Vsauce! Kevin here, with a really simple question. Do you want this box of 1000 candies and a
mystery box which contains either nothing or a million candies? Or... do you want just the mystery box? Obviously you’ll take both boxes because
you’re getting the mystery box either way. Might as well grab some guaranteed candy too,
right? Right. Wrong. Maybe. Honestly, I don’t know. The thing is... When it comes taking both boxes or just the
mystery box, almost everyone watching this video will be absolutely sure that they know
the right answer. This is barely a problem, let alone one you’ll
never solve. But here’s what’s interesting… Half of you will be certain that the obvious
answer is to take both boxes, and the other half of you will be just as sure the obvious
answer is to take only the mystery box. How is that possible? And why is there suddenly a Grandayy genie
on my table? Let’s dissect this problem. Box A has clear value. It’s literally clear -- you can see that
the contents are 1000 candies. The issue is Mystery Box B. The contents of Box B are determined in advance
by our omniscient, all-knowing Grandayy genie, who predicts what you’ll choose with near-perfect
accuracy. If he predicts you’ll choose both boxes,
he’s put nothing in Box B. If he predicts that you’ll only choose mystery
Box B, he’s placed… a million candies. You can’t see inside Box B, you can’t
touch it, and you don’t know what the genie has predicted before you actually choose. Here’s a question. Who even came up with this? Did I just make this whole thing up? No. Theoretical physicist William Newcomb devised
this problem in 1960. And a decade later, philosopher Robert Nozick
detailed the deep philosophical fracture that makes the two equally-obvious choices both
right and both wrong. It’s a contradiction. It’s an antinomic paradox. Here’s why. If you decide to take both boxes, the genie
will likely have predicted that and put nothing in mystery Box B -- maybe genies don’t like
greedy players or something. So if you choose both Box A and box B, you’ll
wind up with only a few handfuls of candy. If you decide to take only mystery Box B,
the genie will almost certainly have predicted that, too, and put a million candies inside…
maybe as a reward for your courageous choice. Either way, it’s now obviously better for
you to take mystery Box B because a million is a much better prize than 1000. That’s one way to look at this problem,
and in a 2016 poll from The Guardian, 53.5% of over 30,000 survey respondents chose to
take only mystery Box B. Here’s what the other 46.5% thought: The genie has already either put a million
candies in the mystery box… or not. He could’ve setup the boxes a day, a week,
a month ago! The candy isn’t going to suddenly appear
or disappear based on your decision. If he’s filled Box B with candy and you
take both boxes, you’ll get a million plus 1000 more from Box A, which you can eat right
away to celebrate your amazingly clever rationale. If he didn’t fill Box B… he just didn’t. You take both boxes and win your small prize
and this way you don’t walk away empty-handed. You can’t really lose. Worst case scenario, the mystery box is empty
but you still get 1000 pieces of candy which is 1000 more than zero. So should you take both boxes or just Box
B? What is actually going on here? Why exactly has Newcomb’s Paradox confounded
minds for decades? Because it’s pitting two equally valid methods
of reasoning against each other: Expected Utility and Strategic Dominance. Let’s recap the two options with a little
math… so we can get serious. You may not have a sweet tooth, so let’s
switch prizes from candy to money: Box A now contains $1,000, and Box B either has $1 million
dollars or no dollars. First, we can see our possible outcomes with
a simple payoff matrix. Basically, we’ll just write out the four
scenarios. Excuse me, Grandayy. If the genie predicts you’ll take Box B
and you choose Box B, you’ll get $1,000,000. If he predicts you’ll take Box B but you
choose both boxes, you’ll win $1,001,000 -- the million in Box B and the $1,000 in
Box A. If he predicts you’re greedy and will take
both boxes but you choose just Box B, then you get zero dollars. And if the Genie’s prediction is both boxes,
and you choose both boxes, your prize is just the $1,000 from box A. To put it another way, these are the outcomes
when his prediction is right and these are the outcomes when his prediction is wrong. Okay. We mapped out the potential outcomes, now
what? How do we figure out which choice is right? Well, we can actually calculate how valuable
a choice is to you -- that’s Expected Utility. It’s like the math of making a decision. You simply take the result of a choice and
multiply it by the probability of the outcome. That’ll give you a numerical value to help
inform your decision. So, let’s say the genie has a 90% chance
of predicting right. We’d calculate the expected utility of choosing
both boxes like this: A 90% chance he’s right means there’s
a 10% chance that he’s wrong. So if we choose both boxes, there’s a 10%
chance we win two money-filled boxes and a 90% chance that we’re left with just the
$1,000. We multiply the .1 probability that he’s
wrong by the payoff of $1,001,000 from both boxes and add that to the 90% chance he’s
right, which means Box B would be empty -- so that’s .9 multiplied by just the $1,000
Box A payoff. This equals $101,000. If we assume that the genie is right 9 times
out of 10, each time we chose both boxes, we’d theoretically gain $101,000. Now let’s find the Expected Utility of choosing
only Box B so that we can compare the two values and determine the best choice. We get a million dollars if we choose Box
B when the genie predicts our choice correctly. If we stick with his 90% accuracy rate, we
multiply .9 by the $1,000,000 payoff and then add .1 times the $0 from the empty box when
he’s wrong for a theoretical gain of $900,000 per game. By using Expected Utility as a reasoning framework,
the best choice is to take only mystery Box B, because an average payoff of $900,000 is
clearly better than $101,000. Obviously! That’s the right way to solve this problem. Until it isn’t. The Dominance Principle waltzes in and shouts,
“In which scenario can I win the most?” Because, look, the genie has put the money
in the mystery box or he hasn’t, your choice comes down to taking whatever is in that box,
or taking whatever is in that box plus Box A. The mystery box has a value of n, and the
genie has determined that value in advance. n is either $0 or $1 million dollars, so your
choice is between taking n or taking n + $1,000. So no matter what’s inside Box B, your decision
is: do you want just something, or do you want something plus $1,000 bucks? You’re gonna get the something either way,
so you might as well grab the extra cash. That’s the right way to solve this problem. Until the Expected Utility people come back
and prove that it… isn’t. Newcomb’s Paradox presents a problem with,
what mathematician Martin Gardner described as, two flawless arguments that are contradictory. Choosing just Box B makes perfect sense. Choosing both boxes makes perfect sense. So… are you still certain one is the obvious
answer? Are we only left with our own personal perception
of the proper solution? I don’t know. Piet Hein, a puzzlemaker, mathematician, and
poet summarized this confusion when he wrote: “A bit beyond perception’s reach
I sometimes believe I see That Life is two locked boxes, each
Containing the other’s key.” My question is: are you team Both or team
just B? Thank you for subscribing to me. Sorry for rhyming? And as always -- thanks for watching. What’s your doorstep like? Is it nice? Is it smart? Well, the smartest thing that you can get
mailed to your doorstep is the Curiosity Box and the brand new box 11 is now available. I actually help make this thing you can see
me here on the brand new magazine. That's me right there. This is a quarterly subscription of science
toys, puzzles, a book, a custom t-shirt and a portion of the proceeds goes to Alzheimer’s
research. So to make your doorstep smarter and support
everyone’s brains go to CuriosityBox.com. And click over here to watch more Vsauce2. Thanks. Bye.
