Board Game Science

This BBC podcast is supported by ads outside the UK.

Ready to buy a car, a home, or just want to take control of your money?

Your FICO score matters, and 90% of top lenders use it to make decisions.

Check your FICO score for free today without hurting your credit score.

Visit myfICO.com/slash free or download the MyFICO app today.

My FICO gives you the score lenders use most, plus credit reports and real-time alerts to help keep you on top of your credit.

Visit myfico.com slash free and take the mystery out of your FICO score.

So what do this animal

and this animal

and this animal

have in common?

They all live on an organic valley farm.

Organic valley dairy comes from small organic family farms that protect the land and the plants and animals that live on it from toxic pesticides, which leads to a thriving ecosystem and and delicious, nutritious milk and cheese.

Learn more at OV.coop and taste the difference.

BBC Sounds, music, radio, podcasts.

Well done for downloading this podcast of BBC Inside Science, which first aired on Boxing Day.

Seasonal cheers from the Inside Science team, and I hope you've settled in for the most important bit of this holiday.

Yes, that week between Christmas and New Year where you lose track of time, potter about eating leftovers and hang out with family and friends.

We've reached peak board game season.

And in honour of that, Inside Science is devoting the whole show to the subject of games.

Coming up over the next half hour.

The oldest board game that still has its instructions, and the man who found them.

We discover how games shape us and why we love them.

Game connoisseur and author Tim Clare shares our complex relationship with simple dice, and mathematician Marcus de Sotoy explains the unfinished geometry of a common card game.

And because we thought we should gamify this show, let me introduce you to my compadre and opponent, producer Florian.

Hi, Marnie.

What have you got in store for us today?

Well, in addition to uncovering the science behind games, we will actually play some games ourselves, of course.

And we will see which one of us will take home the win at the end.

And the prizes?

Bragging rights?

Yeah, okay.

For the rest of eternity.

I'll take that.

I do love pointless competition.

So where do we start?

The first game we're going to play is called the Royal Game of Ur, one of the most ancient board games we know of from more than 4,500 years ago.

And it's set up right in front of us.

Oakie Doke.

We've got a bunch of squares with beautiful tiles on them.

And there's your side, my side, and there's a bridge between them.

How does this work?

Yeah, so you roll dice and you have seven pieces that you need to kind of enter on your side, walk across, get to that middle bit where we can actually knock each other out.

We're actually at war with each other.

And then you have to get out on the other side, which is similar to sort of racing games that we have nowadays, something like Backgammon.

Well,

let the games begin.

One, two.

So I put a counter on here.

Yeah.

One, two.

One, two, you enter it.

Give me the dice.

Over to you.

All right.

Perfect.

And that's two as well.

Now, earlier, I spoke to Irving Finkel, curator at the British Museum and philologist, so someone who studies ancient languages.

And as producer Florian and I keep playing this game, Irving is going to tell the story of the rediscovery of this ancient game.

One, two.

This board was made in about 2600 BC

and it comes from southern Iraq, from the city Ur, U-R, it's spelt in English, where Sir Leonard Willie in the 1920s found graves of the royal family of the dynasty of Ur and when they were buried, the princess and the queen and other members of the court, when they were buried, they took with them this board game and the bits to play it because obviously they enjoyed it during their lifetimes and expected in the world to come they would want to carry on doing it.

So this was a spectacular discovery because the board has twenty squares and you have seven pieces and you have to throw these dice, they're tetrahedrons, not like modern dice.

So if you have a go, you get a score because two of the corners have white and two of them don't.

So if you have a white a white upturned corner, you get a point.

Now when it was originally excavated, I imagine imagine much in the same way as in in my family we have a wall in the basement with a bunch of games and quite a few of them don't have their instructions their original instructions in the box anymore sadly.

I believe something similar happened with this.

Well this is true.

This game probably began in India in about 4000 BC.

In 2600 BC

we find it in Iraq.

It came with the dice, it came with the pieces, and the boards were complete.

And so I, being a naive and youthful curator, thought, oh, I can work something marvelous out like this.

I know what makes a good game and what doesn't make a good game.

So, I just did that.

I made up the rules: four or five.

You start here, you go around there, you get knocked off here, you have to start again.

There's a magic square, you have to, if you land on there, you can have another throne, and so forth.

All the components of a normal race game.

But the archaeological thing is more interesting because A, we know that for about 2,000 years, this same 20 square grid turns up in all the countries of the Middle East from Pakistan to Crete, Syria, Jordan, Lebanon, Israel, Turkey, they all come up archaeologically with boards and it ran without rule books.

People learned from one another and it took root like a plant watered by attention and became a strong thing wherever it landed.

That's part one.

Part two is in the British Museum a meddlesome curator found a cuneiform inscription written in the second century BC by an astronomer who was very well couched in mathematics and the study of the heavens.

So the game becomes something allegorical where the throws of the dice move the planets through the signs of the zodiac and the squares have a special meaning.

And he wrote it down on a tablet in cuneiform writing.

And the translation of it, which I wrestled with for about 18 years, came up with a game which more or less fits on a board like that.

From what you're saying, people writing about it subsequently attributed extra meaning to it.

They saw more dimension in it.

Because what you've got, the reconstructed thing which has been so successful, encapsulates the basic principles of a really good race game, that you can't control the dice, it's a matter of luck, but there's a bit of strategy.

Someone who plays

casting all of everything to the winds and playing flat out to be the winner will win, statistically.

A courageous player will defeat a timid player.

So this is an interesting matter, I think.

So the British Museum, which is home of many of the world's treasures, has a collection of tablets.

It presumably has more games than the Royal Game of Ur.

How did you join the two?

When I found this inscription in the collection, it's a long time since anybody had read it, I realised it had to concern a board game because it had the names of pieces, it had throws of dice, and the question was which game.

But in Mesopotamia, the Royal Game of Ur was the national game and also there weren't many alternatives.

So the rational thing to do was to see if it could be applied to this structure and it more or less does.

I think it's extraordinary that if we could time travel 4,600 years ago,

you could go back, take this board with you,

pop into a bar in Syria, Sure.

And just have a game with someone.

Sure, we have to beat them, of course.

We couldn't have them beating us.

No, no, yeah.

We have to be

ferociously good at it.

You see, the thing is, this game was played all over the ancient world.

For example, Tutankhamun played this game.

They found it in his grave, King of Egypt.

Same sort of board, same setup.

Yes, different decorations, but the same kind of setup with pieces and dice.

And they're found in all the countries of the Middle East.

It's an extraordinary thing.

and it's significant because

board games spread by persons,

not by armies and governments.

And a merchant who goes from one place to another, goes for a drink one night, sees something being played in the pub, watches it, and that looks interesting.

Let's have a go.

And then, when they go home, they take it with them, and maybe slightly differently it's played, and all that kind of thing.

But there's a kind of stratum in society whereby board games spread unstoppably because there's a hunger in the world where people have leisure for a really gratifying board game.

It's a kind of universal thing, it's quite extraordinary.

Thank you to Irving Finkel at the British Museum.

There's something funny about playing a game and knowing that someone in a bar in ancient Mesopotamia experienced the same highs and lows.

Talking of which, you'll go, Florian.

As I do, when I'm hopefully going to take you up

to no.

Very nice.

One, two,

three.

I win.

I win.

One nil.

One nil to the chest.

Fine.

Thank you.

You lose with grace.

Florian, you play a lot of games, right?

How many have you got in your collection?

Yeah, and most of the time I don't lose.

I counted for the programme.

It depends on if you count expansions of games, but it's definitely definitely over 60, maybe more.

I love games too, although maybe slightly less than you.

And a good question to ask, and one that science often asks, is why?

Why do we love them?

Why do we play games so much?

Well, on the line, we've got neuroscientist Kelly Clancy, author of the recently published book, Playing with Reality.

which Kelly is about why humans like to play, right?

That's right, yeah.

We've been playing for our entire history and it's something that we use to learn about the world and about each other.

So it's this really deeply ingrained behavior that we've had basically as long as we've been human.

So humans aren't unique in playing.

Which other animals do it?

Yeah, a lot of mammals, even there's some evidence that like bees play, fish play, reptiles play.

And there's this interesting correlation between intelligence and play.

So more intelligent animals tend to play more.

Is there any evidence on whether animals play play their entire lifetime or do they just play when they're young?

Yeah, most animals play when they're young.

And, you know, they're probably building social bonds.

They're learning about the world.

They're practicing skills like hunting and wrestling and so on.

But humans have this kind of unique property.

It's called neotney.

It's the retention of juvenile characteristics into adulthood.

And we tend to play into adulthood.

And we retain a lot of our kind of childlike characteristics, like curiosity and friendliness.

And a lot of evolutionary biologists credit this as being essential for our huge success as a species because we're playful, because we're friendly, because we can use these tools to build our social bonds, we have these complex societies that has allowed us to build incredible technologies and so on.

So play is actually this really important skill that we carry throughout our lives.

So I think there's a different level of complexity though between something like a couple of dolphins playing with a ball and humans sitting around playing playing chess.

What is it that we get from board games?

Yeah, that's so true.

There's a big difference between animal play and human play.

Human play really brings things into the kind of mental realm, whereas a lot of animal play is more physical and learning about their bodies.

Human play is about learning about our minds and the minds of the people we are playing against.

In the medieval times, people believed chess was this almost, they called it like a mirror for a prince.

It was used to understand yourself better, understand your colleagues better.

It was a really important way of seeing yourself.

So we've established that there are games going back millennia.

Is there anything particular within a game that draws us to it?

So one really important aspect of games is just the uncertainty.

They're exposing us to uncertainty.

And that's actually something really compelling.

to the brain.

The whole MO of the brain is to understand the world, to build predictive models, to be able to kind of anticipate whatever is happening.

And if there's something in the world that the brain can't predict, that's really compelling.

It's like a red flag and the brain is like, okay, I need to learn more about that.

And so the uncertainty that's inherent in games, whether it's dice, which are kind of inherently random and uncertain, or the uncertainty of playing a game of chess and you don't know what move your opponent's going to make, that's all very compelling.

And what makes games fun?

You know, a game is no longer fun when it's...

when you kind of know what's going to happen.

Like kids like tic-tac-toe because they don't really haven't figured it out yet, but as an adult, you're like, okay, I know how tic-tac-toe works.

So the uncertainty is a lot of what makes games so compelling and fun

and what research has been done on the effect of uncertainty on our brains yeah there's a really interesting link between dopamine which is a neurotransmitter that's commonly thought of as being this kind of pleasure molecule but is really a learning signal and so dopamine gets particularly ramped up when a entity is kind of uncertain.

So for example, some researchers were recording from dopamine neurons and were giving the animals a reward, like just some juice.

And if the juice was always given, the animals had a kind of dopamine response.

But if the juice was only given 50% of the time, so it was kind of uncertain whether they were getting a reward, dopamine was ramping kind of crazily.

And it turns out that this uncertainty is actually really compelling and rewarding and giving us this kind of dopamine hit, which is exactly why gambling can be addictive for some people.

Right.

We have gaming to get on with.

So

Kelly Clancy, thank you so much for coming onto Inside Science and sharing this.

My pleasure.

Thanks for having me.

Thank you to Kelly Clancy.

This is BBC Inside Science.

I'm Marnie Chesterton, and this show is being recorded at my kitchen table where producer Florian and I are, like many of you at this time of year, ensconced in a battle of the board games as we unravel the science behind them.

So Florian, what have you lined up for us next?

Well as Kelly mentioned, uncertainty is important in our enjoyment of games, which is the very essential element when rolling dice.

Now there are many different multi-dice games that you play with.

The one that we have here is Yahtzee.

You may be familiar with it.

You roll five dice, you try to create certain combinations of numbers like full house or four of a kind.

Do you want to play?

Sure.

Let's give it a go.

So I get first turn two sixes, two twos.

I could go for the full house here.

I'm gonna keep the sixes I'm gonna keep the twos

and that means I have one die left to roll let me try again it's one how many rolls to get three in total so let me just just need a two or a six

not get it that means that's not good at all oh and Florence picked up the scorecard so I think I'm gonna write it down as two twos it gives me four points not very good

And as we keep rolling our dice, let's hear from author and passionate game player Tim Clare.

He recently published a new book called The Game Changers and is going to tell us why the randomness of dice rolls is so hard for us to comprehend.

If I asked you, can dice remember things, I suspect you'd answer no.

We know rationally they're just lumps of wood or plastic.

The outcome each time we roll is completely random.

But it turns out our brains at some deep intuitive level find that very hard to accept.

Let's imagine you're sitting around the table with your family or friends playing Monopoly.

You roll two dice and get a double, which means you get another go.

You roll again and again you roll a double.

You pick up the dice, roll a third time and it's another double.

Three doubles in a row means you go to jail for speeding.

If you've experienced this in real life, rolled three doubles in a row, that is, not been jailed for reckless driving, you'll know that when you roll that first double, it's no big deal.

But when you roll the second one, something in you snaps awake.

Two doubles in a row.

Ooh.

And when that third one hits, you're like, wow, what are the chances?

Well, calculating the exact odds is on the face of it rather trivial.

Your chance of rolling a double on a pair of six-sided dice is one in six.

Your chance of two doubles in a row is therefore one in thirty-six, and three in succession is one in two hundred and sixteen.

So the maths appears to be on our side here.

Rolling one double is nothing special.

Rolling two back-to-back is unusual.

And rolling three doubles is likely a once-a-game event.

In fact, significantly less than once-a-game.

The average monopoly game is 30 turns per competitor.

In a three-player game, you'd expect to see three consecutive doubles approximately once every 72 rounds.

So, when you roll the dice that third time, no wonder everyone holds their breath.

Hitting that last double is an extraordinarily unlikely event.

Except, no it's not, because as we all know, dice don't have memories.

When you roll for that third time your chance of a double is just one in six.

But for most of us it doesn't feel that way.

Either we feel like the dice can't possibly roll another double because what are the chances of three or we feel like they must because they're on a hot streak.

This disconnect between theory and intuition is sometimes known as the gambler's fallacy.

If we flip a coin and get four heads, it feels to us like we're owed tails, as if the coin is storing up luck and eventually it will course correct and all those tails will come flowing out.

Coin flips and dice rolls are independent events.

A completely fair die can roll sixes 100 times in a row and that is just as likely as any other sequence of numbers.

Between one and six, that is, rolling a 62 would be unusual I grant you.

Research has found that gamblers instinctively prefer slot machines with truly random outcomes versus those rigged to simulate our intuitive sense of what randomness looks like.

So-called negative autocorrelation, where a high-value result increases the likelihood that the next will be low-value and vice versa.

Paradoxically, non-random events feel random to us, in the sense of meaningless, empty of significance.

Actual randomness, by contrast, doesn't feel random at all.

It feels like a story.

Clumps of high or low results make dice feel lucky or unlucky.

The oracle is speaking to us.

This is the magic of dice.

Objects of pure mathematics, they somehow exist at a junction between the rational and the divine.

Our incredible, pattern-seeking brains, usually so good at finding signals in the noise of the everyday world, don't quite know what to do with them.

It's humbling in a way.

that two little plastic cubes are enough to bamboozle us.

It's also, I think, rather beautiful.

When we roll dice, it's a rare admission that much of life is out of our control.

Where will I end up next?

Who knows?

Let's ask the dice.

A happy place comes in many colors.

Whatever your color, bring happiness home with Certopro Painters.

Get started today at Certapro.com.

Each Certopro Painters business is independently owned and operated.

Contractor license and registration information is available at Certopro.com.

Suffs!

The new musical has made Tony award-winning history on Broadway.

We the man to be honest!

Winner, best score!

We demand to be seen!

Winner, best book!

We the man to be quality!

It's a theatrical masterpiece that's thrilling, inspiring, dazzlingly entertaining, and unquestionably the most emotionally stirring musical this season.

Suffs.

Playing the Orpheum Theater, October 22nd through November 9th.

Tickets at BroadwaySF.com.

Thank you, Tim Clare.

And we are almost at the end of asking the dice who should win this game of Yahtzee.

Producer Florian, how's it looking in your end?

I have 275 points.

I'm 176.

More than 100 more.

Aww.

Once more with sincerity.

Okay, so that one's to you, which means the next game, the last one, will decide it all.

What's going to to be the final showdown of this episode?

The final game will be

Double.

Oh, Double.

I know that one.

I've played.

I'm not bad.

This one has some very interesting mathematical quirks to it.

So, for this reason, we're calling up a mathematician, Marcus DeSotoy from the University of Oxford and author of the book, Around the World in 80 Games.

Marcus, are you with us?

Yes, I am.

Double is one of my favourites as well.

So looking forward to hearing how it goes.

So there will be Dobble enthusiasts listening to this around the UK and there will be people who aren't familiar with this game.

So can we describe Dobble to the latter group?

Yeah, it's wonderful.

It's a

tin full of circular cards and on each card are eight little icons from things like spiders, dragons, clowns, no entry signs.

And the way you play the game is you divide, in your case you'll divide the pack between the two of you.

And each time you play, you show one of your cards.

And the amazing thing about this set of cards is that whichever two cards you choose, there'll always be one icon which is on both of those cards.

And to win the other person's card, you've got to shout out before the other person what the icon is that is on both of those cards.

We could do a practice run now.

Are you ready?

Okay, yeah.

We've got our ready.

One, two, three, go.

Clock.

Very fast.

Wow.

You're good at this, Marnie.

How do you even create a deck like that?

There's maths involved here, right?

This is the kind of magic of it.

I mean, it's kind of remarkable.

You look at these cards, you think, surely there's going to be two cards which don't have anything in common.

And frankly, actually, when I play with my kids, I often think there's been a mistake on these two cards, but they're always very fast to say, no, look, it's got a clown on both.

So the amazing thing is there's a wonderful piece piece of mathematical geometry which makes this game work.

Marcus,

we're doing geometry on the radio.

What do you mean by geometry?

Most people think of that as triangles.

Well, I don't think that's too far from what I'm thinking about as well.

So, these cards are basically like points in this geometry.

And if you've got two points in a geometry, you can always draw a line between those two points.

Not if there are three points, then they may may not be in a line, but two points you can always draw a line.

So the lines in this geometry all have names, and the names are these little icons that are on the cards.

So there's the clown line, there's the dragon line, the spider line, and so the cards have all of the pictures of the names of the lines which go through that particular point.

So when you pull out two cards, you're actually identifying two points in the geometry, and then the icon which is on both of those cards is the name of the line which goes through that geometry.

Okay.

And if I picked two random cards, they would be two dots on this mental map.

And the line between them is, oh, look, it's a hand with feet and an eye.

Okay.

Exactly.

So that's the name, weirdly, of that line.

So the people who developed this game knew about this geometry and just turned it into this beautiful game.

But there's something rather unsatisfying about this tin because there are 57 lines in this geometry and 57 points.

Now, there are 57 little icons which are distributed among the cards.

But very frustratingly, there are only 55 cards in that tin, which I find, as a mathematician, deeply upsetting that they've missed two points in this geometry.

And I couldn't understand why they'd done this.

But then a friend of mine came up with an explanation.

How many cards are there in a normal pack of cards?

52.

So that's not 55 or 57.

No, but there are also two jokers

and an advertising card.

So actually, if you look in a pack of cards, there are always 55 cards.

52 that we play with, two jokers and an advertising card or sometimes the rules of bridge or something.

So actually, the machines which stamp out these cards are 5 by 11.

And when the Dobble team came and said, said, we've got this wonderful game with 57 cards, it seems like the manufacturer said, well, but our machines only punch out 55, so you've got to sacrifice two of your cards, namely two of the points in the geometry.

So hang on, do you have any idea what those two missing cards are?

That's the weird thing.

I know that there are two missing, but I've never got around to finding them.

So I would really love it if you could put out a call to your listeners and give give them like a Christmas challenge.

Could you set them the challenge of finding what are the two cards and the icons on those two cards that are missing?

And then we can all make those cards and put them in and make our games a beautiful, complete mathematical geometry rather than this kind of incomplete version they're selling at the moment.

That is a great idea, Marcus.

And we're definitely going to challenge our listeners with that one.

Thank you for joining us.

Oh, it's a pleasure.

So, Marcus DeSotoi there, leaving Radio 4 listeners with the best thing ever, a Christmas puzzle.

And if you want to work out the identity of the two missing double cards, and more importantly, all the eight objects on each one, then please, please do send us an email to insidescience at bbc.co.uk.

Now, we've almost come to the end of this episode, but there's the final double off.

I'm 1-0 up.

Florian?

Fine.

Fine.

What are we doing?

We'll do a slightly shorter version of the game, so we're just going to do it up to four.

You're already 1-0 up.

We're each going to reveal one card.

Yeah.

And then whoever's the first one to get it, we'll put it to the side and get that card.

Yep.

One.

One, two, three.

Cheese.

One, one.

Moon.

Oh, I'm coming back.

Okay, two, one.

I feel like I'm playing against a shark here.

You ready?

Yep.

Let's go.

I can't see.

Ladybug.

Ah.

2-2.

2-2.

Ready?

Glass?

No.

Bomb.

3-2 or something.

3-2.

Match point.

No, no, no.

I said it in first, though.

That counts, right?

3-3.

Alright.

It all comes down to this.

1, 2, 3.

Are you sure you're ready?

No.

Do it.

All right.

I think.

I think that was yours.

Just the power of words evaded you.

I know.

That means it's 2-1 to me.

So

high fives and some sort of trophy for me.

Congratulations, Brianny.

And cleaning up duties for you.

I think in the end we're all winners here because we had fun.

Yeah, we certainly did, but mainly I am the winner.

Bragging rights to me.

On that note, have a great rest of the year from me and producer Florian, whether you're playing games or not, and have an amazing New Year's Eve.

Bye!

You've been listening to BBC Inside Science with me, Marnie Chesterton.

The producer was Florian Bohr, and the show was made by BBC Wales and West.

To discover more fascinating science content, head to bbc.co.uk, search for BBC Inside Science, and follow the links to the Open University.

Don't let them down.

Unlock Elite Gaming Tech at Lenovo.com.

Dominate every match with next-level speed, seamless streaming, and performance that won't quit.

And push your gameplay beyond limits with Intel Core Ultra processors.

That's the power of Lenovo with Intel Inside.

Maximize your edge by shopping at Lenovo.com during their back-to-school sale.

That's Lenovo.com.

Lenovo, Lenovo.

A happy place comes in many colors.

Whatever your color, bring happiness home with CertaPro Painters.

Get started today at Certapro.com.

Each Certopro Painters business is independently owned and operated.

Contractor license and registration information is available at Certapro.com.