The Game You Quit

published on July 13, 2020

Vsauce Kevin here with 100 pieces ofpaper and I'll teach you how to hire theright plumber choose the best parkingspace and even find the love of yourlife by quitting real quick this videois actually sponsored by LastPass Igenuinely use LastPass every single day

I signed up about a year ago because Iwas seriously tired of forgettingpasswords getting locked out of accountsand even dealing with websites havingdifferent rules as to what a passwordcould be so I decided to put everything

In LastPass and just make my life thatmuch easier here's how it works itstores everything safely and securelyand then auto fills your usernames andpasswords everywhere with unlimitedpassword storage and cross-device sync

So if you want to eliminate yourpassword frustrations forever just clickthe link down in the description belowand get LastPass and and thanks again tothem for supporting vsauce2 ok now backto our papers each of these 100 slips of

Paper has a number on it the numbers canbe anywhere from 1 to a Google which is1 followed by 100 zeros the game ofGoogle is to turn them over one by oneand stop when you think that you've gotthe highest number here's the important

Partyour final flipped paper is your choiceyou can't like flip five papers over andthen retro actively choose the secondpaper because it had the highest numberno no no no no no that's against the

Rules so the trick to winning the gameof Google is knowing when to stopalright let's play paper number 1100,000 28 okay that's a pretty bignumber but it's not even close to aGoogle it it can't possibly be the

Highest number out of all of these solet's flip another 94 trillion 288billion 381 million one hundred ninethousand two hundred seventy-six that'shuge but it's far from a Google so Ishould probably keep going I

Think honestly I don't know how am Isupposed to choose the highest numberedslip when I don't even know what thenumbers are the lowest number could beseven or 10,000 the highest number couldbe well anything up to and including a

Google so the odds of me picking thehighest number or what like 1% orsomethingno the ahlet's of me choosing correctlyare actually about one in three becauseI'm gonna employ optimal stopping theory

The branch of mathematics that dealswith knowing when to quit that way youget the highest reward or the lowestcost the game of Google was invented in1958 and it didn't take long formathematicians to figure out an elegant

Approach the key is e the number Eexcuse me papers I got to talk aboutsome a here Oilers number is anirrational number that's roughly 271828a mathematical constant that shows up inexponential growth and even calculating

Compound interest E is one of the mostimportant numbers in mathematicsalong with zero one pi and I and it's acomponent of Euler's identity the goldstandard of mathematical beauty and towin the game of Google we need to flip

Oyler upside down not like that likethis the reciprocal of Euler's numberone over e or one over 271828 or 03six seven eight seven nine orapproximately 37% is the lowest ourprobability of winning the game of

Google will ever be as long as we stickto the optimal strategy we don't need toknow the numbers on the slips and itdoesn't matter if we're playing with 10slips 100 slips or 640 to do oldestiliyan slips we just need to answer one

Question when exactly mathematicallydo we start stopping okay so I can justgo through this solution to the game ofGoogle all right here we go yeah lookinggood good we're not gonna do that whatwe're gonna do instead is that we're

Gonna use e and basic optimal stoppingtheory to find a quick accurate point inwhich we need to stop playing tomaximize our chance of winning let'ssolve the game of Google with just tenslips of paper the trick is to take a

Sample of numbers and then decide tocommit to the very next number we pullthat's larger than any in the previoussample so with 10 slips total do wedecide to take the highest number afterwhat the third the fifth it can't be too

Late in the game because if we waituntil like slip nine will likely havealready revealed and passed over ourbiggest number let's not guess let's getoily if we divide our number of slipsten by E we get three point six seven

Eight eight nine by rounding up to thenext integer we can stop collecting oursample on the fourth slip then we'llkeep choosing slips and stop when wefind one that's higher than any of thosefirst four and there's around a 1 over e

Chance that will be rightthis works for 10 100 or 3781 slipsbecause that's just 3781 divided by E soone thousand three hundred ninety pointnine five we choose until we pulled anumber higher than any in the 1390 first

Slip will be exactly right about a thirdof the time and when we aren't we'dstill be really close look I'll mixthese up and I'll play a totally randomgame using this strategy and we'll justsee what happens

So there's my sample of four slips andnow I'll just choose the next numberthat's bigger than these four all rightmy choice is number six let's see ifthat's the highest number here oopsso the strategy didn't work six wasn't

The highest number it was actually slipnumber ninea one and A three success rate of thisstrategy might not sound impressiveyou're still gonna lose about two out ofevery three times but imagine how low

Your success rate would be if you had nosystem to help you decide and as thenumber of slips in the game of Googlebecomes larger the likelihood that youruninformed guess is actually righttrends toward zero 30-something percent

Is a lot better than say point zero zerothree percent we as humans don'tcalculate probabilities with Euler'snumber ten times a day but our braindoes seem to have a general heuristic aseries of mental shortcuts and basic

Rules that helps us decide when to stopresearchers at the laboratory of neuropsychology at the National Institute ofMental Health ran fMRI scans on brainsthat were trying to decide whether tokeep searching for the best choice or

Commit to the current option and theyfound that several parts of the brainlight up when faced with an optimalstopping problem boilers number anoptimal stopping theory is how in a seaof possibilities you decide this is the

Best parking spot that I'm gonna find orthis is the house that I'm gonna buy orthis is the YouTube video that I'm gonnawatch without even realizing it youplayed the game of Google in your brainto watch this video about the game of

Google you didn't scroll through everysingle video on YouTube and go back todetermine that this was the one to clickon you scan some options clicked me andhere we areyou're Johannes Kepler and I'm

Bachelorette number five in 1611 Keplerinterviewed elevenin the hopes of finding a wife he passedon eleven women Kepler was left alone herejected all of his options and thoughthe'd missed his chance luckily he went

Back to Bachelorette number five shesaid yes and they lived happily everafterKepler found the love of his life but hedid it the hard way all he needed to dowas divide 11 by E to get a value around

4 and then taken the very next optionbetter than those which would have beenBachelorette number 5 the love of hislife hidden in plain math all along andas always thanks for watchingif you want to watch more Vsauce 2

Videos just click right over here and ifyou aren't subscribed yet to Vsauce 2well then hop aboard and if you aresubscribed to Vsauce 2 then welcomeaboard again I didn't plan this it'sokay

That's probably not

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