Vsauce! Kevin here. With a video giveaway
idea for YouTube’s most prolific philanthropist, MrBeast. It gives everyone who watches it,
including you, a chance to win one million dollars. Here are the rules of my hypothetical contest. MrBeast makes a video and if that video gets
one single like, only one thumbs up in the first 24 hours -- the person who liked the
video wins a million bucks. However, if more than one person smashes that like button,
or nobody clicks it at all, then no one wins anything. Oh, and another thing: only MrBeast can see
whether anyone has liked the video. Everyone is playing the game blind to the results.
You’ll have no way of knowing whether you’re the first and only person to like the video
or the 10 millionth. So, what do you do? Do you click like and
magically hope you’re the only person who did? Do you like the video just to troll the
contest hoping it’ll ruin someone else’s chances? Do you just do nothing, and forego
the chance of winning feeling safe in the knowledge that you didn’t ruin it for anyone
else? Here’s the biggest question: Is it even possible to win this game? Welcome to the Platonia Dilemma. A mathematical game devised by cognitive scientist
Douglas Hofstadter. His version went like this: 20 people were sent telegrams by fictitious
oil baron S. N. Platonia. If only one person replied to the telegram, that person would
win $1 billion dollars. If nobody or more than one person replied, no one wins anything.
Collusion, or secretly working together, was strictly forbidden, and participants didn’t
even know who the other 19 potential respondents were anyway, So, like, they couldn’t all
get together and agree that only number 15 would reply and the rest of them would split
the billion dollars, y'know, 20 different ways. In an attempt to rationally solve this dilemma
in your favor, you face four important questions: What should I do? What will other people do?
What should I do after knowing what other people will do? What will other people do
after knowing that I know what they’d do? And the answers to these questions are...
I don’t know. Not sure. No idea. And who knows?! Because the thing is... The more rational
we all are, the more the right answer keeps changing. Cheating the game is a good example
of this and we’ll get to that in a bit but... To make the best of the Platonia Dilemma,
your rationality alone isn’t enough. No. No! We need superrationality. Hofstadter described superrationality as a
state of knowing the perfectly rational thing to do, but also knowing that everyone else
knows and will behave that exact same way. So, you know, they know, you know they know,
and you know they know you know. That process goes on forever, and everyone arrives at the
same exact conclusion. It’s like a rational singularity. Hofstadter decided the best way forward, the
superrational thing to do, was to to roll a 20-sided or icosahedral die and commit to
only replying to the telegram if his pre-chosen number came up. Like the number one. Here’s why. The best odds for someone to win this game
occur when you transcend the rationality hyperloop. You have to move beyond simply trying to figure
out, “What should I do?” “What will other people do?” etc. and create an artificial
probability mechanism. If all 20 people in the game act superrationally,
they’ll each roll a 20-sided die once and commit to replying to the telegram only if
they roll a 1. That leaves about a 37% chance of somebody winning. It is possible for no
one to roll a 1 and it’s also possible for more than one person to roll a 1, so that
means your personal odds of winning are not 1 in 20 which would be 5%, no, your odds of
winning personally are about 2%. But at least this superrational system leaves the game
up to math instead of everyone just guessing. Why not cheat, though? Seriously! Uhh. Why
don't you just lie and reply anyway if there’s only a 37% chance that somebody won? That
way, you would be the winner if none of the other 19 players rolled a 1. Genius! But if
you know that -- then that means other people know that and they’d cheat too, which would
instantly wipe out the boosted odds of winning by lying. The rational thing for you to do is cheat.
But if everyone thinks that, they’ll also cheat and everyone loses. That’s why the
superrational thing to do is not cheat. Hofstadter even suggested removing the cheat
temptation entirely by using a die-rolling machine that instantly replied to Platonia
if, and only if, it rolled a 1. But this is all just theoretical, right. It's
really hard to do that with these sticky things. We don’t actually know how people would
behave in a Platonia-like situation, right? Wrong. It actually happened. Hofstadter convinced
Scientific American to run what he called a “Luring Lottery” in a 1983 Metamagical
Themas column. The basic rules were a little different, but the essence was the same: the
prize for one lucky lottery winner was $1 million bucks, which would be divided by N,
where N equaled the number of entries mailed in. There was, however, a crucial twist. Instead
of each reply counting as one entry, you could write any number on the postcard and it would
count for that many entries. So, a postcard with a 1 on it counts as one entry, and a
postcard with 1,000,000 on it counts as a million entries. A higher number of entries
gave the player a better chance of winning, but it also reduced the potential prize money. Some people submitted googolplex entries,
which is 10 raised to a googol. Others wrote mathematical expressions that filled the postcard,
resulting in incalculably high numbers. Which meant the total entries hit such an unfathomable
number that Scientific American was unable to choose a winner… it became impossible.
And even if they could’ve, the winner would’ve received $1 million dollars divided by such
a high N that the prize would’ve worked out to an infinitesimal fraction of one cent. The takeaway here is that coupling unlimited
entries with people pursuing their own self-interest -- while recognizing that everyone else would
do that too -- quickly bulldozed that $1 million dollar prize into dust. Nobody won. The intrigue of the Platonia Dilemma is less
about how to win the game and more about how to think about how to win the game. It's about
merging math... and you. How you behave, how other people behave, and how we can use our
minds and math to eclipse our imperfect rationality. So if MrBeast launches his version of the
Platonia Dilemma and it’s your turn to like the video… What do you do? What will everyone
else do? Are you rational? Are they rational? Is everyone superrational? The most likely scenario for you or anyone
to win would require all 10 million viewers to act superrationally, with no cheating,
no trolling, and each person rolling a die with 10 million sides. I think MrBeast’s million is safe on this
one. This pocket's not open. So I can't put that
in there. And as always -- thanks for watching. "I want a Vsauce hat!" is a thought that popped
into my brain one day so I designed this hat for myself. If you want to get one for yourself
go to CuriosityBox.com/Store. If you just want to keep watching Vsauce2 videos, well,
I recommend The Missing Dollar Riddle. That's a good one. And if you aren't subscribed yet
to Vsauce2, do that right now if you ever want to see the sun rise again. That's a little
dramatic. The sun doesn't actually rise or set contingent upon whether or not you are
subscribed to Vsauce2. I think.
