Tails You Win: The Science of Chance

(

- All our lives, we are pulled about and pushed around

by the mysterious workings of chance.

When chance seems cruel, some call it fate.

And when chance is kind, we might call it luck.

Scoring a big win,

being saved from disaster,

or meeting that special someone.

But what actually is chance?

Is it something fundamental in the fabric of the universe?

Does chance have rules?

And does it really exist at all?

And if it does, could we one day even overcome it?

This is the story of how we discovered how chance works,

learnt to tame it,

and even to work out the odds for the future.

How we tried, but so often failed, to conquer it,

and may finally be learning to love it.

Chance plays its part in all our lives,

though mine perhaps more than most.

I'm a mathematician at Cambridge University

and trying to make sense of chance is my job.

I study how we can use the mathematics of chance

to calculate probabilities,

numbers that can give us a handle

on what might happen in the future.

Did you know that, on average,

each person in Britain has a one-in-a-million daily chance

of some kind of violent or accidental death?

To put it in perspective, one in a million

is roughly the chance of flipping heads 20 times.

Imagine it like this.

Flip a coin, 20 heads, you're dead.

Heads.

Heads.

Oh, dear.

Heads.

Tails.

Oh, phew.

It's easy to say that it's 50/50

for a coin to come up heads,

but we can even put a probability on things

that seem utterly chaotic and unpredictable.

San Francisco.

In October 1989, a huge, magnitude 7 earthquake

struck totally without warning.

Many people died.

Today, San Francisco

is its usual laid-back and beautiful self.

But the people here know another disaster

could hit at any moment.

I know that my family members,

we all have the earthquake kits

and we try to have things ready,

but, other than that, we're not very fazed by it,

I don't think.

Not until the big one comes.

I believe in being prepared

but I also believe that it is fate.

I've been here for over 20 years

and it kind of puts you in a place

where you live a bit more in the moment,

where you know as much as you prepare,

something could hit at any time.

- For millennia, we've met the uncertainties of life

with just a fateful shrug of the shoulders.

But mathematics can help us quantify fate,

even if we can't banish it.

- What we now know from our studies is that

the likelihood of a major earthquake hitting the Bay Area

is something like 63% over the next 30 years.

But, associated with this 63% number,

which sounds very precise,

there's actually a huge range of uncertainty.

It could be mid-40%

or it could be 80%.

Probabilities are often as much

a matter of judgment as arithmetic.

But they can still really help people decide what to do.

After the 1989 earthquake,

there were a lot of aftershocks

and a woman called me and she said,

"I'm so nervous to be here."

"I think I want to drive to Los Angeles

"to visit my daughter."

And I said, "I don't think that's a good idea,"

and she said, "Why?"

I said, "Well, the likelihood that you'll be injured

"in an automobile accident is much higher

"than the likelihood that an aftershock will harm you."

There's no escaping chance.

But if we can understand how it works,

then perhaps we can even turn it to our advantage.

This was what the first mathematicians to investigate it

hoped to do.

To, as it were, tame chance.

The scholars of the ancient world,

the Egyptians, Babylonians, Greeks and others,

laid down the foundations for geometry,

algebra, number theory, and so much more.

But extraordinarily, they never even got started

on the maths of chance.

It wasn't until the Renaissance

that a few pioneering thinkers

first got to grips with probability.

But unlike the ancients,

they weren't loftily pursuing knowledge for its own sake.

They were trying to crack the secrets of gambling.

The first was Gerolamo Cardano,

from the Italian city of Milan.

Cardano was a doctor.

But he was also an obsessive life-long gambler.

This was written in the 1570s,

the earliest known work on probability.

In it, Cardano set out

a seasoned gambler's tips and insights,

including how to cheat, and in one chapter,

laid out the most fundamental principle of probability.

Cardano realized a probability was also a fraction.

So with the roll of a dice,

the probability for each side coming up was one sixth.

And it gets more interesting with two dice.

With two dice, and 36 possible combinations,

there's only one way to throw a two.

But you're much more likely to get a seven.

Cardano's insight works with games like dice

because we can assume that each of the faces

is equally likely.

Provided, as Cardano puts it in his book,

"the dice are honest."

This may seem simple to us now

but it was the very first step

in working out how to tame chance.

Las Vegas, a place Cardano would have surely loved.

The people who run this city

have the measure of chance so well,

they've built an entire glittering industry out of it.

It's vital, even so, that anyone here can get lucky.

You could even bet one dollar and win a million.

Mike Shackleford is a professional gambler.

His living depends on his command of casino maths.

I analyze every casino game out there

and my goal is to find out the probability

of every possible event in every game.

Almost always, the odds are going to be

in the casino's favor.

For example, in roulette,

the house advantage is 5.26% under American rules.

That means that for every dollar the player bets,

on average he can expect to lose 5.26 cents.

Not only do the casinos

understand the probabilities perfectly,

they also know that most of the punters don't.

And these games can really mess with our minds.

- You'll see a series of outcomes from a slot machine

and believe that there's a pattern to what you've just seen

but that's really just the human brain

playing a trick on you

because what's happened in the past has no predictive value

for what is going to happen next.

Yes, the machine may have had this series of payouts

in the past.

It may have been hot or cold.

But that has no bearing or no influence

on what is going to happen on that next game.

So you could hit the jackpot symbol

two games in a row.

- We just hit the biggest jackpot we've ever hit here.

8,600 dollars.

We just went to this machine about half an hour ago,

so we got lucky.

- Jackpots don't worry the casinos.

They know the slots are programmed

to deliver high house edges in the long run.

Smart players, like Mike, rarely touch them.

A professional gambler plays games

where the odds are in their favor.

Probably the most well known is card-counting in Blackjack.

- In Blackjack, every time a card is dealt,

the odds change for all the cards that are left.

Mike tracks the cards that are dealt,

to work out how those odds are changing.

- So if the player notices that in the first 25% of the shoe

a lot of small cards came out, more than expected,

he knows that the remaining cards

are going to have a surplus of big cards.

So he will adjust his bet size

and he will change how he plays

and by doing that, he can get the odds in his favor.

- On a good day, Mike can get a 1% advantage over the house.

It doesn't sound much

but it could mean a lot of money.

The casinos, of course, don't like card counters

and Mike's been banned from almost every joint in town.

In the world of games,

if you know the rules, you can figure out the probabilities.

But what about the chances of life and death itself?

To be able to put probabilities on our own lives

needed another great mathematical leap.

And this time, the rewards would be even bigger.