The Dot Game That Breaks Your Brain

The Dot Game That Breaks Your Brain


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
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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…

100 Comments

  • Buck Dog

    October 4, 2019

    I don’t want to play this game.

    Reply
  • The Goat

    October 4, 2019

    That yoga mental breakdown tho

    Reply
  • Growtorlee

    October 4, 2019

    1:40 Masturbation exists

    Reply
  • MCG TheReaper

    October 4, 2019

    won a 2 dot game in 3 moves total… thought it had to be 5. The math is wrong, (Red 2 moves, Blue 1 move). The 3n-1 moves is incorrect.

    Reply
  • Ryan B

    October 4, 2019

    Where do you guys find this kind of stuff?

    Reply
  • Heyitssaldownhere .0

    October 4, 2019

    the only thing i could think of while i was watching this entire video was, that the game sprouts actually looks like a soot sprout, with the dots and the name

    Reply
  • Rothnacum1

    October 4, 2019

    I saw niples 😉

    Reply
  • Thunda

    October 4, 2019

    I Better see some 3:28 Memes in this comment section…

    Reply
  • Lionsun1010

    October 4, 2019

    It doesn’t break your brain it’s just confusing

    Reply
  • Aurelia Goulding-Laing

    October 4, 2019

    I can comprehrnd

    Reply
  • NobodybutAW

    October 4, 2019

    "You cant just play with yourself!"

    12 year old boys at 3 AM: intense sweating

    Reply
  • Octi_ Ghost

    October 5, 2019

    P

    Reply
  • Trenton Mourer

    October 5, 2019

    I'm so confused, not because of the brain game, but I watched Kevin play with a Yoda puppet and make it have a mental breakdown.

    Reply
  • Thomas Sturm

    October 5, 2019

    Conway? Ah. It is the same conway as Conway's Game of Life. Makes sense.

    Reply
  • China Re Dulva

    October 5, 2019

    This is why he has no friends

    Reply
  • Man of Culture

    October 5, 2019

    ez i can play..

    but i dont have friend

    Reply
  • Tyler Tenebrae

    October 5, 2019

    What I actually learned:
    A mathematician will fill an entire notebook for 10 bucks.

    Reply
  • Determinated Dog

    October 5, 2019

    Am I In A Genjutsu-
    Oh wait I Can't say it Others don't know the anime!

    Reply
  • Jace Ziegler

    October 5, 2019

    Thats most games. Even chess

    Reply
  • Timothee macuayay

    October 5, 2019

    How about playing that in 3D?!🤔😋

    Reply
  • TheRumpletiltskin

    October 5, 2019

    the blue and red lights are too much bro.

    Reply
  • ElloILikeCookies

    October 5, 2019

    Nobody:
    Nobody ever:

    Yoda: has a spasm

    Reply
  • Mediocre Meme Man

    October 5, 2019

    Yoda took to much cocaine

    Reply
  • Artic Gaming

    October 5, 2019

    This is complicated. I dont understand

    Reply
  • Soals

    October 5, 2019

    What if you use your artistic ability to draw a complex maze like structure that makes the other player have to rely on their ability to navigate without touching a line.
    Seems easier than all this math.

    Reply
  • JT

    October 5, 2019

    Cool calculations. Now add a 3rd player

    Reply
  • elie520

    October 5, 2019

    Actually insane video 😀 I love it!
    Edit: too bad your product placements ends with a lie. Even on a private network, in theory, you're safe to go at leat on you're bank account. At least, the VPN won't help at all on that front.

    Reply
  • Light InTheMeddows

    October 5, 2019

    when your drawing something and your so proud of it to the point you forgot about you battery and how it is on 1%. shutting off

    "Wait… I didn't save my aRT WORK, NOOOOOOOO!" dies

    I dunno I just came up with this because yoda reminded me of myself for some apparent reason. 3:28

    Reply
  • Yoosung Jung

    October 5, 2019

    beginning: "are u sweating yet you should be"
    me: *oddly gets really nervous"

    Reply
  • Lukas Martinelli

    October 5, 2019

    3:30 Til 3:50 vsauce, but way out of context

    Reply
  • Toxic DJ

    October 5, 2019

    3:29 scrunched up Kermit flashbacks

    Reply
  • Yundix

    October 5, 2019

    Way too much time spent on trying to be funny, the humor just doesn't work for me.

    Reply
  • test

    October 6, 2019

    Yoda is me.

    Reply
  • test

    October 6, 2019

    Yoda is a MOOD

    Reply
  • Avarickan

    October 6, 2019

    Just realized that he's got a table made of nothing but whiteboard. I'm going to need one of those some day.

    Reply
  • Vincent Varela

    October 6, 2019

    This has just confirmed my hypothesis,

    yoda is just a little green strong baby

    Reply
  • R Alexandra

    October 6, 2019

    🤔 I’m going to try playing this with my brother

    Reply
  • antonio procalla

    October 6, 2019

    What about 3 or more players?

    Reply
  • comment bot :15

    October 6, 2019

    3:33 this is what ligma does to u

    Reply
  • Mystic Aviator

    October 6, 2019

    3:32 anyone else reminded of Hector Salamanca from Breaking Bad?

    Reply
  • atiqua khan

    October 6, 2019

    3:30 you can draw a line to the same dot back, right?
    So, the monster did not really lose…

    Reply
  • Gábor Papp

    October 6, 2019

    2:34

    Reply
  • Ano N. Ymous

    October 6, 2019

    3:28 Yoda went Gollum

    Reply
  • Ayesha Shah

    October 6, 2019

    You forgot "MMM~"

    Reply
  • Xx_Meme_Lord_xX

    October 6, 2019

    3:31 Yoda vs Dio.
    I want it, I need it now.

    Reply
  • Ashton Polston

    October 6, 2019

    what if u play this game in vr?

    Reply
  • Matt Dobing

    October 6, 2019

    Why does it seem to be only VPN company's that sponser vids?

    Reply
  • Harry Dixon

    October 6, 2019

    My dad: Shouts at me in the morning to get out of bed
    Me:

    3:28

    Reply
  • Neth

    October 6, 2019

    8:26 Futasm: Also known as "Endorsement of Traps"

    Reply
  • tripp hayes

    October 6, 2019

    Why is no one meme this 😂

    Reply
  • Baguette Depain

    October 6, 2019

    Woah, it's almost like exponential things grew fast and we quickly run out of computing power to compute them.

    Reply
  • John Doucette

    October 6, 2019

    Um.

    Reply
  • Highlighter

    October 6, 2019

    how about making it 3D

    Reply
  • Moceit? Yes

    October 7, 2019

    Let me just say, don't listen to the intro with your volume all the way up

    Reply
  • Anthony Tilleman

    October 7, 2019

    I think the real challenge is having to remember all the rules of the game.

    Reply
  • Coozooken Fers

    October 7, 2019

    like a minute in and you're going through soooo much effort to make this confusing lol 'its just two dots, i could draw out all the possible moves' compilation of him just kinda drawing things because he's yet to describe the rules or objective yet is here showing us moves, that's a classic move making things confusing because of you're explanation right there. Yeah so a minute and a half of prepping our brains to be confused before introducing the confusing this is such a weird move. Now it's obvious why there was all that build up at the start lol so it doesn't break you're brain it just looks like a really simple yet fun old game. oh and it's rigged because player one double the chance of success

    Reply
  • The Harmonica Loser

    October 7, 2019

    3:34 Sounds like angry birds

    Reply
  • Cringy Legend

    October 7, 2019

    My math teacher: what’s the possibility of player one winning sprouts with 100 dots?

    Me: brain exe. has stopped working

    Teacher: yOu leArNed tHis lAsT yEaR

    Me:… Ight Imma head out

    Reply
  • Chris33134 Gaming

    October 7, 2019

    You jump scared me

    Reply
  • Isosceles

    October 7, 2019

    Sudoku is more stressful

    Reply
  • Shalestorm

    October 7, 2019

    Yoda's death had me laughing far too hard to follow anything after!

    Reply
  • Jkarggo

    October 7, 2019

    3:33 needs to be a meme

    Reply
  • Kremit The Froggo

    October 7, 2019

    HOLY HELL YODA TURNED INTO AN ANGRY BIRD THAT OVERDOSED ON EVERY DRUG EVER

    Reply
  • The Untender

    October 7, 2019

    I don't even understand the first drawing he somehow created from the two dots…

    Reply
  • Warded Thorn

    October 7, 2019

    This reminds me of tic-tac-toe. As a kid, I thought it was really difficult, but one day I figured out that if I put the first x in the right spot, I could force a win.
    Then I found out the second person could respond with something that actually forces the win into a cat's game.
    Now I can't play tic-tac-toe. It's pointless.
    Edit: lol as soon as I commented this "Yoda" referenced tic-tac-toe.

    Reply
  • Myat Lin Phyo

    October 7, 2019

    stranger things theme song plays ferociously on the background

    Reply
  • Guilherme Costa Coimbra

    October 7, 2019

    Plot twist: Yoda was a paid actor (a pretty good one)

    Reply
  • lilo231

    October 7, 2019

    Nord is better

    Reply
  • ShadowSpade68

    October 7, 2019

    Yoda is me when I lose literally any kind of challenge or puzzle, etc.

    Reply
  • Lightning snake

    October 7, 2019

    . .

    Reply
  • Kaos Null

    October 8, 2019

    "But you can't play with yourself"

    Ummm…

    Reply
  • Gamer josh

    October 8, 2019

    P1: Alright lets start the game! How many dots should we start out with?

    P2: 0

    P1:

    Reply
  • Lord Kami-sama

    October 8, 2019

    Bold of you to assume that I have a mind

    Reply
  • GameFreak Plays

    October 8, 2019

    WtFFFFFFFFFFF

    Reply
  • Logan Mancuso

    October 8, 2019

    Would a game of p1=11 and p2=6 winning moves be a tiny+? Or still a zero game since both have a winning strategy?

    Reply
  • Leo-Aki Siafa

    October 8, 2019

    I don't get this game?How does it work?

    Reply
  • Leo-Aki Siafa

    October 8, 2019

    Is there a time limit?

    Reply
  • Leo-Aki Siafa

    October 8, 2019

    My brother asked "how do you win again?"

    Reply
  • Katie Belcher

    October 8, 2019

    Wait this isn’t Micheal

    Reply
  • Vibezz

    October 8, 2019

    I have no words.

    Reply
  • Mhon de guzman

    October 8, 2019

    May gahd why didnt you make this video much early… I want to contest my prof in graph thoery with this game now that i watched this hahaha

    Already graduated so i cant sad haha

    Reply
  • Ciel

    October 8, 2019

    Lol we play this inside our classroom here in PH when there’s no teacher 🤣

    Reply
  • Golem - BrawlStars

    October 8, 2019

    Vsauce:You can’t just play with yourself.
    Me:I’m about to prove this man wrong.

    Reply
  • Kinky Sushi

    October 8, 2019

    Kevin: "You can't just play with yourself"

    Me: "Oh.. you underestimate my power"
    opens lube bottle, and searches loli on incognito

    Reply
  • McHacks Gamer

    October 8, 2019

    Maths,, sure

    Reply
  • Predrag Radjenovic

    October 8, 2019

    This game was heavily featured in an SF novel published in 1969 called "Macroscope" by Piers Anthony. It was nominated for the Hugo Award for Best Novel in 1970. Go read it if you love SF and missed it…

    Reply
  • Kyojin_9

    October 8, 2019

    1:41

    Challenge accepted 🧴🧻🍆💻

    Reply
  • Kyojin_9

    October 8, 2019

    I wanna protect my MEMES

    Reply
  • The Raven's Edge

    October 8, 2019

    Yoda had a stroke

    Reply
  • Dununerp

    October 8, 2019

    “But you can’t just play with yourself”

    Me: is that a challenge?

    Reply
  • hrithik jho

    October 8, 2019

    Vsauce Kevin here……WHOS KEVIN?

    Reply
  • Julien Valdez

    October 9, 2019

    I have a headache from all of this math

    Reply
  • Kaera猫

    October 9, 2019

    What if the game was to refrain from connecting the dots in the first place? Really plants a seed in your mind, does it not?

    Reply
  • Laykin Renee

    October 9, 2019

    Could have definitely done without Yoda.

    Reply
  • Lilsago1975 /lil

    October 9, 2019

    That room must smell like dry and erase markers 247

    Reply
  • Hatred

    October 9, 2019

    what

    Reply
  • BlueLight

    October 9, 2019

    hi kevin

    Reply
  • Nikolov_Playz

    October 9, 2019

    this vid does not break ur brain
    o realleh?

    Reply
  • Handmade Stick

    October 9, 2019

    MMMMMMMMMMMMMMMMMMMMMMMMMMMMEEEEEAAAAAAAAAAAAAAAAAAAABaaaaaaaaaAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAABAAAAABAMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMEHECKHEEgH

    e x p l a i n

    Reply
  • Randy

    October 9, 2019

    poor yoda

    Reply

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