Vsauce, Kevin here, and I’ve combined one of the deadliest games anyone can play with
one of the stupidest -- which is why I will need two complete morons to play it:
Thomas Edison and Nikola Tesla!
Okay, they’re actually two of the most legendary geniuses of all time, but their rivalry was
SERIOUS -- especially over Tesla’s alternating-current
AC electricity and Edison’s direct-current
DC, which we now call The War of the Currents. Throw in decades of personal disputes and
they’ve got a score to settle -- their balloon avatars will fight to the death with the help
of a toy revolver and a single needle-dart.
They’ll be playing a form of Russian Roulette -- watch my ‘Surviving the Deadliest Game’
video for the math on the original. And the stupidest game humans have played is probably
the classic duel where two people just stand there and shoot at each other. En garde! That’s..
That’s fencing but… you know what I mean.
These two titans of the electron are gonna duel this one gun Russian Roulette style.
Okay?
The game is simple: Player A loads the cartridge, spins the cylinder, and shoots at Player B.
He’s so close that it’s impossible to miss. The gun will either fire or… not.
If it doesn’t fire, he hands the gun to Player B, who then spins the cylinder again
and then shoots at Player A. Then eventually it goes on until one of them is crowned the
Emperor of Electricity.
First, DON’T TRY THIS ACTUAL GAME PLEASE. Especially because I’ll show you exactly
how to try this actual game without trying this actual game.
Anyway, for now, what we really want to know is who’s more likely to win, Edison or Tesla.
Someone’s gotta go first, so I’ll use an unbiased coin flip to determine the order.
Heads for Edison, Tails for Tesla. Here we go… Heads for Edison.
Headison.
All right… here we go first shot for Edison to Tesla…Wait.
To figure out whether there’s an advantage to going first, we can just map out the scenarios
in which Edison wins -- we don’t even need numbers. SORRY, NUMBERS. Let’s use an E
when the gun fires for Edison and an x for when the gun does NOT fire. Here’s a map
of all the possible Edison victories:
This goes on until the gun fires. E’s can only fall on the odd rounds because Edison
went first. And that’s really the difference here -- Edison and Tesla have the same chance
of winning every round -- 1 out of 6 -- but Edison can win on the very first round before
Tesla even gets a turn.
That’s a major advantage, but how much? And how has this first round advantage caused
one of the biggest games in the world to literally change its rule!? We’ll get to that later…
For now it’s time for Edison’s first shot… Let me re-spin the old revolver here. Here
we go. Tesla survives!
Let’s think about this...
The probability of Edison firing the gun is ⅙ from the first round plus the probability
of success in subsequent rounds -- and this goes on and on as long as Edison and Tesla
keep missing. SPOILER: the total probability of the gun firing for Edison comes out to
6/11, or .5454 repeating. So Edison’s got a 54.5% chance of winning this duel, which
means Tesla… Tesla is at just 45.5% -- that’s a 9% disadvantage for Tesla. Even in THIS
balloon rivalry the deck is stacked for Edison.
You can calculate manually how many trigger pulls are in the average game of Idiot’s
Russian Roulette, but Paul J. Nahin’s Monte Carlo simulations of 10,000 trials confirmed
that it’s about 6. Here’s what’s interesting: about ⅔ of those games are over in the first
6 rounds. There’s a long tail with some games going 20 or 30 rounds, but it’s generally
a quick game, so Edison getting the first shot really matters.
WAIT -- YOU can actually run Russian Roulette simulations yourself without a computer program
or… anything more dangerous. You’ve got a random number generator in your pocket.
Open the stopwatch, divide a second into sixths -- 0.01 to 0.17 corresponds to the gun firing.
0.18 to 0.00 means it doesn’t fire. Start the stopwatch, close your eyes, and stop it
-- the decimal value of the seconds is a random firing simulator you can use to map out Russian
Roulette safely.
But now it’s time to get back to our game. And it’s time for Tesla’s revenge….
Hold on. If Tesla going second means he’s at such a disadvantage... how can we make
the game more fair? We can’t just play it 1,000 times alternating who goes first so
advantages even out. Someone’s gettin’ popped! We get one shot at this -- so let’s
just change the rules to compensate for giving Edison the first shot.
NEW GAME: If Edison’s gun doesn’t fire in Round 1, Tesla gets TWO shots. If neither
of Tesla’s shots fire, Edison gets THREE shots -- this goes on until the gun fires.
Does that actually make the game more fair? Is giving Tesla an additional shot after Round
1 enough to make up for his disadvantage?
NEW MAP:
Okay there’s the map of our new version of the game.
And we can do the same sort of calculation as before, but the probability of Edison’s
gun firing is now that . . . with an exponent corresponding to each of Edison’s rounds.
The alternating expanding rounds model reduces Edison’s chance of winning all the way down
to… about 52.4%. That’s 2 points lower for Edison and 2 points higher for ol’ Tesla
here, who’s now sitting at 47.6%.
It’s better. It’s not great, but it’s better.
We can keep tweaking the rules. We can keep running the math. But the most critical part
of the deadliest, dumbest game might not be how it’s played -- but it’s actually that
coin flip that determines who goes first.
Which is what the National Football League, one of the most popular sports leagues in
the world realized when it changed its sudden death overtime rules in 2010. The team who
got the ball first won the game so often that not winning the coin toss to determine who
played offense first meant you’d lose the game nearly 3 out of 5 times.
But check this out. Look what I found. You’re not gonna believe this. And if you do.. I
won’t believe you… Alright look. When the NFL used sudden death overtime rules,
coin flip winners won 52.0% of the time, coin flip losers won 43.4% of the time… the other
4.6% were ties. If we evenly-distributed those ties as wins, that’s 54.3% to the coin flip
winner and 45.7% for the loser. SOUND FAMILIAR? Those are almost the EXACT SAME odds of our
original Edison/Tesla duel game.
Maybe that’s why they called this… sudden death.
Alright, let’s settle this duel once and for all. Here we go. Okay so using our new
game rules, Tesla actually gets another shot. Alright, shot number two for Tesla. Here we
go.
Feel lucky, Edison?
Oh! Edison survives. Now it goes back to Edison’s turn. That’s two misses for Tesla. Here
we go. Now Edison gets three shots. Say your prayers, Tesla. You’re gonna need em.
Oh! Survives once again. Okay. Two more shots for Edison. Here we go.
Oh! Survives another one!
Alright, one more for Edison and then it’s going back to Tesla. Here we are.
Oh! He made it through round two! Now Tesla gets four tries!
Edison, you really should’ve done it that time. Four shots for Tesla. Shot number one.
Oh! Shot number one. Survived!
Shot number two.
Ah! Shot number two! This game.. Maybe we’ll make it to 30 rounds.
Here we go, spinning. Shot number three for Tesla.
Oh! Shot number three! The game continues!
Shot number four. Chance number four. You’d think one of these four would be it. Let’s
find out.
I can’t believe it! I can’t believe it! Four down.
Now it goes to five shots for Edison. Shot number one for Edison.
Alright. The game continues. The game continues.
Shot number two. Jeez! You’d think it.. One of these it would be it. Not so. Not so.
I’m totally randomizing this, folks. No no funny games here.
Shot number three.
Oh
Tesla! No! No! I’m so sorry! I am sorry you have been reduced to this. This is all
that’s left of Nikola Tesla. Just a dressed-up Pringles can. Is all we have left. Well. There
ya go. Edison wins. The numbers worked. I’ve got nothing more to say. Other than...
And as always… thanks for watching.