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.