# A Problem You’ll Never Solve

published on July 13, 2020

Vsauce Kevin here with a really simplequestion do you want this box of 1000candies and a mystery box which containseither nothing or a million candies ordo you just want the mystery boxobviously you'll take both boxes becauseyou're getting the mystery box

Either way might as well grab someguaranteed candy too rightright wrong maybe honestly I don't knowthe thing is when it comes to takingboth boxes or just the mystery boxalmost everyone watching this video will

Be absolutely sure that they know theright answer this is barely a problemlet alone one you'll never solve buthere's what's interestinghalf of you will be certain that theobvious answer is to take both boxes and

The other half of you will be just assure the obvious answer is to take onlythe mystery box how is that possible andwhy is there suddenly a grande genie onmy table let's dissect this problem boxa has clear value it's literally clear

You can see the contents are onethousand candies the issue is mysterybox B the contents of box B aredetermined in advance by our omniscientall-knowing grande genie who predictswhat you'll choose with near perfect

Accuracy if he predicts you'll chooseboth boxes he's put nothing in Box B ifhe predicts you'll only choose mysterybox B he's placed a million candies youcan't see inside box B you can't touchit and you don't know what the genie has

Predicted before you actually choosehere's a question who even came up withthis did I just make this whole thing upno theoretical physicist WilliamNewcombe devised thisproblem in 1960 and a decade later

Philosopher Robert Nozick detailed thisdeep philosophical fracture that makestwo equally obvious choices both rightand both wrong it's a contradiction it'san ant anomic paradox here's why if youdecide to take both boxes the genie will

Likely have predicted that and putnothing in mystery box B may be geniesdon't like greedy players or somethingso if you choose both box a and box Byou'll wind up let's only have fewhandfuls of candy if you decide to take

Only mystery box B the genie will almostcertainly have predicted that – and puta million candies inside maybe as areward for your courageous choice eitherway it's now obviously better for you tojust take mystery box B because a

Million is a much better prize than1,000 that's one way to look at thisproblem and in a 2016 poll from TheGuardian fifty three point five percentof over thirty thousand surveyrespondents chose to take only mystery

Box B here's what the other forty sixand a half percent thought the genie hasalready either put a million candies inthe mystery box or not he could have setup the boxes a day a week a month agothe candy isn't going to suddenly appear

Or disappear based on your decision ifhe's filled box B with candy and youtake both boxes you'll get a millionplus one thousand more from box a whichyou can eat right away to celebrate youramazingly clever rationale

If he didn't fill box B he just didn'tyou take both boxes and win your smallprize and this way you don't walk awayempty-handedyou can't really lose worst casescenario the mystery box is empty but

You still get one thousand pieces ofcandy which is one thousand more thanzero so should you take both boxes orjust box B what is actually going onherewhy exactly has Newcomb's paradox

Confounded minds for decades becauseit's pitting two equally valid methodsof reasoning against each otherexpected utility and strategic dominancelet's recap the two options with alittle math so we can get serious you

May not have a sweet tooth so let'sswitch prizes from candy to money box anow contains \$1,000 and Box B either has\$1,000,000 or no dollars first we cansee our possible outcomes with a simplepayoff matrix basically we'll just write

Out the four scenariosexcuse me Grande if the genie predictsthat you'll take box B and you chooseBox B you'll get 1 million dollars if hepredicts you'll take box B but youchoose both boxes you'll win 1 million

\$1000 million in box B and the \$1,000 inbox a if he predicts you're greedy andwill take both boxes but you choose justbox B then you get 0 dollars and if thegenies prediction is both boxes and youchoose both boxes your prize is just the

\$1000 from box a to put it another waythese are the outcomes when hisprediction is right and these are theoutcomes when his prediction is wrongokay we mapped out the potentialoutcomes now what how do we figure out

Which choice is right well we canactually calculate how valuable a choiceis to you that's expected utility it'slike the math of making a decision yousimply take the result of a choice andmultiply it by the probability of the

Outcome that'll give you a numericalvalue to help inform your decision solet's say the genie has a 90% chance ofpredicting right we'd calculate theexpected utility of choosing both boxeslike this a 90% chance he's right means

There is a 10% chance that he's wrong soif we choose both boxes there's a 10%chance we win two money filled boxes anda 90% chance that were left with justthe \$1000 we multiplied the point 1probability he's wronged by the payoff

Of 1 million \$1000 from both boxes andadd that to the 90% chance he's rightwhich means box B would be empty sothat's point 9 multiplied by just the\$1000 box a payoff this equals 100 and\$1000 if we assume that the genie is

Right 9 times out of 10 each time wechoose both boxes we theoretically gain100 and \$1,000 now let's find theexpected utility of choosing only box Bso that we can compare the two valuesand determine the best choice we get a

Million dollars if we choose Box B whenthe GE predicts our choice correctly ifwe stick with this 90 percent accuracyrate we multiply point 9 by the 1million dollar payoff and then add pointone times the zero dollars from the

Empty box when he's wrong for atheoretical gain of nine hundredthousand dollars per game by usingexpected utility as a reasoningframework the best choice is to takeonly mystery box B because an average

Payoff of \$900,000 is clearly betterthan 100 and \$1,000 obviously that's theright way to solve this problem until itisn't the dominance principle waltzes inand shouts in which scenario can I winthe most because look the genie has put

The money in the mystery box or hehasn't your choice comes down to takingwhatever is in that box or takingwhatever is in that box plus box a themystery box has a value of n and thegenie has determined that value in

Advance n is either 0 or 1 milliondollars so your choice is between takingN or taking n plus 1 thousand dollars nomatter what's inside box be yourdecision is do you just want somethingor do you want something plus one

Thousand bucks you're gonna getsomething either way so you might aswell grab the extra cash that's theright way to solve this problem untilthe expected utility people come backand prove that it isn't

Newcomb's paradox presents a problemwith what mathematician Martin Gartnerdescribed as two flawless arguments thatare contradictory choosing just box Bmakes perfect sense choosing both boxesmakes perfect sense so are you still

Certain one is the obvious answer are weonly left with their own personalperception of the proper solution Idon't know Pete hide a puzzle makermathematician and poet summarized thisconfusion when he wrote a bit beyond

Perceptions reach I sometimes believe Isee that life is two locked boxes eachcontaining the others key my question isare you team both or team just be thankyou for subscribing to me and as alwaysthanks for watching

What's your doorstep like is it nice isit smartwell the smartest thing that you can getmailed to your doorstep is the Vsaucecuriosity box and the brand-new box 11is now available I actually helped make

This you can see me here on the brandnew magazine that's that's me rightthere this is a quarterly subscriptionbox of science toys puzzles a bull cakecustom t-shirt and a portion of theproceeds goes to Alzheimer's research so

To make your doorstep smarter andsupport everyone's brains go tocuriosity voxcom and click over here towatch more Vsauce 2 thanks

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