The Demonetization Game

published on July 12, 2020

Vsauce Kevin here with 100 youtuberssome are friends some are colleagues allare about to be demonetisedforever unless each one chooses theirown channel out of these 100 eggs I'llput one youtuber in each egg and everyplayer gets only 50 guesses if just one

Of the 100 youtubers fails to find theirchannel in the egg everyone loses here'sthe setup all 100 youtubers are in thesame waiting room they're each assigneda number and then one at a time broughtinto the egg room to play the game alone

Once a youtuber completes their roundthey're immediately escorted out theback door so they can't go back into thewaiting room and say like hey rhett andLink you're hidden in egg number 93 orwhatever

No no that's cheating this game is 50blind guesses for each youtuber and theyall have to find their egg or everyoneis demonetisedafter each round the eggs are all resetand resealed so that the next youtuber

Can't see which has been chosen everyplayer has to start fresh so how do youwin when you can't see what's in theeggs and you can't communicate with anyother players the most obvious option isfor everyone to just choose randomly in

Hope for the best I mean you have 50tries that's a lot right 50 out of 100eggs gives you 50/50 odds of findingyour egg not bad but the odds of all 100youtubers pulling this off successfullyare virtually impossible let's crunch

The numbers it's pretty simple with 100eggs and 50 guesses the odds ofselecting the right egg randomly are 50percent or 05 100 successful attemptsat odds of 05 comes out to 0 point 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Zero zero zero zero zero zero zero zeroeight to get the percentage odds we justshift the decimal over two places andyeah there are still 28 zeroes the oddsof me getting drafted in the NBA orwinning the lottery are unfathomably

Higher than this D monetization egg gameworking out for these youtubers theseodds are literally the same as correctlypredicting 100 coin flips in a row tryit try to successively predict coinflips you may get five or six in a row

Right maybe 10 but you almost certainlywon't get 50 let alone the 100 we needto save our youtubers so sorry threeblue one brown and sorry epic RapBattles there's just no hope of winningthis game your channels like everyone

Else's here are canceled unless what ifthere was a mathematical strategy thatour 100 youtubers could employ to givetheir channels a realistic chance ofsurvival let's actually play this gameand try to figure it out I've given each

Of these youtubers a number between 1and 100 and each one will randomly go ina numbered anow we've got 100 youtubers hidden in100 eggs and the secret solution tosaving their channels goes like this

When it's their turn to play eachyoutuber just needs to start by choosingthe numbered egg that matches theirpersonally assigned number if theyaren't in that egg rather than choosinganother egg randomly the next egg to be

Opened is the number of the youtuberinside the one that they just openedeach player will repeat this strategyuntil they find their egg or untilthey've opened 50 eggs unsuccessfully inwhich case everyone loses max mofo is

Player number one so I will play as maxmofo here we go okay egg number one isGus Johnson who is number 62 alright sowe'll just open up egg number 62 andphysics girl and she is number 12 so nowwe just open up egg number 12 nerd City

Number 77 so let's open up egg 77 numberfile number 35 okay let's check out egg35 and here we have Carson number 69this is very very important whatever youdo do not forget 69 we'll talk aboutthat later but for now let's open up egg

69 aspect science number 7 you know whatthis actually might take a little whileso while I find the maxima folk channellets montage20:20 is Max is me max mofo we did itwe found me well we found max and it

Only took 31 guesses way below our 50guests threshold now we need to resetour eggs okay we're all set for youtubernumber two red letter media let's dothisred letter media I found it already that

Didn't take long at all okay now let'sreset and go with youtuber number threeokay now it is time for DannyGonzalez here we goDanny Gonzalez number three did it againanother winner

That is awesome okay I am going to resetthis and then let's talk about what justhappenedokay our strategy is working threeyoutubers have found their eggs the oddsof the first three youtubers

Successfully choosing with randomguessing would have been 05 times 05times 05 which equals 12 and a halfpercent for in a row drops down to 625%five in a row you're looking at threepoint one two five percent and by seven

In a row you're below one percent so howmuch better is our system well rememberthat random guessing has the odds of all100 youtubers winning at zero point zerozero zero twenty eight zeros and then an8% to put it in perspective our system

Increases the odds more powerfully thanturning a penny into all the money inthe world we can increase the odds ofsaving all 100 youtubers fromeffectively zero percent to 31% and I'llexplain how it works but here's a

Question did I just make this wholething up no usually I like to examineold long-standing problems in math andscience but this one is actually prettynew in 2003 computer scientistspeterborough Milt Orson and Anna gall in

A paper titled the cell probe complexityof succinct data structures created aversion of this game in which red orblue slips were dropped in 100 littledrawers to win every single one of the100 players had to correctly guess

Whether their drawer contained a red ora blue slip the game is a littledifferent but the odds of guessing redor blue versus choosing 50 eggs out of100 are exactly the sameMilt Orson's initial thought was that

The number of players increases theprobability of winning the game wouldtrend to zero but by starting with theegg matching their own number eachplayer is guaranteed that they're on apath to an egg that contains them and

It's just a question of whether theiregg is within a cycle of fifty attemptsokaywhy because each egg contains one uniquenumber that points to another uniquenumber and that creates as Nick Perry of

Data genetics described a circular chainone number points into the chain and onenumber points out so if the youtuberuses their own number to point into thechain they will eventually find theirown number rather than blindly guessing

Our system is a way of tapping in tothat circular chain to get mathy aboutit by giving each youtuber a numberwe've created a permutation of the setthat's a one-to-one mapping of all 100numbers to itself

Our strategy makes a cycle so eachnumber returns to itself and it'ssuccessful when all 100 youtubers find acycle length of 50 or less with 100 eggsthere can only mathematically be onecycle longer than 50 but that's all it

Takes for us to lose the game anyway sowhat are the chances of a permutation inwhich there's one cycle longer than 50let's find out the solution to ourchance of success equals 1 minus theprobability of getting a cycle longer

Than 50 let's call the cycle length Lthat gives us 100 choose L possible setstimes L factorial over L permutations ofthe cycle within the set times 100 minusL factorial permutations of theremaining youtubers and that comes out

To 100 factorial over L which is reallyreally easy to work with we know thatthere are 1hundred factorial ways to arrange thetickets so the probability of chainlength L is just one over L our chance

Of success is one – all those long chainfailures combined since we also knowthat only one cycle of 51 or longer ispossible in each set we can calculatethe probability of losing by 1 minus 1over 51 plus 1 over 52 plus 1 over 53

Etc 1 over 98 plus 1 over 99 plus 1 over100 which comes out to about point 6 9 Itold you to remember 69 there's a 69percent chance that we encounter a cyclelonger than 50 so the probability of all100 youtubers having a cycle of 50 or

Under which means they'd win the Dmonetization game using this strategy isthe remaining point 3 1 or 31 percent31 percent isn't amazing but just likethe game of Google around 30 percent isway better than basically 0 the weird

Thing is that even with our solutioneach individual youtubers chance ofsuccess is still 50% just like if theyguessed randomly the strategy changesthe group's chance of success so that'sthat problem solved until you tweak the

Problem Milt ursins game continues toevolve like what happens if we have morethan 100 eggs but some of them are emptyreaching an empty egg would stop thecycle and completely ruin our system buteven this seemingly impossible version

Of the game has inspired computerscientists to develop a strategy thatdefies our expectations of failurewhich is what we do whether we'repretending the floor is lavawhether we're watching superheroes

Defeat galaxy destroying villains orwe're trying to cure diseases that seemimpossible to overcome we test push andexpand our limits because challenges areonly impossible until they are and asalways thanks for watching

Makes a weird sound hey there if youhaven't yet taken advantage of my dealwith curiosity stream you better do thatthere's a link down below for you toclick and you get 30 days for free justgo to curiosity stream comm slash Vsauce

2 and fill your brain with amazingeducational and stimulating in the mindcontent you will absolutely love it ifyou want to love yourself some moreVsauce 2 well first of all you said youshould subscribe I don't know what happy

To my play voice here but you know thebattery is dying on this computer it'snot a computer it's a camera okay thisis going south really quickly subscribeto Vsauce to bring the notificationbells so that you know when I upload a

New video and I'm just gonna uh I guesssee you later bye

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