How to Win Every Game, with Marcus du Sautoy, Part One
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Welcome to Intelligence Squared, where great minds meet. I'm producer Mia Cirenti. On the show today, Marcus de Sautoy. Marcus is one of the country's best known science broadcasters.

He is Professor of Mathematics at Oxford University, where he holds the prestigious Simone New Chair for the Public Understanding of Science. He has presented numerous programmes on television and radio, including the internationally acclaimed BBC series The Story of Maths. His best-selling books include The Music of the Primes, The Number Mysteries and, most recently, Around the World in 80 Games.

Marcus joined us recently on stage at the Pleasance Theatre in London. In conversation with award-winning science broadcaster and mechanical engineer Dr. Shini Samara, he explored the maths and strategy behind the games we love and the tactics needed to master them all. This episode is coming to you in two parts. If you want to listen to the live recording in full and ad-free, why not consider becoming an Intelligent Squared Premium subscriber?

You can head to intelligencesquared.com forward slash membership to find out more or hit the IQ2 extra button on Apple. Now let's join our host, Dr. Shini Samara, with more. Before we start, when I was reading it, I just was so curious with every page how you came about writing something like this. It is so comprehensive.

Well, this is actually a rather private passion of mine for decades, which is collecting games wherever I travel in the world. I mean, like you, I do a lot of traveling for my science, going to conferences, rucking up in places that, you know, we don't share a language except for mathematics.

And one of the things I love to do is, well, also if I ask about the games that you play, I might get some insight into the culture, the people that I'm visiting. So for years I've been just privately bringing back more and more games from my travels. Were you always a traveller?

And you discovered games that way? Well, it was really weird because actually when I was younger, I always wanted... My mum had been in the Foreign Office and I had fantasised... I thought she was a spy, basically. And I had fantasised about joining the Foreign Office because I liked the sound of all the travelling and I watched James Bond movies and saw all these...

And so when I was a kid, I learned a lot of languages but was miserably bad at learning languages. And so I just found the only language I really could speak was mathematics, which is an incredible language. But, you know, everything makes sense. It doesn't have irregular verbs, which all these other languages did. So I got a bit disillusioned with the idea of traveling. And I thought, oh, well, mathematicians are just going to be sitting...

in their office doing long division to lots of decimal places. But, hey, that's... And I really was surprised to discover that actually being a scientist is a very international thing and involves a lot of travel. And so I found myself going to, you know, the early 90s. I went to conferences in Russia when all the political things were kicking off then. I do a lot of travelling to India. Were Tetris original?

Yeah, exactly. I can't believe it. Yeah, Tetris is a Russian game. But I've always been a big gamer. And so games, I do think, and it's one of the kind of theses of the book is, you know, tell me the game you play, I'll tell you who you are. It tells you a lot about somebody. So much so that, you know, I'd just come back from India and...

I discovered in India, we got invited to a wedding out there. And in India, they use games at the beginning of a wedding ceremony in order for the couple to start to get to know each other a little better. Because very often it's an arranged marriage. They don't know each other so well. And games are like a very safe space to sort of get to know who you're going to be spending the rest of your life with. It's the game that they play in the book.

Well, actually, it's a kind of variety of games. So quite a lot of some of the games in the book, but also just kind of weird games that didn't make it into the book. But it's interesting, you said, how did I write this book? Because there was a kind of interesting thing that happened in the writing of this book, which is, as a writer, what you often do is you come up with an idea. I thought, you know, this private passion, I quite like to share it now because I think it

had such interesting insights into the games around the world. And so authors very often write down on little cards sort of the ideas that they think they'll use when they write a book. So I wrote all of the games that I wanted to talk about, and I laid them down in my office trying to chart a kind of narrative through them all.

And I think I'd already had the kind of idea of maybe calling it around the world in 67 games, if that's how many cards I had. And then by some absolute miracle, there were exactly 80.

And I was like, OK, this has to be. And so that's why I called the book Around the World in 80 Games. And then I went back and reread the Phileas Fogg journey around the world, a Jules Verne story. And I'd read it as a kid, but I'd forgotten how important games are in that book, actually, because Phileas Fogg does not care about tourism at all. He cares about playing games, and his game of choice is Wist.

And so when they're arriving in India, and a wonderful new continent appearing on the horizon, and he doesn't look out the window at all because he's just about to win a grand slam at UIST, all 13 tricks. And for him, that's the exciting thing, not arriving in India.

And you do actually start with the Middle East and then India, and we end up in Europe at the end. Why did you decide to go that way around the world? Yeah, so I did think that using the journey that Phileas Fogg made was a kind of clever narrative approach

arc through the book because what I was very nervous of is it just being a list of games and that would not be interesting. So when I write nonfiction, I really try to write it like a novel. I want it to feel like there's a story behind the reason you're taking me this way. And so I thought a journey across land and across sea would be a clever way to do it. But yeah, I had some choices about which way to go.

The Middle East is a good place to start because that's where some of the very first games come from and the first mathematics. And I suppose one of the kind of messages of the book is how close games and mathematics are.

So it was really fascinating to see the first mathematics appears in Babylon and Egypt. They are starting to form civilizations which require mathematical tools to build and to tax people. And so you see the early calculations of pi, for example, appearing because areas of land might be circular arcs from the Nile cutting out strange shapes.

but also the first games. And so, actually, I bought a replica of one of the very first games, which is actually in the British Museum. You were going to be playing games at some point. Oh, yeah, absolutely. It's called the Royal Game of Orr. So this isn't actually the British Museum's version. This is a replica version I bought in the museum shop. But it's a really weird shape, for example. But this is an early form of racing game. It's 5,000 years old.

And what's very intriguing is the dice...

that are used for this aren't the usual cube-shaped dice that we used to in Monopoly, but they're little pyramids. It's tetrahedron, so I've got a larger one here so you can see it. So they would colour corners of the tetrahedron, two of the corners, and then you would throw lots of pyramids, and then you would count how many coloured corners there were pointing up, and then that would be your number of moves in the Royal Game of War. Exactly.

- Originally, dice were made from ankle bones. - Yes, so this is, I think, the reason that the four-faced figure was the first dice to appear in a game, because an ankle bone

lands naturally on four sides. But obviously a bone is not symmetrical. It can be very biased. And in fact, when they were used, these knuckle bones in Roman games, for example. They deliberately chose faces. Yeah, so they knew two sides were more likely than the others. And so the games were weighted according to that.

So I suspect that what happened was they said, "Okay, well we want something which is a bit fairer," and they started carving the four, and what they realized was this little tetrahedron is the symmetrical shape with four faces. - There's a little point of connection between our work, because I was presenting on a BBC Orkney series, the Neolithic balls.

And no one has an explanation of what they were used for. Yeah, so these are incredible. Again, you can find them in the British Museum or on the Ashmolean in Oxford, we have some. But they're 5,000 years old as well, Neolithic stone balls, which have patches carved into the side, a bit like Neolithic footballs or something. And you can see this is...

early humans exploring the world of symmetry and how can I arrange these? So there are a lot with four patches on and then you see them starting to experiment well, are there other ways to arrange it and you find six or eight but sometimes they sort of get it asymmetrical but it's so fascinating my area of research in mathematics is symmetry and to see 5,000 years ago people beginning to play around with symmetry and

But, yeah, you think, okay, so what's the game behind these incredible Neolithic stone balls? And as you say, there doesn't seem to be a game. And, in fact, we're not even sure what they're for, which is, I think, really lovely because in some ways –

it relates to games as well because a lot of people say, you know, why do we play games? What are games for? And I think that entirely misses the point of a game. As soon as a game becomes for something, you know, maybe it's teaching you something or, yes, it's a...

I think it's no longer a game, or you're earning money through doing it. A game is by its nature purposeless. And I think a lot of mathematics actually by its nature is purposeless. And we do it not because of its utility,

but because we just love the joy of spending time exploring the implications of these rules. And I think that's what these Neolithic artists were doing. They didn't want it for something. They were just really enjoying the game of seeing how you can arrange these patches on the other side of these shapes. You mentioned also that animals play

in order to practice being out in the world. Yes, and I think this is because games are clearly important for many species evolutionary development. And play fighting is practicing for real fighting. But I think this is one of the points I make in the book. We're about the only species which continues playing games into adulthood. A lot of animals use games to practice something, but then stop and it all becomes very serious.

So that's why some people have suggested that our species should be called Homo ludens, the playing species, rather than the Homo sapiens, the thinking species. Because for us, our evolutionary development as a species right into adulthood, games have played an important part. So they have been kind of useful, but in a kind of secondary way, in a way.

I also love how you draw parallels between games and uncertainty and our need to predict the future. Yes, you see, I think there's a very strong belief that games may well have appeared at the same time as we started thinking scientifically about the universe. That as soon as we realise that the universe is controlled by rules,

we wanted to understand, well, what are the implications of those rules? Because I would like to know, I'm going to have an edge if I can predict what the rules are going to do in the future. If you understand how the trajectory of a stone, where it's likely to land, that will give you an edge in hunting.

And so some thought was that as soon as we understood the universe is controlled by rules, in a way our games are like mini experiments. And this Royal Game of Ore is a perfect example of this because when you...

Actually, this game was discovered before we knew the rules. And then the little cuneiform tablet appeared some decades later, which gave us the rules. And Irving Finkel at the British Museum decoded them. And it turns out that it's a two-player game, a racing game, an early version of Batcannon, really. But there are 12 common squares that the players race through. And they race five counters through those 12 squares.

So the 12 squares are thought to actually correspond to the constellations in the night sky, of which there are 12. And of course, at the time, 5,000 years ago, there were five heavenly bodies that moved through those constellations. So there's one thought that this game of ore is like a mini version of the solar system crystallized into a game, that you're racing these planets around the constellations.

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Buddha, who's saying do not play games and has a whole list of the games you can't play, which is basically all the games. Yeah, this was a real surprise to me because I thought Buddha was a reasonably fun guy. It turns out he's not at all. And it sort of goes really against the spirit of the country that he grew up in because I would say of all the places I visit, India is really the continent that

just loves its games and so many games I discovered have their origins in India which we can come to but there's Buddha actually saying well you know I'm banning my followers from playing games so there's a kind of whole list of games in the book that so for example games with eight or ten rows so I'm afraid chess is out and

imaginary boards, so you're not even allowed to think about chess. Games with chalked, with lines chalked on the floor, so you obviously were playing hopscotch at the time, but you weren't allowed to play that either. Games

They clearly had a very early form of Jenga as well, because you're not allowed to play things with tiles piled in a stack, which is obviously very dangerous. Or they had a very early version of Pictionary, it turns out, because that was banned as well. The only one I agree with on his list is...

is the 14th one he banned was imitating deformities. Well, if that's a game, I quite agree with that one being banned. But all the rest are like, what a miserable time they were having. But then at some point in the book, you talk about the addictive side of games. And so maybe Buddha was alluding to not getting tempted by addiction. Yes, I don't know. It's kind of very curious because actually one of the...

games that I discovered came from India has very strong religious heritage, which is snakes and ladders. So I thought this was a European game. I played a lot with my sister. The book's dedicated to my sister because we were kind of like opponents in our youth in all of these games. And

Yeah, so I was very surprised to find that snakes and ladders had very ancient heritage and it was used as a teaching tool for the impact of good and bad karma on your life. So the snakes were obviously bad karma and the ladders were all labeled with good actions. And the winning square was, they were always eight by nine boards, so 72 squares. And it was the middle square at the top row, the 68th square, which was the winning square.

And that represented nirvana, moksha, what everyone is aspiring to live a life that eventually allows you not to be reborn. Curiously, of course, in our version of Snakes and Ladders, you would just sit trying to roll the dice to get to the winning square and you'd bounce back and forth. But in India, you got reborn, so you had to start again if you missed the winning square and go all the way around over and over until you got there. So I was very curious that this game actually is...

has kind of deep religious connotations. And there was some... So a lot of the book is about how you can use maths to win at games, which is why I've given all my tricks, basically, for winning at games, which is why you have to go and buy the book afterwards. But, of course, Snakes and Ladders... It's all about winning. It's all about winning, yeah, exactly. No, it's not about winning. Oh, I see. You said that in the book as well. Yeah. It's not just about... No, it's not just about... Actually, it is.

The weird thing is that Snakes and Ladders, of course, there's no strategy to that. How can you use maths to win at that game? So it's a kind of really silly game. I mean, I must admit, when I played my sister, I thought I was being incredibly clever when she went down a snake that somehow I'd caught this. But you can use maths to actually make games.

And in this case, there's a lovely piece of mathematics which helps you to analyze the expected number of throws of the dice that it will take to win a game. And this is really important. When you're beta testing games, there's two ways you can do it. You can just send the game out to lots of people and get them to play it and get feedback. Or you can use some maths to actually analyze, well, how long should this game take? So I took a board that I discovered in the Pitts Rivers Museum in

Oxford, it's a really beautiful old board from the Jain religion. And I analyzed how long it will take to reach paradise. And the mathematics, it turned out, would take 59 rolls of the dice to reach paradise. And I thought that was a bit long. So I did a little experiment and I removed one of the snakes to make it easier. I thought, OK, so can I, by removing a snake, make it easier to get to paradise?

I redid the calculation and weirdly, instead of getting easier, it became harder. I was like,

And it took 75 rolls of the dice. And I was like, this is crazy. Have I misunderstood? No. Snakes make it harder. So why I'm removing a snake is it got easier. And for ages, I thought I'd done a miscalculation. And then I realized what had happened. Because this little snake actually was weirdly helping you. Because it gave you a second chance at a really long ladder, which got you almost to paradise. So if you missed that ladder, the snake dropped you down. You had a second go at it.

So I looked at what the Sanskrit was for this little snake. You know, what was it that... It turned out it was the bad action of drunkenness. So I was like, I'm sure the Jane relation didn't mean this, but actually the message of this board is that drunkenness helps you to reach nirvana. So it's sort of like that.

You don't like games that go on too long, do you? No, you see... Monopoly. Monopoly is... Why is Monopoly everyone's game of choice at Christmas? It's the most highly flawed game out... You know, one of my... I've got six conditions for what I think make a great game. The second one of them is that it shouldn't finish...

before it ends. And you want the game to be, the possibility for somebody to win right up to the last roll of the dice. Monopoly finishes halfway through the game. You just spend hours, that one person who clearly is going to win, just bankrupting all of the other players. So it's like, the other game that I really don't like is Uno.

I didn't put it in the book because Uno, again, you can use the same mathematics for snakes and ladders and work out how long it takes. Uno is quite fun because you don't have to think too much. It really isn't. But it goes on forever because the cards go up and down. And I've analyzed that. It takes 200 turns of Uno for somebody finally to win that game. So, yeah, games that go on too long. Although, you know, there might be – it's about –

I don't mind it going on too long if it maintains its kind of interest and anyone could still win. I think in the book you even suggest how you can cut Monopoly short.

Don't you? Oh, yes. So I've got two stories about Monopoly. One is the longest ever game of Monopoly, which is paid by some students in America. And they got to the stage after three days when there was no money left in the bank. They're like, there's nothing in the rules to know what happened. So they phoned the people who make Monopoly up and said, what do we do when the bank runs out of money? Hold the game. And they sent...

a security van round with Monopoly money in the back. I said, carry on playing. And the guys carried on playing for another five days, at which point it was just going round and round in circles. Nobody was quite, and then they eventually were calling this a draw. They got into the Guinness World Book of Records for the longest game. But then there's the shortest game ever. You can win this game in 20 seconds.

And I've given the sequence of moves. I mean, it's very unlikely to get them. But there is a sequence of moves where you can bankrupt. You know, if you get a double, you get to go again. So it requires you doing two doubles, not three, because, of course, that sends you to jail rather unfairly, I think. But there's a whole sequence of moves that somebody worked out that after just two turns each, the other person is bankrupt and you've won the game. So it can end very quickly.

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So if you zoom out of the book, I mean there's 80 games, is there really no similarities between that many? One of the things I really hoped for in my travels is that I would go to a country and discover a game I'd never ever heard of before, a whole new gameplay.

But what happened... For example, I arrived in China and I went travelling before the conference. It was an international congress of mathematicians. And I ended up in this small little village and there were men playing with these really beautiful little oblong cards. And they all have Chinese characters at the top. And I thought, "Oh, I've never seen anything like these cards before."

And I watched the game and I couldn't understand the game they were playing until a woman who was in the cafe, she was about the only English speaker in the village, and she took pity on me. She saw I was just fascinated. And she explained the rules of the game to me. I still have this little scrappy bit of paper. It was about 20 years ago that I bought these. And

But as she described it, I realised, oh, I recognise that game. Basically, they were playing rummy. They were just collecting things. These are numbers, so there are simple Chinese characters and complex Chinese characters for the numbers. And they were either collecting all the twos or a run of three, four, five. And it was another very Chinese game, which I love, and I brought back a whole box of this, is Mahjong.

But again, if you analyze, Mahjong is beautiful and very kind of, it feels very foreign. And one of the challenges is actually understanding all of the characters that are on there. But there are lovely dragons and winds and things. But when you analyze it, it's rummy again. It's just collecting things.

So I began to get this theory that, you know, they say there are only seven stories that you tell and the Greeks told them all and we just retell them in different guises.

I began to wonder whether maybe there are only seven basic game types and that what we do is just reinvent them in different ways and they look foreign, but they're all actually examples of maybe a racing game or a war game or a collecting game like Mahjong and this card game. Could the book be summarised in... Could I have done it in seven? Or at least like kind of chapters or...

Well, I did think of doing that, actually. But I quite like the way... You know, despite the fact that there are a lot of commonality between the games, what's also interesting is just the way people play games. And the games that...

different regions will choose. And obviously, you don't want to get too specific about one region only playing certain games. But I did discover that in India there's a different style of game that sort of appeared to the ones that were in China. So in India, this relates to your point about chance.

In India, they really seem to love a game that has a high degree of chance involved. I mean, Snakes and Ladders is the ultimate, it's only chance. And I think that reflects a little bit this kind of Indian philosophical belief in fates, in that you sometimes don't have as much control over your life as you think you do. You get pushed and pulled around by your dharma. And so the role of a dice is really important.

So much so, I mean, one of the great games, of course, of all time, strategy games, is chess, which has its origins in India. But what I discovered...

quite surprisingly is that first of all chess was a four player game when it was first played which is why you have two castles, two knights, two bishops because you captured the other person's army. They shouldn't be bishops by the way, they should be elephants but when these pieces arrived in Europe they said what is this piece and it looks like a mitre's hat but they're actually tusks. So when you play the game again call them elephants not bishops. But the other thing was they played it with a dice.

It's like, what? They rolled a dice. It was a four-sided dice. And whatever side it landed on, that was the piece you had to move in your army. So you didn't have kind of just, it wasn't a pure strategy game. And then when gambling got banned in India, they weren't allowed to use a dice. And then some bright sparks said, well, you know, we could play the game and we choose which piece to move. And it became the pure strategy game it is.

Today the other lovely thing about chess, sorry We're going to get to different countries and their the different choices games But there's something really beautiful about chess as well, which I think is something important about games Which is they evolve they change they change according to the different communities

People have their own family versions of games as well. And I actually really approve of that. And I think in the book you mentioned how war influences games. Yeah, so this is clearly a war game. And some thought it was first developed really for looking at strategy rather than the game. But early versions of chess, the pieces were only allowed to move one or two squares maximum because everything was hand-to-hand close combat.

But then when warfare develops such you could have a longbow and you could shoot somebody across the battlefield, that's when suddenly the pieces start sweeping across the board. The elephant could charge across the board and sort of knock a piece out across the other side. And so what's lovely is seeing the game reflect

the change in warfare. For example, the queen is a very modern addition, European addition. It was just a vizier who would advise the king and could not move as much as, you know, only one piece like the king. But then when you come to Europe and queens are very important politically and so this piece became a queen and was very powerful.

India likes chance, but China, less so. You find less examples of chance in games in China. It's more combative. Well, it's more... I mean...

This is a kind of slow burn. You're collecting things, and you only lay your hand down at the end. And I think that reflects Chinese politics. It's a very slow burn. They're quite happy to sit and wait for Taiwan. They're not interested. They will take Taiwan when we are not interested in it, when we're making our superconductor chips somewhere else, and then we won't care about Taiwan. They're just waiting until... Gosh, I didn't mean this to become political, but

You're talking about cards. I love the way you describe a pack of cards. It's portable. It can lead to a multitude of games. I think this is humanity's greatest invention. Yeah. And I have to say, I really love the pointing out of the Eight of Diamonds. Oh, yeah. Did you know this? Go back and look at the Eight of Diamonds because I saw this on Twitter and I got very suspicious of anything on Twitter.

You know, so it said, have you ever noticed that there's an eight hidden inside the eight of diamonds? And it showed a picture of the diamonds laid out. And sure enough, there's a figure eight in the diamonds actually have curved edges. They're not arched.

hard, solid edges of a diamond. But I thought somebody manipulated this. I said, I don't believe that. And I went back and I looked at all my packs of cards. And sure enough, I'd never noticed that the diamonds are curved in the lines. You can actually see the figure of eight. Yeah, so if you lay them out, there's a hidden figure of eight in the eight of diamonds. That's so cool. I love that. Thank you for listening to Intelligence Squared. This episode was produced by myself, Mia Sorrenti, and it was edited by Bea Duncan.

Don't forget, Intelligence Squared Premium subscribers can listen to the event in full and ad-free. Head to intelligencesquared.com forward slash membership to find out more, or you can hit the IQ2 extra button on Apple for a free trial. You've been listening to Intelligence Squared. Thanks for joining us. Hey, music fans. There are some great concerts headed this way. Don't miss out on all the shows in your favorite venues like Deftones at Madison Square Garden,

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