reduces the total possible moves by 1, any dot generated is a "dead" dot if it's enclosed by other dead dots (or zeros), and any dot with the number 1 can't connect to itself. That's all the information needed to devise a min/max for any given game regardless of how many dots you start with.

3:29

when the autistic kid has a temper tantrumGonna play this with friends.

This kind of "wacky" but oh so patronising style of presentation is beginning to look so old fashioned.

Time to sub

Yoda was terrible just give us the info please

No one:

Kevin seeing two dots:

now this is an avengers level threatmy brain after he draws one dot:

3:27 laughing all day.

Hey, Vsauce4…Yoda here

Another great example of how a simple set of rules can lead to a very complex outcome.

The fact that he gawks at a 47 page paper is hilarious. From the perspective of a research mathematician, that's quite a tame size. 100-200 pages is when the stuff gets really mind boggling.

Can't you just make a program that makes a "photo" of the the dots and tell it the rules: don't connect more than 3 lines to a dot, don't cross lines, and connect each the dots to each other, last put a new dot down after every "turn". For the put a dot down for every turn you can put it on a quantum computer to map out all the possible places to put the dot on the new line. And for the where to draw the line you can do the same.

I always wondered what went on in a safe space.

I lost the game

Ahh I see your a fellow left hander yess

Am I the only one here in this comment section who is asking himself why haven't we been playing sprout all this time? I am totally playing this game with my friends and jedi masters

This looks a bit like tree but a game

Ya dot game is a cool came from conways book. I wonder if anybody has the computing power and analysis variants of sprouts with legal edges being 4 instead of 3. Or in general n edges at a vertice. To see if any patterns emerge that can shed light on the original sprout game?

3:40 everybody gangsta until yoda loses.

nordvpn isnt needed really

its easy

11:52 ah yes, the forbidden folder of…

MEMESJokes on you Kev…I’m playing with myself…right…now…. 👿🤤😈

Really not a fan of that Yoda segment

You sure yoda isnt a gremlin

Not to worry. Once Q-bits are utilized to work on this problem, we'll be able to solve it entirely.

Yo who's Vsauce

Mean title but nice video.

Neutral

"you can't just play with yourself"…

But I've been doing that every day.

Ima need a link for that yoda puppet

Did they use Quantum Computing to do all that? I think not.

"You just can't play with yourself"

Me too Yoda me too

damn yoda be salty

Have you considered doing one on Conway's Game of Life?

Soccer players when someone lightly taps them on the field 3:28

3:29

When i lose at any game 3:28

isn't it an infinite amount ? cause a circle has an infinite diameter so cant you just keep placing dots on the same line?

Bucket list of things the internet needs to have:

[X] Yoda puppet having a seizure.

The Yoda tantrum thing was actually hilarious

What happened to Micheal he hasn't even said anything about grants death 🙁

is yoda a chain smoker?

Have u ever got so furious ur face just deform

Good thing to know at 4am

There is only two possible reasons you chose yoda as an opponent.

1:Because he is smart

2:The face he made when he lost

“Nobody can make an educational video of Yoda moaning for 12 minutes straight”

Was the Yoda puppet a bet or something?

At 3:24 the remaining black dot has 2 lines, why can't Yoda draw a cirkel on that dot and place another dot in the circle?

Mate, the only thing scary about it, or the reason why it's a brain breaker, is actually just playing it. If you watched this video then tried it out with your friend you or they would either win. But knowing there are so many possibilities is the brain breaker.