# The Number Illusion You Won’t Believe

published on July 9, 2020

Vsauce Merlin here and I know everythingabout what you know and think everythingI've built a vacation home in your mindand I'm lounging by the pool sippingchocolate milk right now and I can proveit with a little magic that amazed TVaudiences worldwide by having them rub

Their fingers all over their screens itstarts with a clock and each of thetwelve numbers are arranged as you'dexpect you'll be moving around thisclock in a way that's random to meyou'll know which numbers you choose

Along the way but I won't how could Iyou're wherever you are and I'm in mymom's basement right wrong while I am inmy mom's basement but with the power ofmy fake wizard beard no matter whatnumber you choose I will know where you

Are now clear your mind of its usualthoughts memes pizza rolls energy drinksand select a number it can be any numberfrom one to twelve and only you willknow what it is ready go pick a numbergot a number good now I need you to

Spell your number starting at 12 andmoving clockwise one step for eachletter in the word if your secret numberis seven then you'd move five steps s eV E and and land on the five if you pick11 you move six steps elee2000 your

Finger over the screen starting at 12and count your numbers letters untilyou're on your new number okay go aheadall right now spell your new numbermoving one position clockwise for eachletter in that number if you're on the

Three then move five spaces th re4 onthe six then move three spaces s I X andget back to the 12 just keep goingaround the same way a clocks hands moveokay did you do it if we're gonna dothis one more time

Spell your new number again and thenstop I'll give you a second to do thatokay now I have no idea what number youstarted with or the second one youlanded on let alone the third numberthat you landed on after that but I do

Know that you're not on the two so I'mgonna get rid of that and I know thatyou're not on the for either or theeight or the twelve as I sit mydelicious chocolate milk next to yourmind pool I can see that you weren't on

Any of those numbers so we don't needthem hey let's goone more round spell your new number andskip the empty spaces one letter oneposition and stop when you're done ifyou're on the five you'll move 4 spaces

Five-0 and landing on the 10 go aheadare you on the ten no no no you are noton the ten so the ten is gone you're onthe three no no no no no you are not onthe three that's gone too then nine goneor the one gone you're on the six and

You've just witnessed the magic of theKruskal count art hog this beard isreally getting itchy this hat is supertight one second let me pull up oh thetroubles of having a beard oh that'sbetter

So magician David Copperfield hasperformed illusions with severaldifferent variations of this trick fromusing a clock face to celebrities tovacation destinations he mesmerisedaudiences and live shows and TV shows

With his predictive power but the manwho discovered the Kruskal count wasmathematician and physicist martinKruskal who took some delight andknowing that it often confused actualmagicians because it wasn't based on any

Kind of sleight of hand it was based onmath so what is actually going on herelet's let's dissect what happens in theclock trick you're starting at 12 andyou have four possible moves numbersthat contain three four five or six

Letters you've got 12 numbers to choosefrom but we only have four possiblepathways forward and therefore I know nomatter what number you choose you'll endup on the three four five or six afteryour first move for your second move

You'll either move five four four orthree which means that every singleplayer winds up on either the eight orthe nine notice that no point in thegame can anyone even land on the 2 7 1011

Or twelve I know that before we startbut you probably won't notice it as youplay and along the way I remind you thatthese choices are yours and are totallyrandom to me because reinforcing thatrandomness distracts you from thinking

About any pattern that you might beencountering on the third move if you'reon the eighth you'll move five spaces tothe one if you're on the nine you'llmove 4 spaces to the one and that's itit's already game over for you and you

Didn't even know it then the performancereally starts I can take away numberslike two four eight and twelve because Iknow for a fact that you're on the oneit's one hundred percent guaranteed butthere's a very subtle element to

Choosing which numbers to erase thosefour removed numbers have letter valuesof three four five and six so thatsubconsciously reinforces that I'm noteliminating some specific element orpattern like just removing all of the

Possibilities with three letters it'sspread out among the choices so to youit seems just that much more randomreally I can do anything once you're allon the one I don't have to do anythingif we just kept playing you'd all just

Go from the one to the four I could alsoadd in as many rounds as I wantedbecause you're all in sync at that pointor I could remove different numbers toget you to the final number that's bestpositioned on camera which is probably

Why Copperfield wanted to land on thesix in the center of the screenit just looked better on TV so great wefigured out the trick kinda not exactlywhat is happening here what Kruskaldiscovered was that a counting game like

This is really a chain of numbers everynew number is a new link in the chainand when two chains eventually intersecton the samelink then they become the same chainfrom there on out knowing that you can

Appear to predict a highly improbableresult even when you don't know wherethe chain began let me show you anotherexample booth the predictive power ofkruskal's count is seen most easily witha deck of cards so allow me to show you

My wonderful wiener dogs playing cardsI'll shuffle a full wonderful wienerdogs deck of 52 cards and deal out 10you need to choose one of these 10 cardsobviously I won't know which one youchoose because I recorded this video in

The past and you're watching it in yourpresent which is my futurethen you'll proceed to count forwardfrom that card until we get through thewhole deck aces count as one and facecards count as five and every other card

Counts as the numerical value itdisplays so like nine equals nine so ifyou choose to start with card numberfive that's a queen which is worth fiveand you'll go five spaces one two threefour five and land on the ACE which is

One so then you'll go one land on a kingwhich is five one two three four fiveland on a ten and then you'll go ten gotit and you'll continue this until youcan't make a full move so if you land onthis nine you obviously can't go nine

Spaces so this nine would be your finalcard and even though I don't know whatcar you picked to start I'll be able totell you which card is the last one inyour sequence here's how I'll alsochoose a number from one to ten let's

Say I pick four which is a four thefourth card will be my first link in thechain which Kruskal calleda key card and together without tellingeach other because I don't know whichcard you're

Starting with were both going to countforward from our respective cards sinceI'm starting on the fourth card which isa four I'll count four spaces to anothercard one two three four which is a fiveand continue until the end you'll do the

Same thing for your mystery card andthen it's it's Wiener time okay go aheadlet's startyour last card in the sequence is thatnine because so is mineusing the crustal count I can predict

What your final card will be withoutknowing where you started because itdoesn't really matter at a certain pointour chains intersected on the same keycard and followed the same path to theend and this always works doesn't it no

It doesn't about one in six of you arealready typing a rage soaked commentabout how dumb I am for choosing thewrong numberjoke's on you buddy because I knew thatwould happen the kruskal's count with a

Fifty-two card deck only works about 85%of the time and if our final key cardsweren't the same then you chose one ofthe numbers that put you on one of the15% of chains that land me in the failcategory but the longer our chains go

The more chances they have to intersectso if we played two decks of 52 cardsthe odds of me predicting the rightfinal card for you jump to 95% let'sjust see exactly how this can play outI'll shuffle and deal another 10 cards

Color code them and mark each chains keycards as you can see five out of the tencards linked up right away on this nineand then ended up on this 10 the fourthand ninth cards linked up on this sevenand then met up with the others on this

Queen but three of the ten just kind ofdid their own thing and converged on asecond mini chain the fifth eighth andtenth cards linked up together on thisJack and ended up on a six there are acouple of reasons for this first landing

On a couple of nines caused huge jumpsthat reduced chain link opportunitiesthe more key cards in a sequence themore opportunities to overlap with themain chain if we play with two or threedecks our big chain and little chain

Would be almost certain to converge butthis casebeing a weird outlier where the magicianhad a much smaller chance of successthan they usually would that's the waywe know that this isn't magic magic

Works 100% of the time because it'sengineered and manufactured to besuccessful probability isn't quite aspredictablethere's actually a great interactiveversion by Alex Frieden and Ravi

Montenegro from the University ofMassachusetts Lowell that you can playonline and I'll link below because Ilike you yeah this is a fun little trickthat you can use to mess with yourlittle brother's mind but what's the

Pointthe Kruskal count feels like magic butis considered a probabilistic paradoxtechnically speaking it's a vertical oneand it has real-world computationalapplications in 1978 John Pollard

Applied it to code breaking anddeveloped a lambda method for catchingkangaroos also known as the kangarooalgorithm which is a great name for analgorithm but to me the trick is anincredible illustration of how math can

Be at the heart of coincidence what arethe chances you run into your old gymteacher at the supermarket what are theodds that you end up going to the sameCollege as the booger boy who moved awayin first grade we are all living in

Different systems at the same time somelarge some small some open some closedand every one of our actions is anotherlink in our own chains what we call fateor coincidence may really be the resultof a hidden mathematical master pulling

The probability puppet strings of ourexistences together at which point wecan decide how closely we want to alignour chains from thepoint on which is cool because youprobably don't want to go home

With your old gym teacher especiallysince he saw you buy cat food and youdon't even have a cat and as alwaysthanks for watchingdo you live in a country yes you do doyou want to watch things in a different

Country yeah of course you do but youcan't you are region restricted and ifyou're traveling abroad but want towatch stuff from your native land forgetabout it depending on where you are youmight not even be allowed to watch

Vsauce 2 which is the saddest thinghumanly possible so how are you evenseeing this right now you're using NordVPN thanks to them for sponsoring thisvideo and supporting vsauce2 andallowing people in countries that

Literally block YouTube to watch myvideos Nord VPN has remote servers allover the world so when you connect toone of their servers it makes your IPaddress look like you're in anothercountry and regardless of how far the

Server is the speed won't be compromisedyou could even get higher speeds thannormal as your ISP won't be limiting itand therefore you can watch what youwant to watch what you deserve to watchwhich is a win for liberty so to get 70%

Off in one month free go to Nord VPNcomm slash vsauce2or just use my very fancy coupon codevsauce2 and access entertainment thatregion restrictions are locking you outyou can grab the three year plan and

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