Surviving The Deadliest Game

Vsauce! Kevins here.

Playing one of the deadliestgames ever created.

So deadly in fact, that I needed balloon Kevin to act as a proxy forme.

Real Kevin.

I’m real Kevin.

The game is Russian Roulette.

You probably already know how Russian Rouletteis 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 pullthe trigger and… there’s a 5 out of 6 chance that you are safe, and a 1 out of 6chance that it goes pretty badly for you.

I’ve inserted a single needle into eachdart — so that in our version of this game, it's gonna very badly for poor balloon Kevin.

And THAT’S DANGEROUS.

And unsafe.

This wholething is dangerous and unsafe.

And against the Terms of Service for every site on theinternet.

Thankfully, Russian Roulette is mostly just used in movies as a dramatic deviceand I’m using it as a dramatic way to analyze probability.

The important part is that younever do any of this.

Ever.

Okay? Okay! I want to figure out the best way to survivethis notoriously fatal game.

So if balloon Kevin plays a standard gameof Russian Roulette, he has 1 in 6 odds of permanently deflating his dome.

There’sabout 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 timeto 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 possiblespherical 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 ofthe toy.

So do you like your chances, boy? You thinkthat sharpie mustache of yours is better than the real deal? Well.

Let’s see if fate ison your side.

The ⅔ survival chance comes through! Soit’s on to the next round.

My gaseous twin has had it a bit too easyof a chance up until now, the survival math has been very very straightforward.

He’shad 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 cleanerhands.

The choice is this: now that he has managedto 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 himto randomize the cylinder or continue playing with its current configuration? Well.

Answer the question, punk! What’sit 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 cartridgesin there and the toy has been fired once already, does it even matter mathematically whetherAir Kevin spins or not? Let’s find out.

The first option: spinning.

It’s the samescenario with the same math.

You’re basically re-creating Round 1’s odds, which we knowgive you a ⅔ chance of survival.

So… not really a whole lot to consider there.

But if you don’t spin, you know somethingelse… the toy has just been fired on one of the empty chambers, which is how BalloonKevin survived to get to Round 2.

And a little logic reveals the math of whether to spinor not spin.

Think about the positioning: there are 4 possible empty chambers, and onlyone of them is directly before the two cartridges.

Which means, there’s a 75% chance Round2’s trigger pull is on another empty chamber, and just a 25% chance that this balloon isabout to go baboom.

By not spinning, balloon Kevin has earnedhimself about 8 more percentage points of survivability.

And it’s such a straightforwardprobability calculation because we know that the darts are adjacent.

If they were justrandomly placed in the chambers… then things change.

Here’s how.

There are 15 possible positions for 2 dartsrandomly 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 asingle 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 hedoesn't know whether the darts are next to each other or spread out, does he want hissecond shot with a spin or no spin? We know that we have a 75% of surviving onthose 6 adjacent positions.

For the cylinders that have darts 1 space apart, 2 of the 4empty 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 calculationof 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 survivalcompared to 66.

67% — ⅔ — when we do spin.

When we know the darts are adjacent, we cangain 8% survivability.

When we know they’re random, we can avoid losing about 7%.

It’snot some magic solution that allows balloon Kevin to survive what’s probably humanity’smost 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 insignificantisn't it?, No it's not! Consider this! 0.

01% of DNA is responsible for all the differencesyou see amongst humans and only 1.

3% separate us from chimps.

1984 was the last U.

S.

Presidential Electionwith more than an 8% popular vote gap.

Improving road safety by 8% would save 96, 000lives per year.

A $1, 000 investment growing at 8% compoundedannually doubles in just 9 years.

And ultimately, if you’re an incrediblyattractive balloon with nice big googly-eyes, a perfectly-formed cotton ball nose, and surprisingly-muscularpipe cleaner arms, that finds itself locked in a life or death game of chance, you’lltake any advantage you can get to avoid being popped.

And as always — thanks for watching.

Hey! If you want to continue exploring RussianRoulette probability for yourself and use your beautiful balloon head to learn how tothink — Brilliant.

org has a challenge all about it.

Two, in fact, as part of their PerplexingProbability Course.

Brilliant is great for Vsauce2 watchers likeyou because it's an entire platform based on learning math and science by having funwith them.

Their interactive puzzles allow you to expose misconceptions, and help youlearn to think by playing! Perplexing Probability is just one of the60+ courses on Brilliant that teach you by walking you through puzzles and guiding youin figuring out the solutions.

If you haven’t checked it out yet — I highly recommend doingso.

Just head on over to Brilliant.

org slash Vsauce2 and sign up for free.

And the first200 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.

.