Vsauce! Kevins here. Playing one of the deadliest
games ever created. So deadly in fact, that
I needed balloon Kevin to act as a proxy for
me. Real Kevin. I’m real Kevin.
The game is Russian Roulette.
You probably already know how Russian Roulette
is played. Traditionally, a single round is
put in a revolver that holds 6 cartridges.
The cylinder is spun so that it’s impossible
to know which chamber will be fired. You pull
the trigger and… there’s a 5 out of 6
chance that you are safe, and a 1 out of 6
chance that it goes pretty badly for you.
I’ve inserted a single needle into each
dart -- so that in our version of this game,
it's gonna very badly for poor balloon Kevin.
And THAT’S DANGEROUS. And unsafe. This whole
thing is dangerous and unsafe. And against
the Terms of Service for every site on the
internet. Thankfully, Russian Roulette is
mostly just used in movies as a dramatic device
and I’m using it as a dramatic way to analyze
probability. The important part is that you
never do any of this. Ever. Okay? Okay!
I want to figure out the best way to survive
this notoriously fatal game.
So if balloon Kevin plays a standard game
of Russian Roulette, he has 1 in 6 odds of
permanently deflating his dome. There’s
about an 83% chance that my rubbery little
clone wins and a 17% chance he loses… forever.
And that’s that! So here we go. It's time
to test your luck, Balloon Kevin.
Wait...
Let’s make this scenario a little more complex.
Let’s say that there are two balloon-bursting
missiles inside… 6 chambers with 2 possible
spherical air sac-splattering darts that have
been placed next to each other. Adjacent.
There’s a ⅔ chance that my air-headed
doppelganger survives on a random pull of
the toy.
So do you like your chances, boy? You think
that sharpie mustache of yours is better than
the real deal? Well. Let’s see if fate is
on your side.
The ⅔ survival chance comes through! So
it’s on to the next round.
My gaseous twin has had it a bit too easy
of a chance up until now, the survival math
has been very very straightforward. He’s
had no active role in deciding his own fate.
So let’s give him something to think about.
For Round 2, I’m going to give him a choice
and place the life odds in his pipe cleaner
hands.
The choice is this: now that he has managed
to survive one round of the game, does he
want to spin the cylinder before playing again?
Or does he just… play and hope for the best?
The big question is: is it better for him
to randomize the cylinder or continue playing
with its current configuration?
Well. Answer the question, punk! What’s
it gonna be, you blue beanie-wearing balloon
buffoon?
Well, since balloon Kevin isn’t talking,
I’ll consider the options on his behalf.
Given that there are 2 adjacent cartridges
in there and the toy has been fired once already,
does it even matter mathematically whether
Air Kevin spins or not?
Let’s find out.
The first option: spinning. It’s the same
scenario with the same math. You’re basically
re-creating Round 1’s odds, which we know
give you a ⅔ chance of survival. So… not
really a whole lot to consider there.
But if you don’t spin, you know something
else… the toy has just been fired on one
of the empty chambers, which is how Balloon
Kevin survived to get to Round 2. And a little
logic reveals the math of whether to spin
or not spin. Think about the positioning:
there are 4 possible empty chambers, and only
one of them is directly before the two cartridges.
Which means, there’s a 75% chance Round
2’s trigger pull is on another empty chamber,
and just a 25% chance that this balloon is
about to go baboom.
By not spinning, balloon Kevin has earned
himself about 8 more percentage points of
survivability. And it’s such a straightforward
probability calculation because we know that
the darts are adjacent. If they were just
randomly placed in the chambers… then things
change.
Here’s how.
There are 15 possible positions for 2 darts
randomly arranged in 6 chambers. 6 of them
are adjacent, so darts would be in #1 and
#2, #2 and #3, #3 and 4, #4 and #5, #5 and
#6, all the way to #6 and #1.
There are 6 more ways that there can be a
single space between the darts, so #1 and
#3, #2 and #6, #1 and #5, #4 and #6, #3 and
#5, and #2 and #4. Finally, there are just
3 ways darts can be opposite one another:
#1 and #4, #3 and #6, and #2 and #5.
If Bloovin survives the first Round and he
doesn't know whether the darts are next to
each other or spread out, does he want his
second shot with a spin or no spin?
We know that we have a 75% of surviving on
those 6 adjacent positions. For the cylinders
that have darts 1 space apart, 2 of the 4
empty positions come before an empty and 2
of the 4 come before a dart, so that’s 50%.
And it’s the same for the opposite darts.
Our overall safety probability here is a calculation
of those weighted probabilities and it goes
a little something like this.
(6/15 x 3/4) + (6/15 x 2/4) + (3/15 x 2/4)
3/10 + 1/5 + 1/10 = 3/5
By not spinning, we have a 60% chance of survival
compared to 66.67% -- ⅔ -- when we do spin.
When we know the darts are adjacent, we can
gain 8% survivability. When we know they’re
random, we can avoid losing about 7%. It’s
not some magic solution that allows balloon
Kevin to survive what’s probably humanity’s
most deadly game. Doing the math doesn’t
unveil a secret way to win 80% of the time.
It just doesn’t work that way. It could
get ya 8%. And 8% is pretty insignificant
isn't it?, No it's not! Consider this!
0.01% of DNA is responsible for all the differences
you see amongst humans and only 1.3% separate
us from chimps.
1984 was the last U.S. Presidential Election
with more than an 8% popular vote gap.
Improving road safety by 8% would save 96,000
lives per year.
A $1,000 investment growing at 8% compounded
annually doubles in just 9 years.
And ultimately, if you’re an incredibly
attractive balloon with nice big googly-eyes,
a perfectly-formed cotton ball nose, and surprisingly-muscular
pipe cleaner arms, that finds itself locked
in a life or death game of chance, you’ll
take any advantage you can get to avoid being
popped.
And as always -- thanks for watching.
Hey! If you want to continue exploring Russian
Roulette probability for yourself and use
your beautiful balloon head to learn how to
think -- Brilliant.org has a challenge all
about it. Two, in fact, as part of their Perplexing
Probability Course.
Brilliant is great for Vsauce2 watchers like
you because it's an entire platform based
on learning math and science by having fun
with them. Their interactive puzzles allow
you to expose misconceptions, and help you
learn to think by playing!
Perplexing Probability is just one of the
60+ courses on Brilliant that teach you by
walking you through puzzles and guiding you
in figuring out the solutions. If you haven’t
checked it out yet -- I highly recommend doing
so. Just head on over to Brilliant.org slash
Vsauce2 and sign up for free. And the first
200 people get 20% off an annual premium subscription.
So that's a wonderful deal.
Go check it out. Enjoy thinking.
I need a new balloon Kevin.
Thanks for watching! That worked really well.
Oh my God.
