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Two-Face is one of Batman's oldest and most notorious foes,
obsessed with fairness and luck.
He even wields a weapon used in an infamous game of chance.
However, he only uses his deadly revolver
if his trusty coin allows for it.
- The random toss.
The only true justice.
- A typical use of Two-Face's coin
would be heads, ya live,
or tails or scratchy burnt side, ya die.
Seems fair, right?
Cruel, sure, but fair.
A coin toss is 50/50, meaning Two-Face's victims
are subject to nothing more than chance.
Which, Harvey explains, is.
- Unbiased, unprejudiced, fair.
- But is this true?
How fair is a coin toss exactly?
What about coin spinning?
What about giant, coin flipping machines
like he used in the animated series?
Is Two-Face, a man obsessed with chance,
using a system that's inherently rigged?
(intense rock music)
Harvey Dent, can we trust him?
Sorry, Gotham's bright knight was the youngest man
to become district attorney at 26,
being admired for his integrity and dedication to justice.
We first meet him in Detective Comics issue number 66
published in August of 1942.
While prosecuting notorious crime boss Sal Maroni,
Dent reveals damning evidence against Maroni,
a two-headed coin belonging to the crime boss,
which was found at a crime scene.
Realizing that he is all but doomed,
Maroni leaps up and attempts to drench Dent in sulfuric acid
right there in the courtroom.
Fortunately, Batman was also attending the trial
and managed to save Dent.
Half, half of Dent.
Turns out, half is not quite enough, though.
As Harvey eventually descends into madness,
becoming Two-Face, obsessed with duality,
free will, and the number two.
He takes Maroni's coin, scratches up one side,
and makes himself a deal.
He'll flip the coin, and if it lands heads up,
or clean side up, he'll get surgery to fix his scarred face.
If the coin lands with the scratched side up,
he'll dedicate his life to crime.
And, well, crime wins.
Of course, Two-Face's scars are similar to Joker's scars
in The Dark Knight, in that the story behind
how Harvey got them has changed frequently.
The New 52, for example, showed a different mob boss named
Erin McKillen as the one responsible for scarring Harvey.
A different continuity shows a similar origin
to The Dark Knight, where Dent has his face
disfigured by an explosion.
After having extensive plastic surgery to fix
the initial acid damage and live happily ever after
as a whole man again (explosion) boom.
Talk about bad luck.
Though the fact that he was scarred twice
is kind of fitting.
There's also been significant changes to the origin
of Two-Face's iconic coin.
One version has it present in Dent's childhood,
used as a tool in his father's nightly abuses.
The heads, or heads lack-of choice would not only
lead Harvey to develop schizophrenia but also cripple
his ability to make independent decisions altogether.
Wherever it came from, though, Two-Face's coin is crucial
to who he is as a character.
He allows his actions to be dictated by a simple
and seemingly random coin toss.
As is stated in his first appearance,
Two-Face is supposed to be the most unpredictable
crime master of all time.
But is a coin toss truly unpredictable?
Theoretically, we could take into account all of the factors
that go into a toss of a coin and determine how it's going
to land before it does land back in Two-Face's hand.
So, unpredictable, no.
But how about fair, that's the key.
Dent flips a coin to decide his actions,
believing that the odds of a coin toss are exactly 50/50.
Remember, he specifically says that a coin toss is unbiased.
However, in a paper tilted Dynamical Bias in the Coin Toss,
researches Persi Diaconis, Susan Holmes,
and Richard Montgomery discover that vigorously tossed coins
are slightly biased.
In fact, if you were to flip a coin,
it has a higher probability of landing on the side
that was initially facing up.
If the coin starts facing heads up,
it has a better chance of landing heads up and vice versa.
How big is this bias?
A whopping one percent.
Yeah, that's right, a coin toss is not 50/50
but actually 51/49, favoring the starting position.
So, practically, there's no difference.
But, over the course of Two-Face's criminal career,
possibly thousands of coin flips
over years of villainous schemes
means there are definitely decisions he made
that weren't exactly fair but instead took advantage
of the statistical bias.
And for a man obsessed with fairness,
this would drive him crazy.
Crazier.
Of course, there's a much bigger issue with the strategy
of flipping a coin until he gets the result he wants,
so, y'know, probably isn't super concerned
with the one percent bias.
But we're just getting started,
what about spinning a coin?
Is that a better or worse system for keeping the odds even?
Well, as it turns out, coin spinning is far more rigged.
One experiment had a class of 103 Berkeley undergraduates
tasked with tossing a penny a hundred times
and then spinning that same penny a hundred times
while recording the outcome of each toss and spin.
As predicted, tossing the coin yielded results
you would probably expect, with the penny landing on heads
around 50 percent of the time.
But spinning the coin resulted in surprising results
that showed an obvious bias.
The penny was more likely to land tails up.
Some students even had coins that came up heads
fewer than 10 percent of the time.
That is incredible.
A spinning coin heavily favors landing with
the lighter side facing up due to the heavier side
typically forcing the coin to fall over.
With Two-Face, his coin shouldn't have
a heavier or lighter side since it has two heads,
but after it was scratched up, that damaged side
became lighter than the undamaged side.
So, when it spun, like in the bar scene
from The Dark Knight, the coin has a much higher probability
of landing scratched side up.
This guy, Wuertz, yeah.
The odds were stacked against him
the moment Dent placed the coin on the table.
Again, not exactly the fairness Two-Face was after.
And Two-Face's rigged system only gets worse.
Remember in the animated series,
when he strapped Batman to a giant penny
and sent him flying through the air?
The idea was that Batman would either.
Well, I'll just let Two-Face explain.
- Here's the deal.
The coin lands face down, you'll be squashed flat.
It lands face up, it'll just break
every bone in your body.
- But, here's the thing,
that same paper Dynamical Bias in the Coin Toss
actually built a coin flipping device,
much like Two-Face's, only not as giant.
And they found that the way the coin lands
is anything but random.
Explaining that if you hit a coin with the same force
in the same place, it always does the same thing.
Quote, "With careful adjustment,
the coin starting heads up always lands heads up -
one hundred percent of the time."
I'm gonna say that again, one hundred percent.
I mean, when the coin tosses were 51 percent to 49 percent,
I mean that's one thing, but this.
This enormous penny flip was rigged, plain and simple.
Sure, as we saw, Batman escaped,
and the coin would go on to land heads up anyway,
which means Batman wouldn't have been crushed under it.
But that's not the point.
This rig, more than likely, would flip the coin
the exact same way every single time.
Which is precisely opposite from the random luck and chance
that Two-Face is always going on about.
He even says specifically about his plan.
- I thought as long as I had Batman at my mercy,
he deserved a 50/50 chance.
- But that's not what he got, now was it?
- I make my own luck.
- Although, despite Two-Face betraying his
drive for fairness, this plot did leave Batman
with a large penny to deck out the Batcave with,
so, not for nothing.
So now that we've examined what Two-Face
has been doing wrong in his quest for fairness,
I feel like we should point out all the things
that he's actually doing right.
Y'know, insult the man's methods before complimenting him.
I guess you could say I'm a bit.
What's the word for when you're kinda insincere,
and you say different things to different people
in order to get their approval
even if it's sorta contradictory or hypocritical?
Gah, it'll come to me; moving on.
Firstly, Two-Face almost always catches his tossed coin
in his hand, and this seems insignificant,
but it greatly helps the coin toss to be more fair.
Why?
Well, think about what happens to a coin
when it hits the ground.
It has the potential to bounce and spin.
And as we've discussed earlier,
once that coin starts spinning, the bias
for which side it lands on is greatly increased,
ending in a result that wasn't exactly 50/50.
Catching the coin in his hand prevents that outcome.
We've also seen times when Harvey doesn't
look at the coin before he flips it.
He could simply pull it out of his pocket and toss it
immediately before realizing which side
was initially facing up.
Remember that tossed coins favor the side that was facing up
during the start of the toss.
But if Harvey simply took the coin out of his pocket
and tossed it immediately without looking
at its orientation first, we add an additional element
of randomness, as the coin has an equal chance
of starting heads up or tails up.
The paper referred to this as random in random out.
But if he wants true randomness,
a coin toss is simply not gonna cut it.
Instead, the best way we know how to generate randomness
is by observing the quantum world.
Two-Face would have to carry around a device
that would allow him to measure the spin of an electron
or the radioactive decay of an atom.
Something that can't be determined or predicted beforehand.
Something that is only knowable once we measure it.
While that might seem much more cumbersome
and impractical than a coin, quantum mechanics,
as far as we know right now, is where true randomness lies.
So much so, that it led Einstein to proclaim in disbelief,
"God does not play dice with the universe."
I don't know about dice, but how about a coin toss?
What do you think?
Is a coin toss sufficient enough to fulfill Harvey Dent's
crusade for fairness and random chance,
or is it simply not random enough.
Flip a coin right now.
Did it land on heads or tails?
Lemme know in the comments down below.
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Until next time, my name is Scott,
reminding you to read between the panels
and grow smarter through comics.
See ya.