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Narrator: They say life is a competition.

Official YIFY movies site: YTS.MX

The fight to be first.

The survival of the fittest.

Winning.

Nobody wants to be a loser.

Now winning basically means

getting more of what you want in life

and as a mathematician, I can help with that.

Because there is a real science to success,

based on ideas

from some of the last century's most beautiful minds.

♪ Everyone's a winner baby That's the truth ♪

Narrator: From how you can analyse

and take advantage of your opponents...

You need to find a way to be as unpredictable as possible.

Narrator: ..to deciding whether to cheat or play fair.

You can put a good apple in a barrel of bad apples,

it's always going to turn bad.

Being more strategic will help you get ahead.

But if all of this sounds a bit selfish,

I'll also be showing you how co-operation can trump conflict.

And how everyone can be a winner.

Hello, Sherriff!

Hi, Hannah, how're you?

But you came here with nothing.

You see it contradicts all the economical predictions.

Whether it's happier relationships you're after,

a bargain, or a better world,

a look at the science of winning can help,

and reveal some surprising truths.

So join me.

You'll lose out if you don't.

Narrator: To get the best result

in any situation, maths can help.

Let's take just one example,

something as simple as ordering dinner.

Should you choose burger?

Or steak?

Now you absolutely cannot afford it,

but that steak does look incredibly tempting

and it's almost your birthday.

Surely you deserve a 25 pound splurge

every now and then.

Narrator: First of all ask yourself,

what do you really want?

Steak or savings?

Well, you need to decide what winning means for you.

And that might change when your mates arrive.

Let's imagine that everybody has exactly the same choice,

burger or steak,

but you know that your friends are notoriously frugal.

So if they all go for the burger,

and you split the bill evenly,

you could end up getting that tasty steak for a lot less.

Narrator: The 25 pound hit from your steak

combined with the 5 pounds for their burgers

means everyone pays 10 pounds each.

Which frankly, for you, is an amazing bargain.

But hold on.

The waiter's coming over

and he's heading towards your friend

who you know loves a rib eye.

Is she thinking what you're thinking?

Narrator: And what about the others?

And so begins a frankly very British game

of silent guessing and calculating.

If she goes for the steak as well as you,

then you're shelling out 15 pounds each.

But if he goes for the steak too

then that's 20 pounds a head,

which is far more than you can possibly afford.

But is it really fair that your best friend,

who always does the generous thing,

ends up spending 20 pounds for a measly burger?

Narrator: So what's the real win here?

Well, it's complicated.

Do you prefer saving money,

a delicious dinner, or being fair to your friend?

Having been fleeced,

will she ever want to meet up again?

The key thing is that what you want can be scored.

And mathematicians like me give it a fancy name,

your expected utility.

Narrator: We express your preferences as values.

That capture just how much you instinctively want something

against the price.

And then factor in other stuff,

like risk, in this case that your dear friend

might ditch you for busting her budget.

Looks like steak pipped friendship this time.

So there you go.

If you can figure out everyone's preferences,

and you know what you want,

then the key question becomes at the least cost to yourself

and without having any control over other people's actions,

how do you get what you want?

Well, thankfully mathematics

can help you find a winning strategy too.

Narrator: Whatever decisions we make, having a good strategy

means the difference between knowing what you want

and getting it.

It was the mid-20th century maths genius, John von Neumann,

who more than anyone else

turned our winning instincts into a science.

Von Neumann established a completely new field of study

called game theory,

which was concerned with the mathematics

of both cooperation and of conflict,

how to avoid losing,

and more importantly, how to win.

His efforts culminated in this here,

a 'Theory of Games and Economic Behaviour'.

641 pages packed to the brim with formulas

which was once described

as one of the most influential

and least read books of the last century.

Narrator: Written with the economist Oskar Morganstern

and published in 1944,

it proved how we can all get ahead,

when one party's loss is the other's gain.

It's not for the mathematically faint hearted,

but at the core of the book

is a strategic principle

that's surprisingly intuitive and easily explained,

with some cold hard cash.

So you and me are here

and we're gonna have a go on those slot machines.

And I've got a nice bag or 2p coins

that you and I are going to share.

Now the polite way to do this

is just to let you help yourself,

after all, I trust you to play fair.

Narrator: But actually, I really shouldn't.

Von Neumann assumes, rightly so,

that we both want as many coins as we can get.

So what should I do?

Well, I should split this into two piles as evenly as possible,

and then let you decide which half you want.

Now given that you are watching me like a hawk,

the only way that I can guarantee

I don't lose out to you

is by me splitting, and you choosing.

Narrator: I don't get as many 2ps as I might like,

but I win by minimising

the maximum amount of fun at the fair

that I can lose to you.

This is known as the minmax theory

and as strategies go,

you can apply it to pretty much anything.

So if you've got two kids that are fighting over toys,

just get one of them to make two piles

and the other to pick which pile they prefer.

Or if you've got boring household chores.

You write two lists,

and your partner chooses which list.

It sounds pretty simple,

but you have to remember that your split

will take into account your preferences.

So you get to decide

if you think the utility of a huge pile of ironing

and doing all of the hoovering,

is equivalent to the utility unblocking the loo

and sorting out all of the bins.

Now strangely,

von Neumann didn't get into that particular conundrum

in his book,

but his proof that you can always minimise the losses

and maximise the gains,

while taking into account the preferences

of two warring parties, was hugely influential.

Narrator: Such an analytical approach to winning

gripped people's imagination.

And crucially, von Neumann took inspiration

from one rather unpredictable game.

Von Neumann was an exceptional mathematician

and, perhaps because of its strategic complexity,

he was particularly interested in poker.

He said that real life is about bluffing,

about little tactics of deception,

about asking yourself

what does the other man think I mean to do.

And that is what games are about in my theory.

Narrator: When it comes to winning big at poker,

there's one woman you need to know.

Man: Wow, this is bold.

A four bet to 4,100. Sick move.

Narrator: Liv Boeree is the European

top ranking female poker player.

Man: Really strong play by Liv Boeree,

she's clearly been eating her vitamins.

Vitamin B for bluff.

Narrator: I'm meeting Liv to find out how poker strategy

might help us get more of what we want in life.

These days the very best players

are very analytically-minded folks

who are comfortable working with maths

to sort of really get a solid understanding

of the theory behind the game.

And then the psychology is,

I like to think of it as the cherry on top.

OK, let's talk about the basics then,

what calculations are you making?

If I'm gonna bet chips,

if it's 30% of the time gonna be the best hand

and 70% of the time gonna be the worst,

well then I can multiply those numbers

against the chips that are involved

and that will be my expected value from a situation.

And that applies in many real life situations too.

Say I'm like running late for a flight,

and I have two options -

I can either go to the airport and try and make my flight

but run the risk

of then missing it

and losing the value of the flight

and having to buy a new one,

or I could stay home and do the sort of the safer bet

and call and pay the change fee.

Thinking rationally and quantifying things

is the very first step to thinking strategically.

Exactly, yeah.

It's very hard to build strategies

if you don't have a numerical idea

of the value of the outcomes of the different strategies.

Narrator: By evaluating both the chances

of something happening,

and the outcome when it does,

you have a better view of your best options.

But at this level, everyone is just as calculating.

To beat the optimal strategy,

you have to find an edge.

There's something that's called 'game theory optimal'

where, if you're playing this style,

then it means that you're unexploitable basically.

The best case that an opponent can do to counter it

is to also play game theory optimal, therefore,

you just sort of reach the same very high standard of play

and you're trying to not deviate from it at all.

And that's where sort of the more like creativity

and, I guess, the artistic side of the game comes in

where you can do these deviations from the optimal play

to exploit your opponent's weaknesses.

But they could be doing that to you as well.

Exactly.

So you need to find a way

to be as unpredictable as possible.

Narrator: Von Neumann's maths

proves that poker players must bluff, unpredictably,

to avoid exploitation by a savvy opponent.

It's an essential strategy,

and it can be applied elsewhere.

You know, if you're in a business negotiation,

what's the minimum amount you'll take?

There's a great opportunity to bluff

and give a high number,

because you're giving yourself the option for them

to pay you that high number.

Narrator: It might seem obvious,

but bluffing like this

is exactly what gives you the edge over others,

particularly if their loss is your gain.

Anything that's a competition,

then to make yourself unexploitable

will just put you at a huge advantage.

Narrator: So quantify everything folks,

and don't make yourself too easy to read.

In win-lose games,

your carefully calculated strategies

can only get you what you want

if your opponents are in the dark.

But what if you're involved in a conflict

where everyone could lose?

During the second half of the 20th century,

the biggest problem that game theorists had to contend with

was the Cold War.

The US and the Soviet Union

were facing off against each other

and, just as in poker, every strategy,

every move and counter-move, had to be analysed.

Except this time,

the stakes could not have been any higher.

Narrator: As an ally to the US,

Britain had to prepare for the worst.

In 1961, a top-secret facility

was set up here in rural Worcestershire.

Regional Seat of Government 9.

It's one of a network of bunkers,

from which the British Government

would have operated in the event of a Nuclear War.

The moment that the second world war ended

with such a devastating show of nuclear force,

the talk in the West began to focus

on trying to prevent a military face off

that would mean that nuclear bunkers like this one

would become a necessity.

Now the strategy that was on the table at the time

was referred to, somewhat euphemistically,

as preventative war.

The idea being that the Americans would launch

an unprovoked attack on the Soviet Union

before they had the chance to acquire the bomb.

Now yes, that would mean a quick hot war,

but it would at least avoid

a slow, expensive and far more dangerous Cold one.

Narrator: Preventative war

is an argument still used today, over North Korea,

and at the time,

it's supporters included Winston Churchill

and von Neumann himself.

In 1950, von Neumann remarked,

with the Russians

it's not a question of whether but of when.

If you say, "Why not bomb them tomorrow",

I say, "Why not today?"

And if you say, "Today at 5:00",

I say, "Why not 1:00"

You can see where this kind of reasoning

ends and it is perfectly rational.

If someone has to win,

better that it be us.

Narrator: Despite the impeccable logic,

America didn't attack Russia.

And then it was too late, because Russia got the bomb too.

By 1953 there was no outcome

in which only one side could win.

This demanded a new strategy,

something which became known as Mutual Assured Destruction,

or MAD for short.

Basically, the threat of you

using massively destructive weapons on your enemy

prevents your enemy from using those same weapons on you.

Once everybody is armed,

nobody has an incentive

to either initiate a conflict or to disarm.

And so nuclear war was avoided,

but places like this and a hugely expensive,

vast global nuclear arsenal

was the result.

Narrator: Compared to von Neumann's games,

in which one person's loss is the other's gain,

mutually assured destruction, strangely,

is something we come across far more, in real life.

Because most conflicts, whether at work,

with friends or family,

have the potential to end up in a stalemate.

So often, we choose strategies that mean no one wins.

To explain why,

I'd like to begin with a rather unusual detective story.

I'm looking at the Instagram page

of the rapper Ludacris.

Narrator: In 2015

he shared this picture with his millions of followers.

It had originally been posted on the Facebook page

of the police department, in Franklin County, Kentucky.

And it reads -

"Attention Drug Dealers.

"We offer a free service

"to help you eliminate your drug competition."

And then under a quite large marijuana leaf

there are a series of sections

where dealers can identify their competitors.

Narrator: You can fill out who your competition is,

where they live, their phone numbers,

even their hours of operation.

It might seem like a gimmick,

but the fact is Franklin County PD

were onto something.

I think I need to find out a bit more about this,

so I'm gonna call the Sheriff.

[ringing tone]

Hello, Sherriff.

Hi, Hannah. How are you?

I'm good, thank you.

Why would a dealer call in

and tip off one of their competitors?

Obviously if they eliminate it,

the more they get, the more business they do,

the more money, the more potential earnings

that they have, that they'll make.

And, if you get rid of your competition,

you're the only game in town.

Especially by having law enforcement do it.

This has really worked for you then as a tactic,

getting the criminals to do the dirty on each other.

Yes.

It's something that was very simple to do

and at the end of the day,

if we've got drug dealers turning in drug dealers,

that's a win.

Narrator: Police - one, drug dealers - nil.

Well, this was obviously a pretty good score

for Sherriff Melton.

Because what he did was force the local drug dealers

into the most famous conundrum in the history of winning.

It's called, appropriately enough,

the prisoner's dilemma,

and it demonstrates very clearly

the dangers of falling into a lose-lose situation

when acting in your own best interests.

Narrator: Think of it like this,

Imagine Sherriff Melton

has chucked a couple of shady looking characters

from his local beat into jail.

He's got evidence to charge them with possession

but can only get them for dealing

if they rat each other out.

So he puts them in two separate cells

and gives them both his clever flier.

Our suspects must now consider

whether they should both keep their traps shut

and only go away for one year each for possession,

both rat the other out for dealing,

and each get a three year sentence,

or hope that they alone grass the other up,

getting off scot free,

while their competition gets a whopping five years,

otherwise known as the sucker's payoff.

[laughter]

So what to do?

Well, this option is the best.

But there's a risk it could quickly turn sour

if one person decides to basically betray the other.

Good ol' Sherriff Melton knows these two are toe-rags

and they know it too,

so to avoid being screwed over,

the only stable solution for them is this.

They both must implicate the other.

A win for Sherriff Melton,

but lose-lose for them.

This unhappy scenario is called the Nash Equilibrium.

It's a beautifully simple proof,

that was published in 1950 by the mathematician John Nash,

when he was still in his early 20s.

It won him a Nobel Prize,

and it transformed the analysis of winning.

What Nash proved was that in a situation

with several possible outcomes like this one,

where people either can't

or won't cooperate with each other,

there is always a strategy which you and everyone else

is best off opting for.

Now in the case of the prisoner's dilemma,

paradoxically that strategy ends up with lose-lose.

Everybody wants to win by ratting out their competition,

and everyone wants to avoid the sucker's payoff.

And as a result, everyone ends up going to jail.

Narrator: Being uncooperative

can cost you more than you bargained for.

The reason Nash's proof matters so much

is because these kind of dilemmas

constantly appear in real life,

because of the way our individual interests

often clash with those of others and of society.

Whether you are a drug dealer

or just out for dinner with your mates,

no one wants to be the sucker, right?

Narrator: I remember the day I was arrested

and I was locked up for 48 hours.

I remember thinking,

"Oh, this is what happens."

Narrator: If ever there was an example

of Nash's theory in action,

it's in the controversial world of professional cycling.

The global hero at the time was Lance Armstrong.

We were really good friends.

I remember him saying, "I got caught with my hand

"in the cookie jar."

I knew what Lance was doing,

it was like, hang on a second.

Narrator: David is one of the highest profile riders

to talk candidly

about the use of performance enhancing drugs within cycling.

Tell me about the first time that you realised

that cycling, perhaps, wasn't squeaky clean.

In my very first pro race in February 1997,

it was when my room-mate was offered a cortisone pill,

they all carried around little medical bags.

It was omnipresent.

It was white noise is what I've always described it as.

Narrator: For four years, David trained and raced clean,

but the pressure to remain competitive took its toll.

Eventually, despite your initial resistance,

you did decide to give in.

Yeah, I think that is the term, I gave in.

I didn't decide to join them.

I gave in and thought,

"Well, I can't fight this any more."

I was an ethical person,

but over time I just went chtt-chtt-chtt, chipped away.

- It wears you down.

Well, it just, the environment you're in wears you down.

You can put a good apple in a barrel of bad apples,

it's always going to turn bad.

Narrator: It's a classic prisoner's dilemma.

In professional cycling,

riders compete to win.

If doping makes winning more likely,

then abiding by the rules risks the sucker's payoff.

And so the rational thing to do is cheat

because a faster field, and a doping arms race,

has become the new norm.

This dilemma unites all competitive sport,

though it's a lose-lose scenario if everyone cheats,

nonetheless for individuals,

cheating can give you the edge

if you can get away with it.

The fundamental reason I was there

was because I wanted to win, I was very ambitious.

If the goals you want to achieve

are being achieved by the people who are cheating,

why don't I do it?

Narrator: David was the reigning world time-trial champion

when he was caught in 2004,

receiving a two year ban.

But after his punishment,

he returned to racing clean.

Reporter: David Millar, comes up,

hits the line, best time 31:15,

Millar is back.

[cheering]

Every time I won from then on in,

it was to prove a point, that it's possible to win clean.

- And you're appealing because you are clean.

- Because we are clean.

It actually became a valuable asset

to be clean and win races.

It goes back to that whole barrel of apples,

make sure it's a barrel of good apples

with one bad apple, that's easier to control.

These guys will never have to encounter it,

because we have an anti-doping culture

in professional cycling now.

Narrator: David's experience illustrates the profound tension

between individual drive to succeed,

and the greater good.

Our winning instincts can be both our greatest asset

and deeply destructive.

This is something that's relevant to all of us.

If you think about it,

how many times have you been in a situation

where you didn't want to upset the balance of things

for fear that you might end up missing out?

Maybe you have had a job

where you ended up staying later and later at work

just because everybody else was doing it,

and you didn't want to look like you were lazy.

Or maybe you have failed to call someone out

for a racist or a sexist comment,

just because you didn't want to look bad,

you didn't want to make the fuss.

Or maybe you have waited and waited

to tell someone that you love them,

just because if you said it first

and it wasn't reciprocated,

you'd end up feeling heartbroken.

Now all of these situations

are real life examples of Nash Equilibria.

Narrator: Win-wins, it turns out,

are often really hard to achieve.

And we can see the consequences

of our failure to cooperate everywhere.

In many situations in life,

egotistical behaviour

is not only morally problematic

but it is also strategically unwise.

I think a nice domestic example is washing dishes,

no-one loves it, OK.

It is a little bit annoying, you know,

and we all know that it's better for someone else to do it.

But if you are living in a shared house,

the problem begins when all the players

decide to adopt my strategy

and then no one is washes dishes,

the outcome is a tower of dirty plates

and it is not good.

When you are taking into account only your personal good,

and all your thinking is self-centred,

and you don't care at all about other players,

the result may be a total disaster.

Narrator: It's so easy to disregard

the small impact we might make,

just by ditching stuff for someone else to deal with.

But many small acts of selfishness

can have huge consequences.

It's a phenomenon known as The Tragedy of the Commons.

For example the damage to the atmosphere,

the destruction of ocean eco-systems.

Rainforest logging,

these issues are far more important

and it is really hard to tackle with them

even with rules and regulations.

Narrator: Arguably, the challenge for government

is to create rules that align

the interests of individuals and society

to find those win-wins.

But like the rest of us,

our leaders have their own

political and economic goals to pursue

meaning there will always be the temptation

for some to put their own short-term interests first.

[indistinctive chattering]

So in the real conflicts we all face,

can we ever justify being uncooperative?

Definitely, I'd argue, on occasion.

Because some people really don't know

what's good for them.

[children yelling]

I'd like to suggest we take

a potentially very unstable situation.

Taking two small argumentative children on holiday

to demonstrate some strategies that can ensure you win,

in a domestic stand-off.

[crying and yelling]

The first thing absolutely not to do

is to make a non-credible threat.

[tyres screeching]

Right, that's it!

Holiday's cancelled.

Turning the car around! We're going home!

Narrator: The kids quickly work out that you won't do this

as it harms you just as much as them.

Everybody wants a holiday.

So try a far more credible threat instead.

If you don't shut up,

we're gonna be spending the first day of the holiday

visiting an art gallery.

As long as they know you really like art galleries,

and you know they really hate them,

this one is a much better strategy.

Narrator: Even better, try a grand gesture,

called pre-commitment.

If one of you starts arguing again,

you're gonna go to bed at 6:00 all week,

and the other one can stay up as late as they like.

This one is quite a serious pre-commitment,

because you are risking not being able

to pack them off to bed like normal

but you'll just have to hope

that the prospect of them missing out

is enough for them to be smart, and stay quiet.

Narrator: In order to get what you want,

any adversary has to believe

you have the credibility and commitment

to go through with your threats.

But in the end,

no matter how winning your tactics,

there's one thing

that's incredibly difficult to deal with.

[children yelling] It's not fair!

Narrator: In any kind of interaction

our sense of what is and isn't fair

is incredibly powerful.

And in some circumstances,

it can actually make us deliberately lose.

To explore this apparently quite irrational way

of getting what we want,

Haim and I are going to play something called

the Ultimatum Game,

and the rules are very simple.

Two players, one is called the proposer

and the other one is called the responder.

The proposer gets a sum of money,

for example, 100 pounds.

Is that what you've got in there?

Yes, yes, yes. And the proposer have to decide

how to split this money

and the responder must decide whether to accept or reject.

If the responder rejects the split,

both players will end up with nothing.

It's a one-shot game, take it or leave it offer.

OK, well the fairest thing to do obviously to say is 50-50.

50-50, of course.

I could get an extra ten pounds by saying 60-40.

Easily, I think.

However I decide,

I mean I do genuinely get some of the money?

Yes, yes, yes, yes, yes. Real money, a real game.

Everything is real.

Narrator: Now to make some offers

to a series of unsuspecting volunteers.

I think I'm going to split it 70-30.

- I get the 70. - You get the 70.

Yes.

Well, obviously it's really unfair.

- But I'm going to accept it.

- But you have to decide. - Yeah, I'm gonna accept it.

You accept, OK. 30 pounds.

I'm going to check it.

No, don't check it, I am a mathematician.

- Thank you. - Thank you.

Narrator: So unfair offer number one works in my favour.

What is your decision?

OK, I'm going to go for 80 pounds to me,

and 20 pounds to you.

Yes or no, it's a take it or leave it offer.

- No, leave it. - No, leave it.

But hang on, you came here with nothing.

I did, but I feel like if you were like 50 pounds for you

and 50 pounds for me, I'd be fine with that,

I would have said deal.

We both came here with nothing,

so we both should have left with something

and an equal amount would have been better

than an unequal amount.

- Wow. - OK.

You see, it contradicts all the economical predictions. Yes?

Economics say one is better than none,

20 is for sure better than none.

Yeah.

Narrator: Economics says Said here should accept,

but I'm denied.

Next...

- Hi. - Hi.

Hello.

I quite like money,

so 90 pounds to me,

and ten pounds to you.

Um...

You know what, psht, why not?

I'll take 10 pounds.

You have 10 pounds, it is yours.

Thank you very much.

Hannah, you are now such a rich person.

Thank you very much.

Are you happy with your decision?

- It's pretty unfair, but.. - Pretty unfair, eh?

I'm a realist

and I like ten pounds at least in my pocket,

so I'm at least ten pounds richer so...

- So ten is better than none. - Yeah.

Narrator: A man after my own logical heart.

After three offers, I've bagged 160 pounds

of a possible 240 pounds.

So why did I not clean up?

The 20-80 split,

not taking 20 pounds seems bonkers to me.

You know that 20,

it is approximate the world average of the split

that people refuse to take.

People seem to show an unwillingness

to accept unfairness and they are prepared to pay...

- Even 80-20? - Yes.

I mean, they're basically being irrational, right?

People usually behave rationally from their point of view.

So it is really hard to define what it rational,

what it not.

For example Said, yes, he paid 20 pounds,

but to teach you a lesson,

20 pounds, it seems to me a low price,

you see, nothing almost.

Yeah, well.

It was an expensive lesson for me as well.

For you. Yes. But not for him.

Narrator: It might seem like an irrational way

to get what we want,

but what we're looking at here is the long game.

The act of sacrificing a small win,

to punish someone,

means they may well be less selfish with us

and others, in the future.

It's a perfectly rational way

to secure greater collective success.

But most creatures on earth aren't rational.

So why do we see co-operative, even altruistic behaviour,

in the animal kingdom,

that seems to benefit others more than the individual?

Surely this contradicts the theory of evolution,

based as it is on the struggle for life

and the survival of the fittest.

When I learned about evolution at school,

I was under the impression

that it was all about competition,

that every animal was necessarily out for itself,

and the fitter you are,

the more likely you are to win fights for mates,

for food and for territory.

If you can ace those conflicts,

the more likely you are to pass on your genes

and win at the game of life.

It has been said that nothing in biology

makes sense except in the light of evolution.

And evolution has been based on conflict.

It is a struggle for existence.

In animal behaviour,

there exist many examples

where animals fight within a species,

but where they fight according almost to rules,

where they seem to restrain themselves

and don't escalate the conflict too much.

Narrator: You could try to explain

individuals avoiding violence

as being for the benefit of the group,

but that's not quite how evolution works.

If there is a single individual ready to escalate the conflict

and all others are going to run away

when they see that things become serious

then this individual will win everything,

will have many offsprings,

the offsprings will win this trait

of escalating a conflict

and this trait will become more and more frequent.

Narrator: In this scenario,

aggressive behaviour will always win out,

so there has to be an alternative explanation.

It only began to emerge in the early 1970s,

when British biologist John Maynard Smith

was given a manuscript to review

written by an unknown American called George Price.

Now Price wasn't a mathematician,

or a biologist, or a game theorist,

but he had read von Neumann,

and he'd written about Cold War games

and the uses of deterrence.

His paper, titled

'Antlers, Intraspecific Combat, and Altruism',

suggested that things like giant deer antlers

weren't actually for maiming your rivals at all.

Instead they were clever strategic accessories

that would help you limit conflict

and avoid the destructive effects of fighting.

Just like nuclear missiles,

antlers are the kind of weapon

that you could parade in front of your enemy,

hopefully without ever having to actually use them.

Narrator: Maynard Smith was struck by this,

and together with Price created a simple game

to explore how such 'limited war' strategies

could evolve.

And he called it the 'hawk-dove' game.

Narrator: Picture an imaginary species of bird

that only has two inherited behavioural strategies.

One is aggressive or 'Hawkish'

And the other more cooperative or 'Doveish'.

If two hawks clash over something like food,

their strategy means total war.

They'll fight, risking injury

and no guarantee of food either.

Now if a hawk and dove meet,

the dove initially stands up for itself,

but then scarpers.

Finally if doves meet, they'll share.

In each interaction,

both birds receive a score.

And if these are added up over time,

it reveals which behaviours are most likely

to benefit individuals

and so survive down the generations.

On the face of it

if everyone was displaying dove-like behaviour,

it looks like it could work,

as well we being generally nice for everyone.

But unfortunately that's unstable,

because just one meany hawk could come along

and immediately have the upper hand on everybody.

And if that hawkish behaviour really took off,

that too would be unstable,

because of the constant risk, and cost of violence.

Now, what the maths shows

is that a stable population is possible

but only if you have one third hawks

and two thirds doves.

Now those exact numbers might change slightly

if you tweak the payoffs,

but the key point here

is that this was mathematical proof

that there was a strategic advantage

to avoiding conflict.

Narrator: Evolution, it turned out,

is not simply a winner-takes-all kind of game.

And so scientists took

to this new evolutionary form of game theory.

The reason?

To find the ultimate

long-term winning strategy for us all.

It was an ingenious American political scientist,

called Robert Axelrod,

who around 1980 took the next big step.

Axelrod invited economists,

mathematicians, political scientists,

psychologists and sociologists,

all of whom had written theoretical papers

on cooperation and the prisoner's dilemma,

to compete in a computer tournament.

Narrator: The challenge was to design a computer programme

that would play the best combination

of attacking and more cooperative behaviour.

It was a bold move

considering the golden age

of popular computer games and coding

was still in its infancy.

Researchers from around the world

mailed in their computer programmes by post.

It was all to see which of their electronic beasts,

some of which were a lot more cooperative than others,

would emerge the winner.

Narrator: 14 programmes were to play 200 rounds

of the prisoner's dilemma against themselves

and one another.

As you'd expect,

cooperating with your opponent scores well.

But you could get a much higher payoff

by attacking a co-operator all of the time.

But attack an attacker,

and your score will suffer.

And so the tournament ran,

with some players doing better than others.

One strategy for example, was nicknamed The Grudger.

It would cooperate until it was attacked,

at which point it would get the hump

and then never cooperate again for the rest of the game.

Narrator: After competing against everyone else,

The Grudger crawled in in 7th place.

The surprise winner, with 504 points,

was written in just four lines of code

and was easily the simplest programme

that had been submitted.

It was called Tit for Tat.

It would start off by cooperating

and then would just copy whatever the opponent did

in the previous round.

So if the opponent either attacked or cooperated,

Tit for Tat would respond in kind.

Narrator: Tit for Tat's behaviour

over the course of the competition

is basically you scratch my back,

I'll scratch yours.

So was this the winning strategy everyone was looking for?

Well, no.

Because unlike in real life,

these computer programmes, including Tit for Tat,

could play endlessly

without ever making mistakes.

Imagine I decided to use Tit for Tat as my new strategy

for winning at life.

So I would cooperate by default, lovely,

and only retaliate if someone was really mean to me,

just to teach them a lesson.

But what if, idiotically,

I sort of accidentally was a bit mean to someone.

Say, I just bumped into them...

Oh, sorry.

Narrator: If they're also playing Tit for Tat,

they'll have to shove me back,

formally known as defecting.

And then I'd have to do the same, as would he.

We'll defect forever.

Hm, not great, is it?

But some scientists weren't quite ready

to give up on tit for tat just yet.

Karl Sigmund and his student Martin Nowak

started experimenting

with a new kind of evolutionary tournament

but this time, as in the natural world,

competing strategies could evolve and make mistakes.

Narrator: Using computer simulations,

they watched strategies like tit for tat emerge,

and compete, over thousands of generations.

After the first 50 or 100 rounds,

it seemed as if everyone was a defector.

Everyone? Not quite.

There was one little minority

playing something like tit for tat,

and this little minority very slowly increased

and became more and more frequent

and was actually defeating the defectors.

Narrator: The key was to let natural selection

find the winning strategy.

If you wait still longer then you will see

that another more generous form of tit for tat

is going to evolve and to take over.

And here it comes.

Generous tit for tat.

Narrator: This strategy

will always cooperate first.

Ooh, sorry.

Narrator: But when facing defection...

..around one out of every three times,

it'll just ignore it and cooperate regardless.

Of all the possible strategies,

and despite its forgiving ways,

generous tit for tat consistently came out on top.

For me it is still

one of the fondest remembrances

of my scientific life.

There was no master programme behind it,

no design for forgiveness, so to speak.

It came out all by itself.

A purely mathematical simulation

had revealed that winning strategies,

in the long run,

tend to be generous, hopeful and forgiving.

Now this basic moral code just emerged,

perhaps you could even take this as proof

of the existence and advantage of goodness.

Narrator: So why, then, don't we live in a wonderful,

generous and forgiving utopia?

The simulations pointed to an answer.

Over generations of stability,

the main strategy becomes total cooperation.

But this is fragile,

because hawkish defectors can rapidly take over

and do their worst.

And yet slowly,

thanks to strategies like tit for tat,

cooperation emerges again and again.

Despite its fragility, there is hope,

because ultimately, cooperation can't be suppressed.

Thanks to things like altruism, kindness and reciprocity,

it re-emerges time after time.

And these aren't just codes

that are divined by priests or philosophers,

they have pure mathematics

and evolution itself behind them.

Narrator: So where does that leave you and me?

Well, I want you to try something out,

starting tonight.

Now this could work for any kind of relationship,

but let's imagine that it's your partner.

What I want you to do is to co-operate,

but copy their previous move.

So if they come home one day with a big bunch of flowers,

you should get to work on your own romantic gesture.

But if they come home one night

much drunker and later than they promised,

you get to do something equivalent.

But every now and then,

you should forgive one of their slip ups,

because nobody's perfect

and you're gonna mess up too, at some point.

So, there you have it.

Strategies for a happier life and a better world,

all thanks to maths.

I call that a win.

Captioned by Ai-Media ai-media.tv