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 Dot Game That Breaks Your Brain

100 thoughts on “The Dot Game That Breaks Your Brain

  • October 3, 2019 at 4:25 am
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    I haven’t watched vscout in a while wtf is happening
    I like the video as always but the comedy is meh

    Reply
  • October 3, 2019 at 6:01 am
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    U really had fun with him didn’t u lmao did a whole performance 3:30

    Reply
  • October 3, 2019 at 7:36 am
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    wth did I just watch

    Reply
  • October 3, 2019 at 8:18 am
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    Did this with my students.
    A fun way to introduce analization.
    Thanks VSauce!

    Reply
  • October 3, 2019 at 8:49 am
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    When your mom sneaks brussle sprouts in your food 3:28

    Reply
  • October 3, 2019 at 10:50 am
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    Omg! You killed Yoda!
    You ba***ds! 😂

    Reply
  • October 3, 2019 at 2:11 pm
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    1:13 Am I high or do I see a dad, a mother and 2kids?

    Reply
  • October 3, 2019 at 5:46 pm
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    3:01 we were almost at 19 69

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  • October 3, 2019 at 6:57 pm
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    3:35 you can kinda hear Kevin losing it in this part

    Reply
  • October 3, 2019 at 11:12 pm
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    my friend showed me this and i beat him first try

    Reply
  • October 4, 2019 at 12:17 am
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    Holy ship

    Reply
  • October 4, 2019 at 12:49 am
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    Well I mean, you can't break it more than it already is 😎

    Reply
  • October 4, 2019 at 1:47 am
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    Who tryna play two dots with me

    Reply
  • October 4, 2019 at 3:17 am
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    I challenge someone to a game of sprouts

    Reply
  • October 4, 2019 at 3:27 am
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    Other than ur over acting skills. I like cant even with game

    Reply
  • October 4, 2019 at 4:12 am
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    I don’t want to play this game.

    Reply
  • October 4, 2019 at 5:30 am
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    That yoga mental breakdown tho

    Reply
  • October 4, 2019 at 11:26 am
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    1:40 Masturbation exists

    Reply
  • October 4, 2019 at 4:13 pm
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    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
  • October 4, 2019 at 5:02 pm
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    Where do you guys find this kind of stuff?

    Reply
  • October 4, 2019 at 6:19 pm
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    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
  • October 4, 2019 at 8:27 pm
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    I saw niples 😉

    Reply
  • October 4, 2019 at 8:46 pm
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    I Better see some 3:28 Memes in this comment section…

    Reply
  • October 4, 2019 at 8:56 pm
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    It doesn’t break your brain it’s just confusing

    Reply
  • October 4, 2019 at 9:12 pm
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    I can comprehrnd

    Reply
  • October 4, 2019 at 10:22 pm
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    "You cant just play with yourself!"

    12 year old boys at 3 AM: intense sweating

    Reply
  • October 5, 2019 at 3:46 am
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    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
  • October 5, 2019 at 4:25 am
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    Conway? Ah. It is the same conway as Conway's Game of Life. Makes sense.

    Reply
  • October 5, 2019 at 5:05 am
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    This is why he has no friends

    Reply
  • October 5, 2019 at 5:23 am
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    ez i can play..

    but i dont have friend

    Reply
  • October 5, 2019 at 9:46 am
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    What I actually learned:
    A mathematician will fill an entire notebook for 10 bucks.

    Reply
  • October 5, 2019 at 10:59 am
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    Am I In A Genjutsu-
    Oh wait I Can't say it Others don't know the anime!

    Reply
  • October 5, 2019 at 12:16 pm
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    Thats most games. Even chess

    Reply
  • October 5, 2019 at 1:43 pm
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    How about playing that in 3D?!🤔😋

    Reply
  • October 5, 2019 at 4:54 pm
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    the blue and red lights are too much bro.

    Reply
  • October 5, 2019 at 5:03 pm
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    Nobody:
    Nobody ever:

    Yoda: has a spasm

    Reply
  • October 5, 2019 at 6:02 pm
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    Yoda took to much cocaine

    Reply
  • October 5, 2019 at 6:53 pm
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    This is complicated. I dont understand

    Reply
  • October 5, 2019 at 7:22 pm
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    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
  • October 5, 2019 at 7:28 pm
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    Cool calculations. Now add a 3rd player

    Reply
  • October 5, 2019 at 9:21 pm
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    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
  • October 5, 2019 at 10:08 pm
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    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
  • October 5, 2019 at 10:10 pm
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    beginning: "are u sweating yet you should be"
    me: *oddly gets really nervous"

    Reply
  • October 5, 2019 at 10:25 pm
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    3:30 Til 3:50 vsauce, but way out of context

    Reply
  • October 5, 2019 at 10:26 pm
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    3:29 scrunched up Kermit flashbacks

    Reply
  • October 5, 2019 at 10:51 pm
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    Way too much time spent on trying to be funny, the humor just doesn't work for me.

    Reply
  • October 6, 2019 at 12:44 am
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    Yoda is me.

    Reply
  • October 6, 2019 at 12:45 am
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    Yoda is a MOOD

    Reply
  • October 6, 2019 at 1:25 am
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    Just realized that he's got a table made of nothing but whiteboard. I'm going to need one of those some day.

    Reply
  • October 6, 2019 at 4:05 am
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    This has just confirmed my hypothesis,

    yoda is just a little green strong baby

    Reply
  • October 6, 2019 at 4:30 am
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    🤔 I’m going to try playing this with my brother

    Reply
  • October 6, 2019 at 5:19 am
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    What about 3 or more players?

    Reply
  • October 6, 2019 at 5:19 am
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    3:33 this is what ligma does to u

    Reply
  • October 6, 2019 at 6:11 am
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    3:32 anyone else reminded of Hector Salamanca from Breaking Bad?

    Reply
  • October 6, 2019 at 7:35 am
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    3:30 you can draw a line to the same dot back, right?
    So, the monster did not really lose…

    Reply
  • October 6, 2019 at 10:03 am
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    2:34

    Reply
  • October 6, 2019 at 12:31 pm
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    3:28 Yoda went Gollum

    Reply
  • October 6, 2019 at 4:03 pm
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    You forgot "MMM~"

    Reply
  • October 6, 2019 at 5:03 pm
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    3:31 Yoda vs Dio.
    I want it, I need it now.

    Reply
  • October 6, 2019 at 5:41 pm
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    what if u play this game in vr?

    Reply
  • October 6, 2019 at 6:33 pm
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    Why does it seem to be only VPN company's that sponser vids?

    Reply
  • October 6, 2019 at 6:41 pm
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    My dad: Shouts at me in the morning to get out of bed
    Me:

    3:28

    Reply
  • October 6, 2019 at 7:44 pm
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    8:26 Futasm: Also known as "Endorsement of Traps"

    Reply
  • October 6, 2019 at 7:58 pm
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    Why is no one meme this 😂

    Reply
  • October 6, 2019 at 9:22 pm
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    Woah, it's almost like exponential things grew fast and we quickly run out of computing power to compute them.

    Reply
  • October 6, 2019 at 9:48 pm
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    Um.

    Reply
  • October 6, 2019 at 11:56 pm
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    how about making it 3D

    Reply
  • October 7, 2019 at 12:20 am
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    Let me just say, don't listen to the intro with your volume all the way up

    Reply
  • October 7, 2019 at 2:10 am
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    I think the real challenge is having to remember all the rules of the game.

    Reply
  • October 7, 2019 at 2:30 am
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    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
  • October 7, 2019 at 2:39 am
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    3:34 Sounds like angry birds

    Reply
  • October 7, 2019 at 2:47 am
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    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
  • October 7, 2019 at 2:55 am
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    You jump scared me

    Reply
  • October 7, 2019 at 4:19 am
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    Sudoku is more stressful

    Reply
  • October 7, 2019 at 6:52 am
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    Yoda's death had me laughing far too hard to follow anything after!

    Reply
  • October 7, 2019 at 7:14 am
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    3:33 needs to be a meme

    Reply
  • October 7, 2019 at 8:37 am
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    HOLY HELL YODA TURNED INTO AN ANGRY BIRD THAT OVERDOSED ON EVERY DRUG EVER

    Reply
  • October 7, 2019 at 11:51 am
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    I don't even understand the first drawing he somehow created from the two dots…

    Reply
  • October 7, 2019 at 3:14 pm
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    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
  • October 7, 2019 at 4:45 pm
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    stranger things theme song plays ferociously on the background

    Reply
  • October 7, 2019 at 6:11 pm
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    Plot twist: Yoda was a paid actor (a pretty good one)

    Reply
  • October 7, 2019 at 7:01 pm
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    Nord is better

    Reply
  • October 7, 2019 at 11:43 pm
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    Yoda is me when I lose literally any kind of challenge or puzzle, etc.

    Reply
  • October 7, 2019 at 11:58 pm
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    . .

    Reply
  • October 8, 2019 at 12:31 am
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    "But you can't play with yourself"

    Ummm…

    Reply
  • October 8, 2019 at 12:50 am
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    P1: Alright lets start the game! How many dots should we start out with?

    P2: 0

    P1:

    Reply
  • October 8, 2019 at 12:52 am
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    Bold of you to assume that I have a mind

    Reply
  • October 8, 2019 at 1:22 am
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    WtFFFFFFFFFFF

    Reply
  • October 8, 2019 at 1:40 am
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    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
  • October 8, 2019 at 1:46 am
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    I don't get this game?How does it work?

    Reply
  • October 8, 2019 at 1:46 am
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    Is there a time limit?

    Reply
  • October 8, 2019 at 1:47 am
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    My brother asked "how do you win again?"

    Reply
  • October 8, 2019 at 1:50 am
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    Wait this isn’t Micheal

    Reply
  • October 8, 2019 at 2:50 am
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    I have no words.

    Reply
  • October 8, 2019 at 3:10 am
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    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
  • October 8, 2019 at 6:35 am
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    Lol we play this inside our classroom here in PH when there’s no teacher 🤣

    Reply
  • October 8, 2019 at 9:40 am
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    Vsauce:You can’t just play with yourself.
    Me:I’m about to prove this man wrong.

    Reply
  • October 8, 2019 at 10:06 am
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    Kevin: "You can't just play with yourself"

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

    Reply
  • October 8, 2019 at 11:15 am
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    Maths,, sure

    Reply

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