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.

SPLASHING SOUND EFFECT

APPLAUSE SOUND EFFECT

GASPING SOUND EFFECT

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, 1 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 judgement 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 realised 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 2.

But you're much more likely to get a 7.

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 analyse 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 favour.

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 favour.

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 favour.

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?

EVIL LAUGHTER

BELL TOLLS, SPOOKY MUSIC

To be able to put probabilities on our own lives

needed another great mathematical leap.

And this time, the rewards would be even bigger.

For most of history, it was almost a given

that we had not the slightest inkling

of when our time on earth was up.

Death visited when he wanted

and the results were never pretty.

Thank goodness for the consolation of eternal life in the hereafter!

The sculptors who carved this terrifying monument

were capturing the brutal truth of our mortality

as a warning to everyone here, quaking in the pews.

But around the time this was carved, about 300 years ago,

scientists began trying to work out

the mathematical chances, for each individual,

that Death would soon be paying them a call.

The revelation was that you could study one group of people,

the residents of this parish, for instance,

and see how old they were when they died.

From this, you could estimate the chances of death

at each age for everybody else too.

This was a radical idea.

Count the dead

and Death would become less of a divine punishment

and more of a predictable force of nature.

The man who really cracked

how to apply the maths of chance to human lives

was Edmund Halley, the famous astronomer.

Edmund Halley had no interest in what went on in there.

What fascinated him was what had happened out here.

Most people now remember him for his famous comet,

but I salute him as one of history's greatest nerds!

Halley realised that he could calculate

the probabilities of life and death.

All he needed was some good data.

83...

52...

27...

In faraway Breslau, now a city in Poland,

locals were spooked by an ancient superstition

that being aged 49 or 63

was particularly risky.

To prove the superstition wrong,

a Breslau clergyman collected details of all the town's deaths

and circulated these to the leading scientists of the day.

Halley got hold of the data

and realised the results would have an impact far beyond Breslau.

Halley constructed a table

that was made up of, essentially, two columns.

The first column was age

and the second column was how many people were alive at that age.

The first column started at birth with 1,000 people,

and as the ages increased,

what we saw is that the number of people alive decreased

and this wasn't uniformly.

Halley found nothing special about 49 or 63.

But his data showed that the older you got,

the greater the chance of you dying.

It seems obvious to us now.

But before Halley,

people thought the chances much the same for everyone,

young and old alike.

And Halley's table had an immediate practical benefit.

Halley's tables were also ground-breaking

because not only did he publish

the probability of death at a certain age,

he took that one step further

and applied that to the price of a pension

or the price of life assurance.

He included formulae as to how you could actually come up

with a price for a pension.

People in the 17th century wanted to buy pensions

and life insurance, just like they do today.

But before Halley, anybody who provided them

was in danger of going bankrupt.

So Halley's breakthrough would form the foundation

for the entire pensions and life insurance industry.

And death would never seem as capricious and mysterious again.

And what of Edmund Halley?

He lived all the way to 86,

off his own table!

Costly if you were his pension provider!

Today, the insurance and pensions industry is huge,

and has collected so much data

they can correlate your life and death chances

to your gender, your address,

your job and your lifestyle.

And knowledge of the odds could help us all.

So what do we know about what affects our chances,

for better or for worse?

Imagine this 100 metres is 100 years of possible life.

How many of those years are we actually going to see?

How far along this track are we going to get?

When I was born, the average British male

expected a much shorter life than if born today.

I was born in the 1950s and back then,

my expected lifespan was just 67 years.

But thanks to medical advances

and changes to the way we live and work,

our chances are continually getting better.

The average lifespan is actually rising by three months a year.

If I were born today, I could expect to live to 78.

Even better, the longer you live,

the longer you can expect to live,

because you've been lucky enough not to die young.

So at my age now,

I can expect to live not to 67...

..or 78...

..but...

..82.

But what's not so cheerful

is the effect of all those things I might do throughout my life

that could stop me getting this far, or even further.

Research tells us that

for every day you're five kilos overweight, like I am,

you can expect to lose half an hour off your life.

Aah!

Sad to say,

if you're a man sinking three pints a day

then that's also half an hour.

But what about exercise? Won't that make things better?

Yes, it will. But there's a catch.

A regular run of half an hour

and you can expect to live longer.

Half an hour longer.

So I hope you actually like running.

Cos that's how you just spent your extra half hour.

Surprise, surprise, the worst news is for all you smokers.

Two cigarettes costs half an hour.

But the average smoker's on nearly 20 a day.

And it all adds up.

Doing something that costs half an hour a day...

Well, that's more than a week off each year

and, in the long run, that's a whole year off your life.

For that 20-a-day smoker,

that's a staggering 10 years you should expect to lose.

All these figures tell us a lot.

But as for chance itself,

that's certainly not disappeared.

When I say I can expect to live to 82,

I'm not actually making a prediction.

It may be shorter or, with luck, it may be longer.

82 is the average.

Imagine 100 possible future me's, each equally likely.

I'm 58 now and as the years roll by,

in more and more of these possible futures, I die,

until by the age of 82

about half of my future selves will be dead

and about half still alive.

Which is going to be me? That's just chance.

Beyond 82, more and more drop dead.

And there's a very small chance I could live to be very old indeed.

If I were a smoker, it's just possible I'd beat the odds.

But overall, my chances wouldn't look nearly so good.

Of course, many people would say going on about risks

is being a big killjoy.

The writer Kingsley Amis famously said,

"No pleasure is worth giving up

"for the sake of two more years

"in a geriatric home at Weston-super-Mare."

But I believe understanding the risks

might actually help us to have more fun, not less.

OK. Just put one arm through there for me...

the other through there and turn around. Thank you.

What we'll do is we'll start strapping you in.

Many of my favourite experiences would be impossible

without taking some risk,

but I'm about to do something I've never done before

which really does involve risk.

The best way to compare risky activities

is to use the micromort,

a cheery little unit which represents

a one-in-a-million chance of death.

Skydiving is actually safer than you might think.

There's only about a seven-in-a-million chance of dying.

That's seven micromorts.

That's about the same risk as 40 miles on a motorbike.

But there's still a risk.

And you may think I should be old enough to know better.

But I think it could be rational to take more risks when you get older.

An average 18-year-old has a chance of dying in the next 12 months

of about 500 micromorts.

But at my age, the equivalent is 7,000 micromorts.

7,000 micromorts doesn't sound great, does it?

But my extra risk of skydiving is only seven micromorts more.

That's not much difference.

So the risk is actually pretty low.

But the funny thing is,

now I'm actually in the plane and there's no backing out,

it suddenly seems a lot worse.

Will my parachute fail? I don't know.

Will we be blown into a tree? I don't know.

Will I be sick with fright over my jumpsuit?

The probability of that is getting close to 100%!

It's the moment of truth.

Here we go!

Yes, I'm a Professor of Risk

and I've made a sound decision rooted in the numbers,

but as I fall, I can't help thinking

there's a chance I'll die very soon indeed.

I could buy myself a pair of silver hairbrushes.

Oh, hello!

I'm having a go at these premium bonds.

They're wonderful things - you can't lose.

Look, there are staggering prizes each month,

you can get your money back any time you like,

and, what's more, all your tickets go back into each draw

whether you've been lucky before or not!

I might win a thousand quid!

I love a bit of a flutter.

Not a word to Bessie about that!

In 1956,

Britain introduced a brand new kind of savings scheme,

Premium Bonds,

that instead of paying you interest

gave you the chance to win big prizes.

At its heart was something created by mathematicians,

a world of pure chance, randomness.

This is a world where every element

is disconnected from every other,

that operates beyond our influence or control.

The Premium Bonds monthly prize draw

needed complete randomness

to make sure it was scrupulously fair.

There was quite a lot of human interest in randomness

for the first time,

where people began to think about,

"what are the chances of my winning?"

But what it required was

a source of random numbers

and a special purpose computer was built for this

and it was one of the very first special purpose computers.

We're going to an electronic machine, if you understand what that is,

but thank goodness its complicated name is ERNIE for short.

ERNIE stood for Electronic Random Number Indicating Equipment.

Truly random numbers are hard to produce,

and ERNIE got them by sampling the electrical noise

from a series of vacuum tubes.

It was state-of-the-art engineering.

Randomness really, in a certain extent, means unpredictable,

but also, for the purposes of ERNIE,

it needed to be unpredictable and unbiased

and my job as a young mathematician

was to show that it really was unbiased

to any particular Premium Bond number.

This was quite a skilled and lengthy task

to say those weasel words that mathematicians use,

"We have no reason to suppose that ERNIE is not random."

For me, as a mathematician, complete randomness is fascinating.

It's full of curiosities.

And unexpectedly, it turns out to have its own rules,

patterns and structure.

This is officially the most boring book in the world. Ever.

It's called One Million Random Digits

and that's literally what it is.

Page after page of random numbers.

Say what you like about this book, though,

at least the plot is unpredictable.

Printed in 1955,

these numbers were produced by an early computer rather like ERNIE.

And people have used them since

for everything from randomised clinical trials

to encrypting communications.

I might not read this book cover to cover,

but I promise you there are some really interesting parts.

I mean, look at this. 00000.

And here's another great bit.

12345.

It seems really strange to see these.

I mean, how can these be random?

But, of course, they're as random as the numbers next to them.

Not only can you expect to find patterns like these,

you can even calculate how often you expect to find them.

A perfect sequence of five numbers.

There should be 50 of these in the book.

And the same number five times in a row,

there should be about 100 of these.

You can even expect,

somewhere in these one million random numbers,

the same number to occur seven times in a row.

And I've found it.

6666666.

What makes randomness so useful

is that it is completely unpredictable...

but in a predictable way.

So predictable that it has its own shape.

A lottery is a great example.

Each National Lottery draw is...

well, random.

There seems no pattern at all.

But there are also seemingly strange results.

Today, after something approaching 2,000 National Lottery draws

over 20 years, there are huge differences

in how often different numbers have come up.

Number 38 has been picked 241 times...

..while number 20 has come up just 171.

It might look like something's wrong,

but taking all the results together,

the totals match the shape of randomness remarkably well.

And even the outlying results

are just where the shape shows they should be.

Here we go. Let's pick some numbers.

It's not a great bet, I admit.

There's only a 1-in-14-million chance of me winning the jackpot.

In fact, I'm very unlikely to win anything at all.

There's only a 1-in-56 chance

of me getting the smallest prize of £10.

Overall, the lottery only pays back

45% of the money it takes in.

Far, far worse than any casino game.

If you must play,

though you can't change your chances of winning,

you can improve your chances of not sharing the jackpot.

Many people pick birthdays or other significant dates,

so avoid the numbers up to 31.

You may even want to steer clear

of that supposedly lucky number, 38.

In the end, it doesn't matter what numbers you choose,

every combination, say 1, 2, 3, 4, 5, 6,

is as likely as any other.

That's because it's completely random.

But randomness can confuse us.

For example, use the shuffle feature on the original iPod

to play its tracks in random order and before too long

you're very likely to land on the same album again.

People found it so off-putting

that the shuffle on later-generation iPods was supposedly tweaked.

Apple famously explained,

"We're making it less random so it feels more random."

Patterns and connections like this are what we call coincidences.

And no matter how much we should expect them,

they nonetheless still make our heads spin.

I love coincidences so much

I decided to try to collect them.

Luckily, it's an interest the nation shares.

Let's talk about coincidences now, at 7:24, why do they happen?

-Professor David Spiegelhalter, good morning.

-Good morning.

You are an expert in risk and chance, is what I'm reading,

at Cambridge University,

but why are you interested in chance and coincidence?

Well, it's part of my job.

I'm Professor of the Public Understanding of Risk,

so everything to do with chance, uncertainty and coincidences

is what I'm interested in.

And we've set up this website where we're collecting coincidence stories

which people are sending in,

and the sort of things where people, when they happen to them, say,

"Ooh, what are the chances of that?"

And we're trying to work out what the chances of that really are.

It's like a family having three children all with the same birthday,

born in different years, but all three children being born

on the same birthday. You'd think, "Wow, what are the chances of that?"

Well, we can work those out.

Since there's a million families in this country with three children,

we'd expect there's about 8 families like that.

Now, we've found three of them.

People read great significance into these things, though.

Are they misguided in doing that?

Well, it's Friday 13th, exactly the day that shows people do believe

in luck and fortune and things like that...

But I suppose I'm being a bit scientific about them,

so some of them we try to take apart and do the maths,

but other ones are just amazing.

There's a lovely example last year where a French family,

their house was hit by a meteorite.

Well, that's pretty surprising itself,

but their name was Comette. Isn't that just beautiful?

"What are the chances of never experiencing a coincidence?"

says Steve in Cheshire.

Oh, very low indeed. That would be really, really bizarre.

Good one, Steve.

7:29. What are the chances of any decent weather over the weekend?

'Pretty good, actually, Rachel.

'We've got some clear skies out there at the moment,

'but because of those clear skies

'temperatures are hovering at or just below freezing...'

The radio show was a huge success.

The stories flooded in. Over 3,000 of them.

We got lots of coincidences with numbers, names and words.

And loads of calendar ones,

including one more of those rare triple birthdays.

Some of these stories are really amazing.

Lots of them are about running into friends and acquaintances

in the most unlikely places. And I love this one.

Mick Preston was on a cycling holiday in the Pyrenees

and during one stop-over, he wrote his friend, Alan, a postcard.

But, incredibly, on the way to post it, he bumped into Alan,

who just by chance was on holiday in the same place,

so Mick gave him the postcard in person.

As Mick himself said,

that was a waste of a good stamp!

What's striking is that although these and other coincidences

happened a long time ago, people were so jolted by them

they still remember them years later.

I think our brains are hard-wired to look for cause and effect,

to try to come up with reasons why things happen.

So when things happen for no apparent reason at all,

we find it really spooky.

We just don't seem to easily accept

that we might not be able to understand or control

what happens in our lives.

Random events that have no explanation beyond chance

saturate our lives...

..but some people think they can eliminate the random -

control everything - and that chance has nothing to do with them at all.

Ed Smith was once said to be the golden boy of English cricket.

For years he held an idea about chance -

or, as he called it, "luck" -

that he shared with many of his fellow sporting professionals.

When I turned full-time professional in 1999,

we had all these meetings

about how we were going to approach the season

and someone put his hand up and said,

"I don't think we should say, 'bad luck,' to each other.

"That's an excuse. It's not bad luck.

"If someone gets out, it's their fault."

I think as sportsmen we're conditioned to think that,

that you are in total control.

I mean, if you, if you walk out to bat in professional cricket

and you say, "Well, maybe I'll be lucky and maybe I won't,

"and maybe someone will bowl a good ball I'll be out, and I can't do anything about it,"

then you're stacking the deck against yourself before you even begin.

Ed played for England and became captain of Middlesex.

Everything went well for him,

until one day during a county cricket match at Lord's.

So, we're in the middle of this match, it's going well,

we're pretty much cantering to victory.

We're on a bit of a streak of five, six wins in a row, everything's going well

and I'm doing the most routine thing in cricket, I'm running a two.

It happens all the time, you know...

it's not particularly demanding, athletically,

to run 20 yards and then come back again.

And I ran the first one and then you just rub the bat in,

and I just, sort of, collapsed.

And I'm lying in this, and have this shooting pain in my ankle,

and it was only quite a few weeks later that there was an X-ray,

and it turned out that I'd broken my ankle,

and I wasn't going to play any time soon!

I missed the rest of that season and then I retired, effectively,

at the end of that season and didn't play professional cricket again.

In a single moment, Ed's entire career vanished.

He had been touched by chance.

No-one and nothing was to blame.

I think I found it hard to accept. You know, my own willpower,

my determination to control, to shape my own life, was so great

but the reality is that I wasn't in control.

The fact that I had a broken ankle was just a fact.

It was a circumstance that had happened to me.

So, it was like a clash between, er, my own desire to control everything

and the fact of luck, and, you know, luck won.

The moral of Ed's story is clear -

don't beat yourself up about every failure.

But the opposite is also true -

don't be too chuffed with yourself about every success.

Remember this?

I know you can't get rid of luck, but right now I wish you could!

The parachute hasn't failed at least!

I don't seem to be being blown into a forest!

And I haven't even been sick!

That was so cool! Can we do it again?

You know, the really interesting thing is that whilst I was confident

I would land safely, I couldn't be absolutely certain.

The question is, "Why not? Why does chance exist?"

The story of science, for centuries, has been a triumph -

unlocking the mathematical laws behind everything,

from the atom to the universe.

So why is there still room for the random? For unpredictability?

Why, instead, can't everything in nature be determined?

In which case, we could get rid of chance altogether

and I would be out of a job.

In the 1680s Isaac Newton revolutionised science

with a set of universal laws.

He calculated the orbits of moons and planets...

even predicted the timings of eclipses

and, of course, explained the fall of an earthbound apple.

Oh!

Newton's friend, Edmund Halley, predicted the returns of comets...

..and other scientists eagerly worked to discover new laws

and make more predictions.

"The Enlightenment", it came to be called.

In 1779, the French scientist Pierre-Simon Laplace

had a bold vision.

If some vast intellect

could not only comprehend all the laws of nature,

but could also measure everything, even down to the tiniest atom,

then he might predict the future precisely.

And uncertainty would simply disappear.

Hmm.

In theory, with the right mathematics,

everything in the physical universe could be measured and predicted,

just like the movement of the stars and the planets.

So, for example, if I threw a dice

I could predict exactly how it would land.

This theory is what we call "scientific determinism".

In theory, if we gather the data and do the calculations,

we should be able to get rid of chance altogether,

but, in practice, prediction has proved frustratingly hard.

It's as if there is something about our physical world

that makes prediction all but impossible.

Despite the promise of the laws of Newton

and all the scientists who followed him, we remain in the dark.

But why?

In the 20th century, scientists - like meteorologist Ed Lorenz -

discovered that even tiny influences could have immense

and unpredictable consequences.

As Lorenz put it, "The flap of a butterfly's wings in Brazil

"could cause a tornado in Texas."

The theory of determinism had to acknowledge complexity and chaos.

The laws of physics weren't wrong,

but the real world was just too complicated

to ever fully comprehend.

Also in the 20th century, physicists, like Werner Heisenberg,

delving ever deeper into the nature of matter,

realised there was an absolute limit to what they could ever know.

In his work on quantum mechanics,

Heisenberg set out the uncertainty principle -

essential parts of the subatomic world

could at best only ever be described as a probability.

The dreams scientists once had of conquering chance

have been shattered.

Quantum mechanics has shown us a subatomic world

that is fundamentally uncertain.

Beyond the subatomic, we are still governed by mechanical

and therefore deterministic laws,

but, paradoxically, the mathematics of chaos and complexity

means that things are still ultimately unpredictable.

So what is chance?

Is it real? Is it something out there in the fabric of the universe?

Or is chance in here? Just an excuse?

What Laplace called, "Merely the measure of our ignorance?"

Or is it a bit of both?

After centuries of discovery,

we are still not much closer to knowing what chance really is.

One thing is certain - chance is here to stay.

What's more, it has actually been put to work.

Faced with complex and unpredictable problems,

scientists have found ways to use chance itself

to convert blind uncertainty into computable probability.

In the early years of the Cold War,

nuclear physicists at Los Alamos

were working to design a new atomic bomb.

They wanted to predict when an atomic chain reaction

might go critical,

but the physics was so complex that at each step in the chain

they were uncertain about what would happen next.

So they turned to the mathematics of chance.

For each step, they chose an outcome at random

and then calculated what the resulting chain reaction would do.

Then they randomly chose a new set of outcomes

and calculated a new result.

They did this repeatedly until they had hundreds of different,

but equally likely, possible results.

And combining them all gave the Los Alamos scientists

an extremely accurate probability

for what the chain reaction would do for real.

They called it the Monte Carlo method,

like rolling a dice over and over again.

And the bomb worked.

Today, that very same Monte Carlo method,

creating arrays of possible futures to compute probabilities,

is being used to try to solve problems in many different fields.

And what's most exciting for me and my fellow Brits

is that this might help to answer

that all-important question: When I go out, do I take an umbrella?

In the 1920s, the economist John Maynard Keynes

wrote a famous book about chance.

And for the ultimate metaphor of impenetrable uncertainty

he chose the British weather.

He wrote, "Is our expectation of rain, when we start out for a walk,

"always MORE likely than not,

"or LESS likely than not, or AS likely as not?

"I am prepared to argue that on some occasions none of these alternatives hold,

"and that it will be an arbitrary matter

"to decide for or against the umbrella."

But we want certainty.

And so we demand it from our weather forecasters.

And then after wet weekends and washed-out holidays

we blame the poor old forecasters for getting it wrong.

Hello, it was a disappointing day in many places

and I'm optimistic it's going to be a better day for most of us tomorrow.

Britain's most famously wrong weather forecast

was on 15th October, 1987.

Good afternoon. Earlier on today,

a woman rang the BBC and said she heard a hurricane was on the way.

Well, don't worry, there isn't.

But there was!

That night England was lashed by the strongest winds

for almost 300 years.

NEWS: Southern England suffered the full fury of the freak hurricane force winds,

in their wake, a trail of devastation,

the worst damage to property since the Second World War.

Nowhere escaped unscathed.

Today the most advanced meteorologists don't try making predictions

like Michael Fish did.

In Reading at the European Centre for Medium-Range Weather Forecasts,

they use a form of Monte Carlo method

to make forecasts using probabilities instead.

To show why they do this,

they've revisited the same weather data Michael Fish had in 1987.

What this shows us is that October '87 was an exceptionally

unpredictable and exceptionally chaotic situation

and so it was always going to be impossible to make a precise, deterministic forecast.

Weather forecasts go wrong because even small errors

at the beginning can grow into huge differences after just a few days.

And that's as true for everyday weather as it is for hurricanes.

To tackle the problem, Tim Palmer and his colleagues

routinely compute 50 different forecasts,

each with slightly varying starting points to reflect the uncertainty.

Before returning to the hurricane, Tim shows us an everyday example.

So we're looking at today's weather forecast

right at the beginning of the forecast period.

These are all basically giving the same type of weather.

A weather forecaster would look at these pressure maps and say,

"There's a northwesterly airstream coming down over the UK,

it's giving us slightly cool temperatures,

but fundamentally it's exactly the same no matter which of these 50 forecasts you're looking at.

Taking the same set of forecasts to three days in the future,

it's a different story.

Now there are discernible differences.

For example, member 14 has a stronger wind, there are tighter gradients

in the pressure than member 15 and that's telling us that

although we can be certain of the general direction of the wind, it's coming from the northwest,

the strength of the wind we cannot be so certain about.

So we have to make a prediction in probabilistic terms.

To work out the probabilities, Tim counts how many

of the three-day forecasts show a particular kind of weather.

It turns out that in about 30% of the forecasts

there are gale force winds over much of England.

Similarly rainfall, we find across much of England about 30%.

What this DOESN'T mean is that it's raining for 30% of the day.

What it means is that over the 50 possible futures,

in 30% of them it is raining.

So what can Tim see using the new method with the 1987 hurricane data?

There's around a 20 to 30% probability

over parts of southern England of hurricane force winds.

Now, the probability normally of hurricane force winds

in southern England is negligibly small,

so even though there's a divergence of solutions, there's real information here.

Adapting the Monte Carlo method and embracing chance

gives much better results.

But in Britain the forecasts most of us see don't give us

this kind of information yet.

We should now be trying to get this type of information out on the daily weather forecast.

And indeed I think it will enhance

the credibility of meteorologists themselves to be able to say

not only is weather forecasting an uncertain science,

but we can actually quantify the uncertainty in a very precise way.

If you were a cynic, you might think that weather forecasters

who give you probabilities and not predictions are just

hedging their bets, ducking out of doing the one thing they're supposed to

so they can never be accused of being wrong again.

But I don't agree.

Better a reliable probability than a wrong prediction.

And knowing the probabilities we can all make our own decisions.

THUNDER CLAPS

Like to bring that umbrella.

Remember that San Francisco probability?

A 40 to 80% chance of an earthquake?

In 1906, the city's worst-ever earthquake

killed 3,000 people

and destroyed almost 30,000 buildings.

Even if a similar catastrophe in the future can't be predicted,

it certainly can't be ignored.

So today scientists are applying new mathematical methods to the problem.

They're computing probabilities literally building by building,

so bold decisions can be taken about what to do.

In Berkeley, across the bay from San Francisco,

one major fault runs right across the pitch

of the California Memorial Stadium,

home of the Golden Bears Football Team.

They're rebuilding the stadium at a cost of over 200 million dollars.

The fault starts

just to the west of the south scoreboard,

and you can see in the bowl

there are those double stair-step curves at two points,

-that's where our joints are for that piece of the stadium.

-Right.

It allows this part of the building to move independently

in an earthquake from the two sides of the stadium on either side of it.

-Right.

-The base of the entire part of that building is on layers of sand

-and high density polyethylene plastic.

-That's amazing.

It allows that part of the building to move a little easier than it would otherwise,

so when the ground moves six feet horizontal and two feet vertical,

it can just go along for the ride and the rest of the stadium is protected.

The stadium is just one part of a massive building

and strengthening programme all round San Francisco Bay.

A colossal 30 billion has been committed in total.

Will it be enough? They can only hope so.

Even if we knew exactly what earthquake is going to occur,

we may not know exactly how strong the shaking will be

and how it will vary across the city because of different soil types.

So you set a standard, you agree the buildings will be built to that

and then you hope that that's good enough.

You can't actually engineer chance out of the system altogether.

At least in San Francisco they've a good idea of what to expect,

even if they can't know exactly.

But there's one last sting in the tail.

Chance can sometimes come up with something you never even thought of.

As we know, there are known knowns,

there are things we know we know.

We also know there are known unknowns.

That is to say we know there are some things we do not know.

But there are also unknown unknowns,

the ones we don't know we don't know.

And if one looks throughout the history of our country and other free countries,

it is the latter category that tend to be the difficult ones.

Donald Rumsfeld may have just been trying to excuse an unfolding disaster in Iraq.

But "unknown unknowns" are a real and profound challenge for us all.

And don't we just know it.

The Bank of England is the rock-solid institution

to which we all turn in these turbulent times.

Surely I can find some certainty here?

I'm meeting Spencer Dale.

The Bank of England is the main financial institution in the country.

People want it to tell them what's going on in the economy, but can you predict what's going to happen?

Unfortunately not. Forecasting the economy is very difficult to do,

in part because the economy is very large and complex

and it's made even more difficult because it depends on people

and their decisions and that makes trying to model behaviour

and how the economy is going to change over time even more difficult.

Every quarter, the Bank makes a forecast for the nation

in the form of what it calls a "fan chart".

And it deliberately builds in uncertainty.

The chart shows that Britain's future economic growth

might have a 5% chance of lying in each one of the shaded bands.

This was the Bank's chart from 2007,

just before the big crash.

At the time we made this forecast,

we thought in three years' time

the annual growth of the economy may be anywhere

between 5% or close to zero.

But the Bank is even less certain than that.

It also leaves room for the unknown unknowns.

This only shows 90% of probability.

So it's shows you 90 times out of 100 we think the economy will go somewhere in this range.

So there's a one-in-ten chance it could just do anything?

There's a one-in-ten chance it will fall outside of this fan chart.

We don't try and put precise probabilities on those very extreme outcomes.

With these charts, the Bank is making one thing clear -

we must expect the unexpected.

And soon after the Bank made this chart, chance struck.

It was a genuinely surprising event, the economy to behave in a way

which we hadn't seen for almost an entire generation.

The environment which we operate in is inherently uncertain,

the future is uncertain

and the impact of our decisions are often very uncertain.

Some people might want to hammer the Bank of England

for not knowing what's around the corner.

But you can't blame them for the nature of chance.

And though the Bank can't give us the information we want,

I think they show the way to the wisdom we need.

There's just no use in looking for absolute certainty.

We can never rely on predictions.

We can tame chance, but only up to a point.

Putting numbers on chance is a powerful way

to get a handle on the future.

But these numbers can only ever be as good

as the information we have to hand.

Though we try to measure reality with precision,

sometimes they're little more than guesses.

What all this means is that uncertainty

is an essential part of being alive.

And whether our uncertainty

ultimately comes from out there or in here

won't, in the end, matter,

because either way surprises will most certainly happen.

For instance, in this year of the Diamond Jubilee,

I found a chicken nugget in the shape of Her Majesty the Queen!

What's the chances of that?

Subtitles by Red Bee Media Ltd