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 all right 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 could draw out all the possible moves for a game this simple look i'll show you [Music] 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 sprout 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 you 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 three lines coming from it or going to it once a dot has three lines it's an unplayable dead dot the winner of sprouse 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 all right yoda dude okay hang on all right fine just go right all right 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 sprouts was created in 1967 by cambridge mathematicians john conway and michael martin alternators 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 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 [Music] explain why i lost you must all right 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 move as player 2 rendering player 1 helpless player 2 can engineer the 2 dot game so that it ends on a 4th move win for them but conway and patterson figured out when the game has to end check it out they discovered that a game of sprouts must be completed by three n minus one moves where n equals the number of starting dots so that means a two dot game is concluded in no more than five moves because three times two minus one equals five so problem solved right no why because the game can play out in so 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 six winning outcomes what's amazing to me about sprouts is this is all just with 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 eight moves to determine a winner since three times three minus one equals 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 times n plus 1 over 2. so here we have our number of dots at start and number of initial possible moves n times n plus one over two and number of moves to determine a winner that's three n minus one so if you have two dots to start the game the initial possible moves would be three with three dots to start that jumps to six for four it's ten for five it's fifteen 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 four or five 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 dennis mollison a professor of applied probability at harriet watt university conway bet mollison 10 shillings before the 1971 decimalization of the british monetary system and equivalent to a little under 10 bucks today that he couldn't complete a full analysis of a six sprout 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 zero one or two dots could always be won by the second player games with three four and five dots could always be won by the first player the second player can always win with six 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 zero 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 photosem the fundamental theorem of zeroth order morabundity which states that any sprouts game of n dots must last at least two and moves and if it lasts exactly 2n moves the final board will consist of one of five insect patterns laos beetle cockroach earwig and scorpion surrounded by any number of lice scorpions are arachnids not insects but these guys don't have no time for no biology and that's fatasm 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 slater 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 three loss three win pattern with a cycle length of six dots in 2001 ficardi and luccio published a new analysis technique for the sprouts game that showed a simpler proof of sprouts to seven dots by hand now we're up to eleven so we're making progress on the pencil and paper front but what about 1 272 dots or a billion dots were not even close like really not close julianne lamont and simone vienno created a computer program called glop that could calculate sprout's 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 patterson 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

Channel: Vsauce2

Views: 2,957,737

Rating: 4.7644424 out of 5

Keywords: vsauce, vsauce2, vsause, vsause2, brain teasers, riddles with answers, riddles and brain teasers with answers, brain teasers for kids, critical thinking skills, game you win by losing, birds in a truck riddle, parrondo’s paradox, game you quit, game that learns, problem you’ll never solve, missing dollar riddle, birthday paradox, ant on a rubber rope, game you never win, game you always win, what is a paradox, battleship algorithm, pizza theorem, can being stupid make you smart

Id: XKsTGdN-4_M

Length: 11min 27sec (687 seconds)

Published: Mon Aug 26 2019

Reddit Comments

[u/[deleted]]

Curious how many dots can be counted with google’s new quantum computer.