All language subtitles for BBC.RICL.2019.Secrets.and.Lies.1of3.How.to.Get.Lucky.720p.HDTV.x264.AAC.MVGroup.org.eng

There are some things in life
that you just don't see coming.

The world is random, unpredictable.

Unlikely things can happen.

So, are you blessed
with good fortune?

Or are you...

..one of the unlucky ones?

But maybe there is a way
through this mess of chance.

Maybe the secret to being lucky
is in trusting the maths.

APPLAUSE

CHEERING

Good evening, everyone!

My name is Hannah Fry.

Welcome to the Royal Institution
Christmas Lectures.

And let's start as we mean to go on.

So, who wants to be our first
volunteer for the evening?

Let's get you, there. If you want to
come down. In the pink jumper.

Round of applause as she comes to
the stage! Thank you!

What's your name? Megan. Megan.

OK, Megan, how are you feeling
today? You feeling lucky? Yeah.

OK, good. All right. If you just
want to come here,

just stand just there.
Now, Megan, above your head...

AUDIENCE LAUGHS NERVOUSLY

..we've got a bag of gunge
and there's just a little rope,

just there. What do you reckon
we're going to do? Megan?

For some reason, I feel
like it's going to fall on me!

Well, we thought about it.
We thought about it quite hard.

But actually, it's not going to
fall on you.

You're going to be the one
who's going up there to help us

cut the ropes, so if you want to nip
up there with Fran, just there.

Now, instead, I am going to stand
maybe not quite underneath it,

but what we've got here, the bag
of gunge is attached to a rope.

And just at the other end of the
rope there, there's a tiny, little

weight that's balancing it there.

And once Megan cuts the rope,
the gunge is going to fall

down this way.

And then, either I've done my sums
correctly, in which case the gunge

is going to stop once it hits
about here, or it's going to drop

all the way to the floor,
go splat,

and then everyone in the first row
is going to be covered in gunge.

OK?
Definitely one of those two things.

Now, if we manage to get
through this unscathed, I want

you all to burst into spontaneous
applause.

And if this doesn't work,
I'm just going to do the rest

of the lectures covered in gunge.
OK?

All right? Sound good? All right,
Megan, how are you doing?

Yeah! OK.
You ready to cut rope?

Are you ready?
Do want to give us a countdown? OK.

Erm, five, four...

Three, two, one...
ALL: Two, one...

Whoa!

Ha-ha!

APPLAUSE

Thank you very much, Megan.

You haven't ruined the lectures,
so well done for that.

That was great.
OK. So what happened there?

We had a bag of real gunge there,

which genuinely almost did,

in fact, splat all over us.

Oh, no.

LAUGHTER

It's fine.

Something quite special
happened there, something quite

extraordinary there happened,
to stop that gunge

from splatting everywhere.
If you want to watch this back

in a little slow-mo. So the weight
was just enough to make the rope

swing around that bar

and wrap around enough times
to cause the friction to stop

the gunge from dropping.

We've got another angle of this.

So here's the second angle.

Now you think it's going to drop all
the way down. Just the last minute,

there's just enough there
for it to wrap around itself.

Unwrapped itself there for a second.
But we were safe, we were OK.

We didn't get splatted. Now, here's
a slightly smaller version here to

explain what happened.

Now, we calculated that if this
weight here is 14 times lighter

than the item on the other end,
then that is enough to make sure

that it would always stop
itself from falling.

Now, I knew that for sure,
of course. You all knew,

surely, that I knew that for sure.

But still, you know, it's inevitable
that you feel a little bit worried.

And that's, I think, is something
that you have to accept.

You know, we're all humans.
We are...

We find it hard to override
our instincts.

We're not built for calm
and rational thought.

But that is the reason why we
created mathematics. It's a way

to step outside of ourselves
and be objective, a way to calmly

calculate something and be sure of
the answer, rather than just rely

on what our messy minds
might tell us.

And you know what? I'm a very big
believer that maths can offer you

a new way of looking

at almost anything, because I think
if you take the time to look,

thank you very much,

there are mathematical patterns
hiding behind almost everything,

even things that feel like they are
very far away from being

mathematical, even things that you
think should be completely random.

Now, we're going to come back
to this one in a moment.

But in the meantime, my fellow
mathematician, Matt Parker, has got

a perfect example for us, haven't
you, Matt? Hello. Yes.

I've got a huge group of people out
here in the entranceway to the RI.

If you'd like to come out
and join me. Sure thing.

So, thank you very much,
everyone who came along.

Bizarrely, all wearing red hats.
That's fantastic.

And all of you wearing yellow.
Well, how fortunate!

This must be the new fashion.

So we're going to try an experiment
with all of you in a moment

to see what happens when
you're moving through a crowd.

OK. When you're moving in a crowd,

I mean, everyone's making
their own decisions.

It's random, surely?

It feels very random,
very chaotic, unorganised.

You're being bounced around.

However, there are some patterns
and, actually, we...

WHISPERING: ..want them to walk
naturally, so we're not going to

tell them when the experiment
starts. OK. Watch this.

CONVERSATIONAL VOLUME: Actually,
I'm really sorry, everyone.

We've just realised, don't move
yet, that we wanted the yellow hats

on this side. We wanted, I know,
the red hats on... It's not me,

it's coming from upstairs. So I
think we're clear. OK. If you can.

Quick as you can. If you just swap
over sides, exactly where you

are but opposite across.
OK, so you can see here,

we've got an overhead camera rigged
up so we can see.

Come on, everyone,
as quick as you can.

Hurry up. Come on, faster, please.

We've got a TV show to do.
Here we go.

So... They're not all jumbled up.
It's not random, is it? No.

Right. Look at this.
So, because everyone...

Having some mild issues here.
Everyone's just following each other

and you end up with these
very clear lines.

So if these were random,
it'd be a complete mix.

Instead, we've got
these fantastic stripes.

Come on, everyone.
Let's keep it moving.

You end up with these
fantastic stripes.

So, everyone. That was fantastic.
Thank you so much.

And that was the experiment.

So, thanks very much
for getting involved.

Thank you. Thank you, Matt.

Now, it turns out there are actually
a lot of similarities

between the
maths of how people...

AUDIENCE LAUGHTER

Be quiet down there! ..how
people flow through a corridor

and how fluids behave.

And if you can understand how people
move when they're in a crowd,

you can predict how they'll react

in the case of an emergency and
that's something that's incredibly

important if you are designing
buildings

or stadiums or train stations,

to make sure that your design is
as safe as it could possibly be.

And that, really, that is the point.
That is what maths is all about.

It's all about discovering
those invisible patterns

like this beautiful pattern left
here by that swinging pendulum.

Isn't that gorgeous? Much neater,
I think, than you would expect.

But, you know, maths isn't
just about spotting patterns.

It's also about using them
to your advantage.

So here is something that might look
as though it's random.

Best part of Christmas, obviously.
Who gets the toy?

Who gets to wear the hat?

Now, here you go, if you want to
have a go on this,

because you only do this,
go for it...

..a few times a year,

you may not notice, there we go,
you can have that one...

..you may not notice that there is,
actually, a pattern to this.

But luckily, I have done
hundreds of these.

And there is a knack to winning.
But I can explain to you.

So what you have to do - I'll teach
you, right, then I can show you.

So what you want to do, you want to
hold your end lower than the other

person, use two hands with a really
sort of steady, firm hold,

and you don't want to do
any twisting or pulling.

You don't want to really tear this.

So what you're trying to do,
ultimately, you're trying to let

the other person do all of the work
so that then...

Ahh! ..you end up winning.

Well done!
You can have the hat, now. Enjoy!

Now, I've got to be straight
with you.

This isn't going to work
every single time.

Especially not if your opponent
knows the same trick as you

and you're just steadily
trying to get lower and lower

than the other person.

But the maths of prediction isn't
about saying what's definitely going

to happen. It's about considering
all of the possible outcomes and

working out what's likely to happen.

So, to show you what I'm talking
about here,

join me in welcoming University
Challenge mathematician

and schoolteacher Bobby Seagull.

Hey, Bobby!
It's very good to see you!

APPLAUSE DROWNS HANNAH'S SPEECH

What have you been doing there,
Bobby?

So I've been flipping coins
hundreds of times.

OK. On a sort of fair,
unbiased coin.

You'd expect the chance of a head or
tail to be 50/50. Yeah.

So I thought, let me try and test
this by flipping a coin six times

in a row. So you'd expect, six times
in a row you'd expect three heads,

three tails, right? Yes.

But sometimes things don't quite
work out the way we want them to.

So, have you been flipping
a coin six times in a row,

many times in a row?

Yes, Mr Seagull's a true maths hero
teacher, flipping it 2,000 times.

No, no, no. I had to
enlist the help of school students.

Nice. So we went across London,

found students from Westminster
Academy... Thank you.

..and students from my very own
school, Little Ilford.

And that's these guys here, right?
Yes, exactly. These students here.

So we got them to line up, all with
a coin in their hand, and flipping

the coin six times. OK.

If they get a heads, they take
one step in that direction.

And can you guess what happens
when they flip a tail?

I'm going to go this direction.
You're right.

And let's see what happens
when they flip the coins.

So this is like a visual
representation of the six flips.

OK, so that's the third
flip there, is it?

Yep. And that's the fourth.

You can see wind blowing
the ties about.

So, spreading out, every extra flip,
they're spreading out more and more.

Exactly.

And now, if we get the students
to move down towards the graph...

Oh, it's like a human bar chart!

..you start to see a pattern
emerging.

Ah, those are very good. So there's
way more people in the middle there.

Yes. And roughly the same number on
the tails and the head side.

And a few have got
six tails and six heads.

So these are three heads, three
tails on this side. Exactly.

All here, I mean, these guys must
have thought they were very lucky.

And down here, all tails. Exactly.

But you didn't just do
this once either, did you?

I mean, this is like nested,
lots of levels to it.

Exactly. So many classes
repeating it many times

to get us a better dataset. OK.

Here we see, this is
Westminster Academy students.

So, I mean, pretty much every single
time we're seeing most people

being in the middle. But you always
get these bits at the end.

You always get the extremities.

But the beauty comes when we try
and combine all the information.

So here we see all these little
dots, they're a student,

a proud, hardworking maths student.

And you put them together
and we get what looks

like a normal distribution curve.
Ahh!

And this is what the maths would
have predicted from the beginning.

Exactly. Very lovely.
Thank you very much.

Bobby Seagull. Thank you!

APPLAUSE

The point that we're trying
to make here

is that life is full of randomness.

But even in the midst of chance,
maths can still tell you what might

happen and also tell you just how
likely that might be.

Which, of course, is precisely
what predictions are all about.

So, OK. Let's take a prediction
about the future

that we are all very familiar with -

what the weather is going to be
like tomorrow.

So I got this from my phone earlier.
This is my weather app.

And this here, it says that tomorrow
the chance of rain is 20%.

Question is, what does that 20%
actually mean? When it comes

to talking about the chance of rain,
what does that 20% actually mean?

Who wants to kick us off? You want
to make a guess as to what you
think

20% means in that context?

The chances are probably 20%,
it's going to cover.

OK, yeah, 20% is going to cover.

So you think it's about 20% of
the space will get covered in rain?

What do you reckon? 20% of what?
Do you want to give me a guess?

Anyone here want to give me a guess?
Yeah, go ahead.

How much of the country
is going to have rain in it?

OK, good. Good response. OK. OK.

Well, let's ask someone
who really knows.

I want to introduce you to someone
who, as you will find out, their

life depends on correctly
predicting the future.

I'd like you to join me in
welcoming Professor Chris Jackson.

Hey, Chris. How are you doing?
Hi. Good, thank you.

APPLAUSE DROWNS HANNAH'S SPEECH

So how did they do? In terms of
understanding that 20%, how did

our audience do? They did pretty
well, yeah. They did very well.

What does it actually mean?

It means that if I was to live

the same day over and over 100
times, it would rain

on 20 of those days.

Does it tell you whether you should
bring an umbrella or not, though?

I'm a pessimist.
You should always bring an umbrella.

Yeah. I'm the same.
No-one likes getting wet, right? No.

No-one likes getting wet. But you
don't predict the weather, do you?

No, I don't.
Something much more risky.

Yeah. I try and understand when,
how volcanoes behave

and when they might erupt.

And you use those predictions
to actually go in volcanoes?

Yes, I do. And we've got some of
your photos here.

I mean, that's pretty close, right?

Yeah, it's pretty close. But
it's important work we're doing

as scientists.
You know, we handle the risk.

And so you're calculating
this risk at all times, are you?

Yeah. We have visual observations on
the volcano, how active it is.

But also, we have an idea
of what the likelihood is

that this volcano may erupt
while we're there.

Have you ever had a close call?

I've never had a close call.
Not yet, at least.

OK. All right.

Well, of course, because this is
the Christmas lectures,

we've got a model of a volcano
to demonstrate.

So you can tell us
a bit about how your predictions

work, using this thing here. OK.

Yeah. So, the thing with volcanoes
is they're very difficult to see

inside and underneath.

So we have to rely on a number
of observations while we're looking

at the volcano.

So one thing we can use is analysis

of the gas that comes
out of the volcano.

So by looking at the amount of gas
and the type of gas, because gas

is contained in magma,

if we measure that, we can
have an idea if magma's moving

into the volcano and the volcano

might be about to erupt.

And so if you see this kind of gas,
you're calculating the risk

of an eruption all the time?
Yes, exactly.

How much gas and what type of gas
may actually kind of give us

an indication of what the nearness
of an eruption is, yeah.

And are there other things
that you're looking out for?

Yeah. So another thing
we can look for is,

magma moves into the volcano,
it pushes against the rock,

the rock fractures and releases
energy in the form of earthquakes.

So, if we can measure the
earthquakes, where they are in the

volcano, then we can actually
measure the earthquakes in terms

of how strong they are as well.

With the gases together,
we may be able to use that in some

sort of like forecasting sense,
so, what's the likelihood?

Are there some signs that are sort
of absolute no-nos, where you won't

enter a volcano after that point?

Yeah, I think if, you know, there's
lots of gas, lots of earthquakes,

maybe even lava coming out the top
of it, that's probably time

to leave! Time to...

Time to take a bit of a step back.
Time to step back, yes.

Maybe let's do that! Let's do that.

So this one looks like
it's imminent. OK?

NERVOUS LAUGHTER

Thank goodness you've got
big glasses on then, huh?

Have you ever
been at an actual volcanic eruption?

I have. Yes. Because this stuff
is really serious, right?

This is not just playful...
Absolutely serious.

It's serious for the people who work
in and around volcanoes.

But it's even more serious

for the people who have to live
with them every single day.

Yeah.

So this one looks
like it's imminent.

This one looks like it's imminent.

I'm going to say, you know, probably
90% chance at the moment

it's going to erupt. OK.

NERVOUS LAUGHTER

Whoa!

AUDIENCE GASPS

That's 100% chance!
Yeah. Impressive!

AUDIENCE WHOOPS

Fantastic! Thank you very much!
Cheers. Thank you!

There is something that's important
to say about a 90% prediction.

10% of the time that volcano
won't explode.

And while it sounds like I'm saying
something quite obvious there,

when you are dealing with
the messy world of uncertainty,

you need to understand
that being wrong is sometimes part

of prediction, because sometimes
errors can have unexpected

consequences. Now, let me show you
what I'm talking about here,

because we have just had a delivery
of 100 Christmas presents

and the rumours are that, hiding
amongst these hundred presents,

there are five brand-new
smartphones.

And one of you gets to come
down and open one

of these presents at random.

So, who wants to come down?

LAUGHTER

What a surprise. Perfect.

All right. Let's see
who we can find.

If you want to come down there,
yeah. Perfect. Round of applause.

What's your name?
Yee-ling. Yee-ling, perfect.

OK, Yee-ling. All right. So if you
want to stand just over there. Now,

you're going to get to pick one of
these presents completely at random.

Five of them are phones, the other
95, they're kind of rubbish presents

like socks and satsumas.
No-one wants any of them.

And because you only get to pick one
present, we want to give

you the best possible chance
at getting a phone.

But luckily,
Matt Parker has invented

a very special present scanning
machine to help you.

Haven't you, Matt?

Look at this! All right. Yeah.
Amazing!

This is my Xmas Ray Detector .80.

And what we can do is we can put
these presents

through the scanner. Actually,
do you want to come with me

around over here? If you want to
stand behind like the conveyor belt

over here where they come out, if I
turn this machine on and I start

putting the presents in the top
here, it will try and detect if

there's a phone in them.

If there's no phone, it just spits
them out the same way they went in.

If it thinks there's a phone,
it rewraps it. Look at that!

Ooh! That's a winner.

So, if it says 'phone',
you put it on the table.

If it doesn't say 'phone',
we don't care. Right?

Just down there somewhere.
Is that OK? Are you ready?

I'm going to start
piling them in here.

You sort them out. Here they come.

You seem pretty happy with this
machine, Matt. I'm very proud.

It is a... How accurate is it?

This machine is 80% accurate. OK.
80% accurate. That's pretty good,

Matt, 80% accurate.

OK. So, then, one of these, then,

that's rewrapped as a phone,

what do you reckon are the
chances that this is a phone?

Shout out what you think it is.

AUDIENCE OFFERS SUGGESTIONS

OK. All right.
Let's think this through, then.

So, your machine,
how accurate is your machine?

80% accurate. OK.

So your machine is 80% accurate.

There are five phones in total.

80% accurate means that it's only
going to find four of them, right?

Which does, Matt, that does mean one

phone's going to end up
on the floor.

Yes. The downside to 80% accurate
is it's 20% inaccurate. Ahh!

But on the upside, 80% accurate.
OK.

So, I mean, you make a good point.

Thank you! OK, one phone
on the floor.

It's not the end of the world.
Still gives you a really good chance

at finding a phone.

There's something going
on there, though.

Hang on, hang on, hang on, hang on.
Stop the machine.

Whoa-whoa-whoa. Whoa-whoa-whoa.
OK. Hang on. Matt...

Yeah? There are way more than four
phones on that table.

Yeah. It's 80% accurate

at both detecting a phone

and detecting NOT a phone.

Are you saying, hang on, are you
saying this machine is taking socks

and satsumas and wrapping them as
phones when they're not? Yeah.

20% of them.

I don't know if I brought
this up earlier, Hannah,

but it's 80% accurate.

AUDIENCE CACKLES

Yeah, but Matt, there's 95 socks and
satsumas here. Yeah.

20%, that's not, that's 19 rubbish
presents in that pile of phones.

Yeah, but 80% of them are down here.

So, the problem is like,
this is 80% accurate,

it doesn't mean these are going
to be 80% phones. Yeah.

It just means, I'd like to recap,
that my machine is 80% accurate.

OK, OK, OK. But right, by the time
you're finished, you're going to

have, what, 23 presents over here?

Only four of them
are going to be phones.

That gives you a four in 23
chance of finding a phone.

It's about 17%.
So it wasn't... OK.

Well, do you want to pick one
at random?

I mean, you can open it,
have whatever's inside.

It's overwhelmingly likely
to be a satsuma.

Well, you can keep it, though.
Merry Christmas.

Thanks for your machine, Matt.
My pleasure. Amazing!

80% accurate!

That kind of error, mislabelling
satsumas as phones,

it's something that's called
a false positive.

And it goes to show how maths
can sometimes really prove

your intuition is wrong.

Now, false positives,
they're everywhere.

You see this every time
you go through an airport.

Think about all of the people that
are pulled over from the scanner

for having lip balm and hair
straighteners in their luggage.

And the number of people
who are false positives massively

overwhelms the number of real
weapons that the security team

are looking for.

But there is a really dark side
to this kind of error, too,

because imagine if, instead
of scanning for presents,

we were screening for cancer.

Now, even if a cancer screening
test, like a blood test

or a mammogram, the ones
that work with 89% accuracy

because they are not perfect, there
will always be false positives.

There will always be people
who believe that they have cancer

when, in reality, they actually
have nothing to worry about.

This is kind of present scanning,

but from the perspective of the gift
box and you can imagine

just how much pain and anxiety
it might cause to be mislabelled.

Now, this doesn't mean
that you shouldn't be screened,

but it's really important
to understand

what these results mean.

But OK, if you can accept that being
right isn't always possible,

if you can really understand these
numbers, then you can still use

them to your advantage,
because sometimes luck

really is a matter of life
and death,

or in this case, zombies.

So to explain this properly, I would
like you to join me in giving

a warm welcome to an epidemiologist

from the London School of Hygiene
and Tropical Medicine, Ros Eggo.

OK, Ros, you study the
mathematics of disease, right?

How much of it is luck and chance?

Well, there's a lot of chance
that's involved

in the transmission of disease.

So if there's an epidemic happening
at the moment, the chance

of you getting it depends
on how many other people

there are that have the infection
at the time.

And then if you happen to meet one
of those, which is more likely

when there's a lot of people
who have it,

there's also a chance you'll get
it from them or not.

And if you have some
pre-existing immunity, maybe

you've been vaccinated
or you've had it before,

then the chance of them passing
it to you also goes down.

So there's a lot. So, then, how can
maths help you? Mmm.

It's really difficult to predict,
on an individual level, if somebody

will get it. But on a population
level, with these nice, big numbers,

there's some things we can
predict - when the epidemic will go

up and when it will come down.
We try and predict the peak.

And we try and predict which groups
might be at risk of infection.

Well, talking of epidemics,
there are some rumours

of a zombie
apocalypse about to hit.

OK, so, everyone here, underneath
your seats,

you should have a zombie mask

and you should have some
ping pong balls.

Now, these are your zombie germs.
Mm-hm.

So how it works is, if a zombie germ
touches you, you become a zombie.

You put up your zombie mask
and then you take your zombie germs

and you throw them straight
up in the air as high

as you possibly can. OK.

And in a moment, I'm going to start
off this infection.

So everyone start with your mask
down to kick us off,

but you can make a prediction
about what might happen here. Um.

So over here, nobody has any
protection against zombies,

zombie infection.

So we're going to expect a lot
of cases and possibly quite quickly.

OK. All right. Let's give it a go.
Is everyone ready?

Everyone got their balls in their
hand? All right. We're going to

start this infection. Here's
the zombie germs coming at you.

I'm going to... I'm directly
targeting people.

OK. Oh, already.

So, we've got little, actually,
a few different patches here.

We do, yeah.

In fact, they're starting to get a
little bit frightening around here.

And it's travelling backwards
through, and now a big cluster of

zombies there, right in the middle.
Uh-huh!

How realistic is what they're doing,
compared to how normal, real

diseases spread?

Well, obviously, for real diseases,
it's not quite so frightening

as what's happening up here.

But we use similar type of methods,
using chance to pass on infection

to understand how real diseases
spread around.

But for zombie infections,
nobody ever recovers.

Nobody, OK.
And that's, in the real world,

people usually recover.

I think there are, in fact, OK,

so if you...

..it's still going!
It is still going!

And if you are not a zombie,

could you stand up for us?
How many people are there?

Oh, we've got some!

Three people who managed to escape
the zombies!

You also can't target people
directly with your zombie germs.

That wasn't part of the rules.
OK. Everybody, sit down.

Thank you very much. Well done.
Now we can do this again, but this

time, we can use some kind of
zombie defences. Exactly. Yeah.

So over here, there's going
to be some protection against

infection, and these people are
going to be completely protected.

OK. So those of you who have,
you've got protective masks

under your seat and this makes you

completely immune from zombie
infection. It does, yeah. OK.

So if the zombie germs touch
you and you're wearing a face mask,

you're wearing a protective mask,
don't worry about anything.

Don't put up your zombie mask,
don't throw any germs around.

You're completely immune.
And we'll see what happens now.

And what's your prediction
about what will happen in this case?

Well, there's a lot of protection up
here. So I think the epidemic will

be over very quickly and maybe
not many people will be infected.

OK, let's give it a go. Here we go.

OK.

So, it's still started.
We've got a few.

Oh!

OK, I mean, that stopped
almost immediately.

OK. So those of you who are not
wearing a protective mask, but also

not a zombie, could you stand up?

Oh, goodness me.
Look at that! Wow, that's a lot.

And there's a point to it.
Thank you very much, everyone.

You can sit down. There's a point
to all of this, right?

Yeah, exactly. So the protection
that we had in the population

from the people wearing masks
who are vaccinated against infection

has protected everybody
in this part of the audience

from getting infection.

And is this the same thing
that happens

when we're vaccinated
against diseases?

Exactly. It is.

So we have here, kind of,
this community

has immunity from infection.

And so, even the people
who weren't themselves vaccinated

have been protected
by the protection

in the whole community.

So how much does the maths
of modelling disease

make a difference
back in the real world?

So we take experiments kind of like
this, but in the computer,

take things that we know
about how infection spreads

and about the population
in general,

and the goal is to use the computer,
use our simulations, to figure out

ahead of time what would be
the best interventions.

What should we do to decrease
the number of cases in everybody,

without it having to happen?

So it doesn't matter whether
you're talking about flus or Ebola

or, I don't know, TB in cows, you
can use these mathematical ideas.

Exactly. Yeah, for human diseases,
for animal diseases, even for

plants, it's really useful.
And demonstrates that vaccines

really do make a difference.
It does. It does.

Would you rather live over here with
all these zombies or over here?

Definitely over there.
Definitely over here.

Ros, thank you very much.
Thank you.

There is a really simple point
in all of this. If you've got maths

on your side, it's not just
about spotting patterns.

It's about using what the numbers
tell you

to bend the world to your will.

And there is one game of luck, skill
and stats that actually captivates

millions of us every single week,
because believe it or not,

the Premier League is awash
with mathematicians.

So, here's the staff photo
from Liverpool Football Club.

You've got the team manager there,
obviously a very important job,

but here,
this is a group of mathematicians.

These guys are the unsung heroes
of Liverpool football team

and it's their job to make
the team as lucky as possible.

So please join me in welcoming
Tim Waskett.

So, that's you in that photo,
Tim? Yeah. That's me, just there.

All right. So how on Earth do you
go about changing a football game

into something to do with numbers?

So the primary currency that every
football game is based on is goals.

Obviously, that's the most
important thing.

And it's our job to turn every
action on pitch, every pass, every

throw in, every tackle, every shot,
into a goal probability.

And I think we've actually got
an image from your team.

So this is showing you
the darker the colour,

the darker the red,
the more likely you are to score?

I mean, from there, it's pretty
easy, right? Yes. Exactly.

So this is taken from literally
hundreds of thousands of shots

through major leagues
all over the world.

And by looking at where the shots
take place, how often they became

a goal, gives us a probability
of a shot from a similar situation,

ultimately ending as a goal.

Now, I understand that there's
a little game that you play

with all of this, of trying to guess
what the maths says

is the probability of a particular
shot going in. Yeah.

I think we have a little clip.

So, we call this
"the expected goals game". OK.

So what game are we watching here?

So this is a friendly between
Tranmere Rovers and Liverpool,

this is a pre-season friendly.
And you paused the footage just...

Yep. So, he's about to do
a header.

So he's about to do a header and
he's right in front of the goal,

there, very close. So what do we
think the probability of this shot

turning into a goal is?

What does the maths calculate the
chances of this turning into a goal?

We have some options.
Do you reckon it's 50%,

75% or 99%? OK.

Shout out your answers.
What do you think it is?

What do you reckon the maths says
is the chances?

AUDIENCE RESPONDS ENTHUSIASTICALLY

Oooh, 75 came out quite clearly
there.

All right, what did
the maths say?

Well, the actual answer here is 99%.

SIMULATED CHEERING

So, that means in exactly the same
position with exactly the same

surroundings, if you reran these
100 times, it would only not

result in a goal once. Exactly.

So, 99 shots of a similar sort
of position will end in a goal,

and only one will get saved by the
goalkeeper. Oh, OK. All right.

Let's try one more. We've got
another clip for you.

Here we go.

Oh, OK, so he's much farther out
here. Much further out,

and he's also not central
onto the goal, he's off to one side.

So we know it's going to be a lower
chance.

It's going to definitely be
a lower chance.

But what does the maths actually
calculate it to be?

So we've got
some options for you.

All right. Do you reckon

the maths says that this is 4%,
7% or 10% chance of getting a goal?

What do you reckon? Shout it at me.

AUDIENCE RESPONDS

Oh, everyone's going
in the middle there.

What's the answer?
You're spot-on. It's actually 7%.

And let's see what actually
did happen.

Ah, a miss! One of the reasons

that that was only 7% and not
any higher was because he shot

it straight at the goalkeeper.

I mean, that's always a big mistake.

But it's not just about strikers
that you're translating

into numbers, is it?
No, exactly.

So this is the easiest thing
that we can do, but we can do

a similar calculation for every
other event on the pitch.

So any time the ball is passed,
for example.

OK.
So to help us to demonstrate this,

I'd like to invite onto the stage
Bertie and Jamie

from a London youth team.

Thank you very much, guys.
Thank you. So...

Bertie and Jamie are just going to
have a bit of a kickabout. Yeah.

Tell us how this works, then. So
for roughly 200 games per weekend,

we get data involving
every single ball touch in the game.

So, the way the data is collected,
every time that a player passes

the ball, they'll mark it
on the pitch and they'll say

this is the position on the pitch
and the player who made that pass,

and then there'll be somebody
watching for the other team

making their passes.

So two people will be going
backwards and forwards, marking

up all of these events. So roughly
every second or so, there's a new

pass, so it's pretty frantic.

So you just have someone there to
kick and kick and kick. It doesn't

sound like the most exciting way to
watch football. No. Well,

thankfully, it's not us who has to
do this work. We actually have

a data supplier who provides us with
these data, these files for us. OK.

Bertie and Jamie, thank you very
much for your help there. Thank you.

So what do you end up with once
you've done all of this?

So for every game we get

approximately 2,000
ball touch events.

And that tells us the position
of the player who makes the pass.

But what that doesn't tell you is
where all of the other players

are on the pitch at that moment.

But you can get hold of
those numbers?

So we can. For the Premier League
games, we get

what we call tracking data.

And so this is a set of cameras
all around the stadium and that's

monitoring the position
of all of the players.

So, 22 players plus
the position of the ball.

And it does that for 25 frames
a second for the full 90 minutes.

So you end up with approximately
1.5 million data points.

That is a lot of numbers!

And in fact, we've got here on the
gigantic spreadsheet, essentially.

So, this is just one game.
And you're watching a game

of football here, basically.

Yes, exactly. Through numbers.

OK. Interesting. I mean, maybe less
exciting than watching

Match of the Day. Well, it
depends on your perspective.

But you're not just
collecting these numbers, are you?

What do you do with them?

So this data can give us a goal
value for every position

and for every player on the pitch.

And what does it end up
looking like?

I think we've got a little...
Yeah, we have a little animation.

OK. So tell us what we're looking at
here. So this is what we call

pitch control. So you can see the
players are in the circles there,

and the arrows represent
the direction and speed

that they can travel in.

And you've got a blue team
and a red team. Yep.

So the red team here
is actually Liverpool.

And the areas in red are places
that the Liverpool players can get

to sooner than the players
who are in blue. Ahh!

Based on how quickly people run.
Yes.

And based on where the ball is.
Exactly.

So, for example, the ball,
in this particular example,

is that yellow dot there.

And if this player, who is currently
in possession of the ball,

this is number ten,
this is Sadio Mane,

his best option at this stage,
is to probably pass to one

of these red areas. And, in fact,
he ends up passing the ball up into

this red zone here to be picked up
by player 66,

which is Trent Alexander-Arnold.

So this is a real game and we can
play on watching the game

through this heat map here.

So, this thing here,
what's this telling us?

So, this is what I was
talking about before, about turning

everything into a goal probability.
So this value now, 1.3%,

this is the probability that a goal
will be scored with the ball

in this position within
the next 15 seconds.

It's quite hard from there. Really.

From there, yes. Because you're so
far back. You've got a long way to

go before you reach the goal.
It's very accurate.

But we can play on this game and see
how it evolves.

So, the ball does get passed over.

Yeah. It gets successfully received.

Still not a very high chance
of scoring a goal from there.

No. But now, Trent
Alexander-Arnold,

his best option is to run
into this position, here. Ahh.

So he's now dribbling
the ball forward.

So, are you using this information
to look at what did happen and work

out what should have happened?
So, we use this in a number of ways.

The main way we use this is

to evaluate player performance
after the game.

And in this particular game,
if we play on one more time,

what was the result of this
sequence?

So if we pause it right about now,

you can see Trent Alexander-Arnold

now has the ball
very close to the goal.

He's in a good position,
but his best option now is to pass

into this red area here,
where it can either be received

by Mane or Shaqiri,
who is number 23 down here.

One of these two players
is most likely to get

to this red zone.

And in actual fact, what happens
in this particular situation,

is that Mane receives the ball

right round about here,
and he scores a goal.

Which is exactly what
you want. Exactly.

So are you using this stuff
to just analyse your team

or are you using it to analyse
other teams, too?

So the advantage of this is we see
all of the players at the same time,

which means that we can
analyse all of the players

within the Premier League and a
large number of players in all sorts

of other leagues around the world,
using the ball touch event data.

And that gives us some really
good information on which players

are doing well and who we might
be able to sign in the future.

Ultimately, to give you the best
chance possible at beating your

opponent. Exactly. Amazing.

Tim, thank you so much for joining
us. Thank you.

APPLAUSE

That's the thing about being lucky.

Sometimes it's not just
about what YOU do,

but also about
who you're up against,

and if winning is what you're after,
something rather intriguing happens

when you start to look
at the maths of competition.

OK, so for this, I would like
two volunteers who are willing

to compete against one another.

OK, perfect.
If you want to come down here.

That's one, and we'll get
someone from over here.

Round of applause.
Welcome to the stage.

APPLAUSE

What was your name? Nat.
Perfect, OK, Nat.

Thank you. And what was your name?
Jasmine. Hm?

Jasmine. Jasmine.
OK, Nat and Jasmine, right, OK.

This game is called
Goodie or Baddie,

right, and the reason why is because
in every round you have two choices.

You can either decide
to be a goodie,

in which case
you put on your red hat,

or you can decide to be a baddie,

in which case
you put on your purple hat.

And what we're going to do is
we're going to play four rounds,

and in each round you have
a chance to win some points.

If you get to 12 points
in those four rounds,

then you win an amazing goody bag,
OK? I mean, it's pretty special.

So this is the way that it works,
OK?

If both of you decide
to be a goodie,

then you will end up
getting three points each.

If both of you
decide to be a baddie,

you will end up
getting one point each.

But if one of you
decides to be a goodie

and the other person
decides to be a baddie,

then the baddie takes everything.

They get five points
and the other person gets nothing.

OK? Remember, four rounds.
You have to get 12 points.

You happy? OK, all right.

Turn around, so you can't
see each other's choices.

Here we go. OK. Here we go.

So, red for goodie,
purple for baddie.

Make your choices now.

Oh!

Turn around
and have a look at each other.

Oh! OK. All right.
Five points, five points there.

One, two, three, four, five.

OK. All right. Round 2. Round 2.
Here we go. Here we go.

OK. Round 2.

He stole some points off you
that time.

Let's go for Round 2.

Go.

Oh! Payback!

Turn around, turn around.

Only one point each.
You blocked him there.

OK, right. Round 3,
Round 3, here we go.

Make your choice for Round 3.

And turn around and
have a look at each other.

Argh. Argh!

You got him back. You got him back.

OK. There's still one round left.

One round left, turn around.

Here we go. OK.

Do you want to take your hat off
and make your choices?

Go for it.

LAUGHTER

What an unsurprising ending.

Turn around, have a look at
each other. OK.

So neither of you... I'm afraid
neither of you got up to the line.

Neither of you got into our points.

But you know what's strange, though?

There were four rounds.

12 points was all you needed
to win a prize.

If both of you had just played
goodie every single time,

then you both would have walked away
with an amazing prize.

The fact you played baddy,
you blocked each other.

But, you know what?

It's understandable, because,
OK, let's say...

Mind if I take this hat
off your head for a second?

Let's say your opponent
had chosen to be a baddie.

In that situation,
you've got two choices, right?

You can be a goodie, in which case
you get no points at all.

Or you can be a baddie,
in which case you get one point.

So, if your opponent's a baddie,

being a baddie is definitely
the best thing to do.

But what if... Do you mind switching
your hats for me?

If your opponent instead had chosen
to be a goodie,

let's think about what was
available to you.

Be a goodie -
you get three points.

Baddie - you get five points.

So even in this situation it's best
off for you to be a baddie.

So it turns out it doesn't matter
what your opponent does.

In any one round, it is always best
for you to play the baddie,

even though if you both
just played goodie,

you both would have ended up
getting a prize.

So thank you very much to my
volunteers.

You're both very bad!

APPLAUSE

Not very Christmassy, is it?
Being bad to each other.

Actually, this is a very famous
game among mathematicians

and it goes to show that winning
isn't always about luck,

but it also, I think, highlights one
of the great tragedies of humanity

that sometimes the tempting thing
to do right then and there,

doesn't actually lead
to the very best outcome overall.

And actually, you see this
time and time again,

the very tiny little selfish
choices that we all make,

they add up to mean that eventually
we can all lose out.

So it doesn't matter here whether
you're talking about climate change

or plastic waste
or North Sea fishing.

We often get sidetracked by the
really small choices in front of us

rather than holding
the big picture in our minds.

And part of that is a mathematical
reason, as we've just seen

with that game, when the incentives
aren't set up

to encourage really good behaviour.

But I think it's also worth
remembering that as humans,

we are not these perfectly
rational objects.

If you really want to be lucky,

then you have to take all of the
weirdnesses of humans into account.

So, OK, let's have a look at some
of your weirdnesses as an audience.

Underneath your seats, you should
have a whiteboard and a pen.

What we're going to do, if you get
those out and get them ready...

What we're going to do is
when I say "go",

I want you to pick a number
completely at random

between one and ten.

I want you to write on your
whiteboard when I say go,

and then we'll hold them up. OK.

Number between one and ten,
completely at random.

Go.

And then hold it up
when you're finished,

and let's have a look at
what you've got.

OK, OK, let's have a little look
at what we've got.

OK. What can I see here?

OK, OK. All right.

I'll tell you what, if you wrote
down a one, could you stand up?

Oh! Hardly...

Certainly not 10% of the audience,
that, is it?

Thank you very much, sit down.

If you wrote down a ten,
could you stand up?

Oh, again, only a smattering.

How intriguing. All right. Sit down.

If you wrote down a seven,
could you stand up?

Ooh! I see!

All of a sudden...

Thank you very much.
You can sit down.

Now, in fact, actually, if you
play this with big groups of people,

it almost always happens that seven
is the most common number,

to be chosen. Huge swathes
of people will choose a seven.

And there's a kind of strange
reason for that.

If you're picking a random number,
one feels like it's too small.

Ten feels like it's too big.

Five is kind of too much
in the middle.

Two's even - can't choose that one.

Eight's sort of too neat.

All the other numbers fall away,
and you're left,

if you're picking a number
at random,

with only seven really feeling like
the random number.

I guess the point in all of this
is that you have to remember

that human behaviour really
isn't actually random.

Humans are not very good
logical machines.

And what that means is that if you
really want to make yourself lucky,

you've got to go beyond
the world of maths,

because, you know, there
is actually some evidence

that shows that just thinking you
are blessed with good fortune

means you can actually
make your own luck.

And there is someone who knows
quite a lot about this.

This is Dr Michael Gervais
in Los Angeles.

He's known as the secret weapon
of top athletes around the world.

Hello, Michael. How are you doing?

I'm fantastic. Great to be here.
Thank you, Hannah.

You have worked with
a number of amazing people,

haven't you, Michael?

I've been fortunate, yes, for sure.

What is it that you do?

Well, by trade and training,

I am a sport and performance
psychologist.

So you're trying to get people
in the right mind-set to win?

Yeah. There's three things
that we can train as humans.

We can train our craft,
our body and our mind.

And world-leading thinkers and doers

are not leaving one of those three
up to chance.

And the science is informing us
of best practices to be able

to train our mind, to be able
to adjust to the unfolding,

unpredictable, unknown.

So do you have any top tips for us

as to how to train our minds
to get the best out of ourselves?

I wish I had tips and tricks
and hacks and short cuts,

and there really aren't many,

and so if we can learn from
the best in the world

how to fundamentally organise your
life, to strengthen your mind,

to deal with the unknown.

And what we've come to find out is
that there are a handful of skills

that people practice - mindfulness
being one of them,

optimism being another.

And those are trainable skills.

Confidence is a trainable skill.

Being able to be calm in any
environment is a trainable skill.

So there's a handful of a few
that are most employed by most.

I hear that you've worked
with a few daredevil skydivers.

I think we have a little clip of
one of the people you've trained.

Just tell us what Luke Aikins did.
He's here in the green. Absolutely.

So, Luke Aikins is one of the most
extraordinary base jumpers,

aeronautical flight folks
in the world.

And what he did -
he was the first ever to do this -

is that he jumped from 30,000 feet,
which in and of itself is a big deal

because you need oxygen masks to be
able to carry enough oxygen.

But he did it without a parachute.

Without a parachute?!
He was the first person...

Yeah, and he's the first person
to do that,

and he jumped into a 16-storey net
that he and his team built.

And so you were behind the scenes
in advance of this event,

trying to get him to focus
in the right way?

Yeah. When your life is on the line
and the stakes are high

and consequences are real,

nobody leaves very much
up to chance.

And so training your mind is one
of the ways to help somebody

have great command of themselves
under duress.

And so absolutely, yeah,
this is one...

This is an incredibly
dangerous project.

Do you think he's mad?

LAUGHTER

I get that question a lot.

No, he is actually just like some of
the greatest mathematicians

in the world, just like some
of the greatest historians,

is that they go to the edges
of their potential.

And when somebody goes to the edges
of their potential,

they're taking the next
natural step.

And in some cases,
it changes humanity.

In other cases, maybe it
changes a family legacy.

But this is what the greats do,
is they add to their body of work

by extending their capabilities.

Now, in those extended areas,

in that place where they're not
quite sure

if they have what it takes,

that's where luck... We want to
diminish the amount of luck involved

and make sure that we're increasing
them out of skill.

And so is a lot of this about
helping them overcome their nerves?

Well, certainly the emotional
component to exploring one's

potential towards mastery,
towards high performance

and achievement and success -
emotions are part of it.

And emotions and thoughts
and environment

are the three legs to the stool.

And while we might not be able
to ever really manipulate our

environment, we can manage
our thoughts

that influence our emotions.

So those are the three components

that we want to make sure
we're investigating.

That's amazing. Dr Michael Gervais,
thank you very much for joining us.

APPLAUSE

Feeling lucky - just feeling lucky -
can change your chances of success,

and as Dr Michael Gervais
was saying there,

it's all about fighting
your instincts,

about overriding your gut,

stepping outside of yourself
and being objective,

and I think there is something in
there that maths can empathise with.

OK, how about those people
who are really lucky?

So how about the ones... Not just
ones who have maths and bravery

on their side, but how about people
who walk away with the really big

prizes, the ones who stand
out from the crowd, right?

The real one-in-a-millions?

Well, I'll tell you what.

Let's try and find one,
because what we're going to do

is we're going to whittle down
all of you

to find the luckiest
person in our audience.

You know how
we're going to do it?

We've got a game show.

APPLAUSE

So, are you feeling lucky?

I'd like to welcome my glamorous
assistant, Matthew Parker.

Now, OK, everybody, if you would
like to stand up

underneath your feet,
you should have two hats.

One is yellow. One is blue.

What we're going to do is
we're going to run a series

of semi-random rounds.

All you need to do is put on
your blue hat or your yellow hat,

whichever you think is most
likely to win.

If you are unlucky and you get one
of the semi-random rounds incorrect

I'm afraid you then have
to sit down.

You are out of the game.

If you get it correct,
you stay standing up.

You're through to
the next round.

OK, are you ready to play?

Let's go.

Round 1.

Which of these two
balloons is going to explode

in a ball of fire?

Is it yellow or blue?
Make your votes now.

Everyone's voted.

It's quite loud.

Cover your ears. Here we go.

Ready? The blue one is...

BALLOON POPS
..not explosive.

Which means the yellow one...

DEEP BOOM
..is!

Blue, you are wrong. Sit down.

Yellow, stay standing up.

Everybody, hats off.

Round 2.

APPLAUSE

Round two is a race.

If you think the blue channel
cockroach will win,

put on your blue hat.

If you think the yellow cockroach
will win, yellow hat.

Everyone ready?

And they're off.

LAUGHTER
Come on!

SHOUTS OF ENCOURAGEMENT

FROM AUDIENCE: Come on, blue!

Blue, blue, blue!

Oops.

And the winner is...

Blue!

APPLAUSE

Yellows, sit down.

Blues, stay up. Hats off.

Round 3.

APPLAUSE

OK, everyone.

I've got a pancake here.

One side of it is yellow.
One side of it is blue.

Once I flip the pancake,
which side will land face up?

Yellow or blue?
Make your votes now.

Here we go. Ready?

Oh!
SHE CHUCKLES

It's yellow!

Blues, you lose. Sit down.

Yellow, you are through
to the next round.

Everybody, hats off.

Round 4.

I found this person backstage.

Is their name Dave? Is it Tom?

If you think it's Dave, blue hat,
Tom, yellow hat.

Look at him. That's the facial hair
of a Dave,

but the shirt of a Tom.
What do you reckon?

OK.

Hats on.

And the correct name is...

It's Tom!

Blues, sit down.

Yellows, stay up.

Hats off.

Round 5.

APPLAUSE

Who is tonight's extra special
celebrity guest?

Is it Operation Ouch's
Dr Xand van Tulleken

or Operation Ouch's
Dr Chris van Tulleken?

Yellow or blue. Make your bets now.

And the answer is...

Hey, everybody!

Which one are you?

What?! We've known each other
for years.

It's Xand van Tulleken! OK.

Yellow, you are through to
the next round.

Thanks, Xand, that's all we
need from you.

Blues, sit down.
Everybody, hats off.

Round 6.

APPLAUSE

All right.

Am I wearing blue socks?

Am I wearing yellow socks?

Vote now with your hats.
Blue or yellow socks?

Blue hats for blue,
yellow for yellow.

Yellow, blue, blue, blue, yellow.

OK. Are you ready?

They are...

Have you ever...blue?

Ready?

Yellow!

Blues, you're down.
Yellows, stay up.

Who've we got? One over there.

We've got two over there.

We've got one over there.

OK, everybody. Hats off.

Round 7.

APPLAUSE

Which one of my two party blowers is
going to be longer when I blow it?

Is it going to be blue or yellow?

Make your vote now.

OK. They've made their bets.
All right, here we go.

PARTY BLOWERS SQUEAK

And the answer was blue.

Yellow, you lose.

Blue, you're through
to the next round.

Final Round.

APPLAUSE

OK.

We've got three people left.

This one is a straight run
between me and Matt

as to who can get the balloon on
their head to pop first.

Who wants to go... We need to...

You need to pick a team this time.

So who wants to go for me?

Thank you.
And who's going for Matt?

Thank goodness that music
doesn't get annoying.

We have got... Let's have a look.

We've got two blue and one yellow.
Interesting.

Interesting. OK.

OK, ready, Matt? Ready.

Three, two, one.

Go.

AUDIENCE SHOUTS ENCOURAGEMENT

BALLOON POPS

CHEERS AND APPLAUSE

Right.

Tie breaker, will the blue/yellow
coin land blue or yellow?

You've gone for yellow.

You're going to go for blue.
Are you ready?

And the winner is...

Yellow! You're the luckiest
person in the room!

The luckiest person!

APPLAUSE

Amazing!

The winner!

Abi, the luckiest person
in our audience,

we've got a crown for you.

We've got a trophy for you.

We're not going to
give these to you just yet

because we really want you to prove

that you are the luckiest person
in the audience.

So what you've got to do, Abi,

is you have got to just land
a ping pong ball into that, OK?

Now, we know you're lucky.

I mean, you just beat everyone
in this room,

so we're not going to make it
too easy for you.

Come and follow me.

We're going to shoot the
ping pong ball from up here.

Let's see how lucky you really are.

We want you to get that crown.

We want you to get that trophy.

So if you just want to stand
in there.

Your job now, Abi, is to try
and fire it into there.

Let's give her some encouragement.

Yes! Come on!

CHEERS AND APPLAUSE

Come on, you're the luckiest person.

Not bad.

OK, we'll give it another go.

Come on. We really want
to get the crown. Come on.

Oh, it's pretty close.

It's almost like they weren't lucky
and someone just had to win!

We can speed this up
if we bring in the string.

Thank you for the string!

Of course, because the more times
that you do something,

even if it's really unlikely,

eventually it becomes
a mathematical certainty.

Here we go.

Abi, we're going to put
some safety glasses on you. OK.

We're going to give you
a scary-looking glove.

OK, so this sets fire.

Can you give us a test click,
make sure it's working?

OK. You're going to, in a second,
we'll count down.

You're going to set fire
to the string. Are you ready?

Count down from...
Everyone. Three, two, one, go!

Whoa!

Surely one's going to go in!

Come on!

Whoa.

Hang on, hang on, hang on, hang on.

There's one in there!

CHEERS AND APPLAUSE

You're the luckiest person
in the audience!

So, OK, everyone.

We have just discovered how we can
use our understanding of maths

to get lucky, and in the next
section, we're going to explore

how we can up our chances of winning
at even bigger challenges,

and learn that bending the rules
can sometimes be good.

Goodnight.

The luckiest person!

CHEERS AND APPLAUSE