[APPLAUSE] ADAM KUCHARSKI: OK. Thank you. It’s great to be here. Thank your for the invitation. My name’s Adam Kucharski.
I’m a searcher specializing in the mathematical modeling of infectious diseases and, as well as that, a writer most recently of this book about the relationship between science and gambling. Now, on the face of it, my day job couldn’t really be further from casinos and plastic chips and playing cards. But actually, the relationship between science and gambling is quite a close one. The two subjects are actually very intertwined. And that’s what I want to talk a bit about today– a few stories and examples of how lonely people have taken ideas from science and math and used that to take on games of chance, also how many gambling games and betting situations have inspired a lot of the concepts and are fundamental to modern science.
What I want to do is start with lotteries, because for me it was lotteries– a story about lottery, actually– that first got me interested in the math of betting several years ago. Now, I’m sure any of you who’ve looked at the lottery or play lottery will know it’s incredibly hard to win. But the way in which we measure how hard it is to win is a fairly recent development.
Although mathematics goes back millennia, the ideas behind measuring probabilities of event is something that only really started to take off in the 16th century. And it was actually a person called Gerolamo Cardano, who was during the Renaissance in Italy, he was a physician. He was the first person to describe the clinical symptoms of typhoid, for example. He was also one the first to describe games of chance mathematically.
And what he did is outline what we now know as a sample space. So this possible space of events. And obviously, if you want to know the probability of an event, you just hone down on the particular one of interest.
So for a lottery, the UK National Lottery, you pick six numbers from a possible 59. There’s just over 45 million possibilities there, which obviously gives you pretty poor odds of winning. But there’s a way of guaranteeing that you can have a winning ticket, and that’s simply to take a brute force approach and buy out every single combination. Now, that might sound a little bit absurd, but let’s just stick with it for a moment.
For the UK lottery, each ticket cost 2 pounds. That’s an outlay of about 90 million pounds, if you’re desperate to guarantee that you have the winning ticket. Clearly that’s not realistic.
However, not all lotteries are the same. And in the 1990s, the Irish lottery had a much smaller sample space. And in fact, there were about 1.94 combinations of numbers that you could pick. Each ticket was 50 piece.
So actually, it would cost you under a million pounds to buy out every single combination. And this is what a syndicate spotted. And they thought, well, this is plausible now. This is something we could do. So they got a hold of tons and tons of blank tickets and, by hand, filled out every single one of those possible combinations.
Now, if you’re going to spend a million pounds to essentially buy the jackpots, in most weeks, the jackpot is going to be maybe a few thousand. That’s a pretty poor investment. You’re spending a million to buy maybe 400,000 pounds. But if there’s a rollover, potentially you come to a situation where you’ve got a positive expected value. You would actually, if you have all these tickets, gain a profit.
And that happened in the May bank holiday in 1992. The rollover reached about 2.2 million pounds. The syndicate put their lottery strategy into action.
They went around with all these tickets from location to location, going to shops that maybe would normally sell 1,000 tickets and going in and asking to buy 15,000. Lottery obviously twigged what they were doing, and despite the fact that it was completely legal, somewhat frowned upon it and tried to stop them. So in the end, unfortunately, they only managed to buy up about 80% of the combinations of tickets. Luckily for them, that still included the winning ticket.
Unluckily, that week, there were two other jackpot winners. So they had to split this jackpot. But when you added up all the lower-tier prizes, they actually walked away with a profit of 300,000 pounds.
Now, for me, that was a great example of how you take a pretty simple mathematical insight, a good dose of audacity and hard work, and convert it into something that can be profitable. Now, in this situation, it was just a brute force attack. Essentially they just went for every single combination to get the jackpots. That’s pretty simple mathematically. That’s not particularly interesting. But if you delve down into lower-tier prizes, things get a little more intriguing from a mathematical point of view.
At the other end of the scale, say you want to guarantee a lottery that you’re going to match one number in a particular draw. Obviously all you have to do in that case is just buy out tickets with all the numbers in sequence. You don’t have to buy many tickets to make that work.
How about two numbers? Well, for the old National Lottery in the UK, where you pick six numbers from a possible combination of 49, people working in combinatorics have showed that the minimal set of tickets you need to guarantee matching two numbers is 19. So this is known as lotto designing in combinatorics.
If you want to match three numbers, however, that’s an open question. Actually, nobody’s worked out what the minimal set of tickets you need to guarantee matching three is. Some people attacked it numerically. So they just run through and crunch through and learn possible combinations. And the lowest of what I could find, at least, was somebody who came up with 163 tickets to guarantee matching three numbers.
But actually, it’s an open question as to whether there’s a lower set out there. So there’s a lot of interesting math even in lottery, which on the face of it seems like a pretty trivial problem to work on. But it’s not just modern mathematicians working these kind of problems. As I said, people like Cardano, throughout history, have been interested in it.
And many of the big figures in maths have also worked on games and gambling. This gentleman, for instance. This is Henri Poincare, really one of the great figures in around 1900, one of the few mathematicians that the last mathematicians really to work in every field of the subject as it was when he was alive. And one of the things he was particularly interested in was predictability. So this notion of unexpected events. And he categorized it by what he called degrees of ignorance.
For him, unexpected outcomes were the result of ignorance about the causes. And he classed this three levels of ignorance. He said the first one is a situation where what the rules are. You have the information. You just need to use elementary calculation to get the answer. So if you do a high school physics exam, this is kind of the situation you’re in.
You know what the laws are. You have the information. You just need to do some calculations and ideally get the correct answer.
The second level of ignorance Poincare said is something where you know what the rules are, but you don’t have enough information to make an accurate prediction. And he used roulette as an example. He said, in this situation, because you got a roulette ball going around a table, a very small change in the initial speed of the ball can have a very large effect on the outcome. Now, this idea subsequently developed into what’s known as sensitive dependence on initial conditions.
In the ’60s and ’70s, became one of the central components of chaos theory, popularly known as the butterfly effect, the sense of dependence, the idea that a very small change in a weather system in one location can have a very large effect somewhere else. So it’s not necessarily a random system. It’s just that these very small imperceivable changes early on can have large effects.
And then we say, according to Poincare, that those are due to chance. But that wasn’t where he stopped. There was also this third level of ignorance he focused on, and this was a situation where you don’t know the rules. The rules are so complex you can’t pick them apart. And in this, all you can hope to do is watch enough realizations of the system and try and gain some insights into what might be happening.
Now, when mathematicians and scientists initially start tackling roulettes, they focused on this level. They didn’t treat it as a physics problem. They treated it as one of observation. Let’s look at a lot of roulette spins and try and look for something unusual. See if there’s a bias in the table, something that we can exploit. This raises the question, though, of what do we mean by odd, what do we mean by a bias.
And actually, while Poincare was in France thinking about roulette tables, in the UK, Karl Pearson, the statistician, was also thinking about roulette. And to him, we can never really have any sense of the true process in nature. We can only analyze what we can observe. And because he wanted to understand randomness, he needed to generate a phenomenal amount of data, because this was what he wanted to hone his methods on.
In fact, he once spent his summer holiday tossing a coin 25,000 times to generate a random data set to analyze. He was also interested in roulettes. Unfortunately for him, at the time, the “La Monaco” newspaper would publish the results of roulette spins in Monte Carlo Casinos. And for Pearson, this is a perfect data set which you can analyze in terms of what’s going on. And the first thing he looked at– so we take a roulette table.
You’ve obviously got these black and red outcomes, and then this zero. And if you remove the zero, you’d expect black and red to be about 50-50. And in his data, I think red came up about 50.15% of the time. So based on what he had, he said, this isn’t implausible, that this difference is kind of acceptable. But then he started looking at pairs of numbers. And obviously, if you’re doing a lot of roulette spins, you’d expect sometimes by chance to get a string of the same color appearing.
But in the data, Poincare noticed that the two switch too often. You didn’t get these strings of the same color appearing. What was happening was you’d get black and red switching more than you’d expect. In fact, he said that, had he been watching these tables since the start of geological time on Earth, he wouldn’t have expected to see a result that extreme. Pearson actually, in the end, was quite angry about this. He thought that Monte Carlo were rigging all their tables, wrote a lot of angry letters, in fact, suggested they should be closed down and the proceeds donated to science.
But there was something else going on. As it happened, those journalists at “La Monaco” weren’t actually sitting by the tables and recording all the numbers. They were instead sitting in the bar and making them up, which explains what was going on. But these ideas that Pearson honed and have become an important part science– think back to that sentence.
The probability of observing an event as extreme as the one we observed, given that he said it was random. That’s the early foundations of a p-value. This is a statistical test. And so whether in my line of work, where we do things in clinical trials or you’re testing any kind of hypothesis, all of this theory originated with Pearson throwing coins and looking at roulette tables.
And as well, these kind of theories have been applied by gamblers to understand roulette tables. In the first half of the 20th century, many gamblers would actually watch the tables and instead of sitting in the bar and collect the data and look for biases. And when you had tables that were worn down or certain areas of numbers were appearing more often than others, they used this to capitalize and have an advantage over the table. Over time, casinos worked out what they were doing and made sure that the tables were incredibly well maintained and shouldn’t exhibit any noticeable bias over time. But in the ’60s and ’70s, a number of physics students realized that this puts you back in the second level of ignorance, that if you have an incredibly well maintained table, you can essentially treat it like a physics problem.
One of them compared it to a planet orbiting a point. You should be able to write down the system of equations governing that process and solve it given enough information. And the ’70s in particular, one group at the University of California, Santa Cruz– it’s quite a well-known story.
But what they did was divide up the spin into what happens. Initially, it starts with the ball going around the rim. Often it would go around a couple times before the croupier calls no more bets. You’ve got a window where you can obtain information and capitalize on it. Then it would drop down onto the track, spin freely, and then eventually hit one of these deflectors and end up in one of the slots. And what they realized is that actually, in this system, if you collect enough information over time and calibrate your model to the particular table, that initial period of the ball going around the rim gives you enough information to be able to make not perfect predictions but certainly enough to get an edge over the casino in terms of where the ball will land.
That’s all well and good doing that in a classroom. But if you want to do it in a casino, these aren’t calculations you can do in your head. You need a way of computing them. So they designed wearable computers, wearable hidden computers to carry out these calculations in a casino. And as it happens, the first ever wearable computer was designed for this purpose.
So a huge amount of wearable tech now. This is where it all originated. Obviously, they had some teething problems.
They quite often get electric shocks from their computer, which is not ideal when you’re trying to keep a low profile in a casino. In other situations, this sensitivity to initial conditions came to play. Like if the weather change, for instance, they’d need to recalibrate their model.
Another occasion, the team started losing money and couldn’t really work out why until they realized that further down there was an overweight guy leaning on the table and screwing up all of their predictions. But in many cases, these ideas stimulated a lot of thinking about these kind of process. And the research didn’t become gamblers necessarily. Many of them went into technology or finance or academia. But they treated it as almost a playground for ideas.
It was a way of just testing out this problem-solving ability. And interest in games and gambling has continued from an academic point of view. One example is poker and games. Obviously, there’s a lot of interest in AI around game-playing algorithms now. Poker, as it happened, was one of the first inspirations for game theory. Back in the 1920s, John von Neumann was a brilliant mathematician.
He was the youngest professor in the history of the University of Berlin. Wasn’t so good at poker, though. And on the face of it, poker is a perfect game for mathematicians, right? You’ve got a probability. You get dealt a certain hand. You’ve got a probability your opponent gets dealt a different one.
But of course, reality is a bit more complex than that. And as von Neumann said, real life consists of bluffing, of little tactics of deception, of asking yourself, what does the other man suppose I’m going to do? And trying to understand this push and pull between different strategies, he looks at some very simplified versions of poker. And he started off, for example, with two players. Each of them dealt a single card.
They both put some money in the pot at the start. And then the first player has a choice of either just sticking with their existing money in the pot, and then they compare their cards. Or this first player can raise the stakes and see if the other player reacts. It’s a very simple game.
Von Neumann observed there’s essentially a tug of war going on between these two strategies, because each player is simultaneously trying to maximize what they get and minimize their opponent’s payoff, because in a game like poker, anything your opponent wins comes out of your pocket. So you’re trying to really push and pull between these two approaches. And in the middle, there’s an equilibrium point where neither player will have anything to gain by unilaterally changing the strategy. So if you’re familiar with game theory, this is kind of the early ideas of a Nash equilibrium, the situation where neither player over time would expect to gain anything by changing what they do. When he analyzed this very simple version of poker, he found that if the first player gets dealt with a high card, it makes sense for them to raise the stakes.
Intuitively that’s pretty obvious. If you have a good card, good chance of winning. If you’ve got a middling card on that draw, you haven’t got a great chance of winning, so you don’t want to up the stakes. In this case, it makes sense to stick with what’s already in the pots. Interestingly, though, when the player was dealt a low card, this equilibrium strategy said that they should raise the stakes. And if you think that through again, it kind of makes sense that, if you’ve got a low card, if you stick with what’s in there and just turn over your cards, you haven’t got a great chance of converting it into a victory.
The only way you can profit is to try and scare your opponent out of the pot by raising the stakes. Now, at the time, poker players had obviously implemented things like bluffing. This was a common tactic, but it had always been seen as one that was more a quirk of human psychology than something that was a mathematical feature. But this was essentially von Neumann proving that bluffing is a necessary part of these kind of games. Essentially, he constructed a mathematical proof that bluffing is a necessity in these kind of games of chance. The strategy in this very simple version of poker is what’s known as a pure strategy.
There’s a set of fixed rules of, if this happens, do this. If you get a high or low card, you raise the stakes. If you get a middle card, you stick with your bet. And many games have similar pure strategies that you can follow. So anything that has perfect information– something like noughts and crosses or checkers or chess– in theory has a strategy, a fixed set of rules, that if you follow them, you will get the optimal result every time.
The challenge, particular things like go, is obviously finding those kind of strategies. And sometimes they might be intractable. But in theory, there’s one there. There’s a whole class of games that that doesn’t work for. So one obvious example is rock-paper-scissors.
It might be admirably consistent of you to always pick the same one. But if your opponent works out what you’re doing, you’re clearly not going to gain much in the long run. Really what you want to do is alter the choices you make to make your opponent’s decisions as difficult as possible. So for rock-paper-scissors, it doesn’t take much to spot that the way to make your opponent’s decisions as hard as possible is to simply pick randomly between these three options. And so over time, if you do that, you wouldn’t expect to lose on average.
For a simple game of rock-paper-scissors, that’s pretty trivial to spot that that’s the strategy. Obviously, for poker, there’s a vast number of different combinations you could have, and the situation becomes far more complex. It’s not something you can just write down a neat solution for.
And actually, one of John von Neumann’s colleagues, called Stanislaw Ulam, was interested in these kind of questions. He wasn’t a typical mathematician in that he didn’t really enjoy trudging through lots of equations. On one occasion, his colleague found him solving a quadratic on a blackboard. And when he got to the end, he was so exhausted and bored that he went home for the day.
[LAUGHTER] So really that wasn’t his kind of thing. He was once playing solitaire. He was playing Canfield, which is originated in casinos. And he wanted to work out the probability that, if you lay out the cards, you have a situation where you can win.
And he quickly realized that actually trying to write down all the combinations that that would involve is just a bit arduous and what would be better is instead just to simulate a few times– lay out some cards, see what happens. At the time, with von Neumann, he was working at Los Alamos on the nuclear projects and looking at neutron interactions inside the early developments of hydrogen bombs. And again, it was a similar problem, where you had a lot of random interactions of something that’s very hard to solve analytically, and it made more sense to simulate. Because they were working on a government project, they needed a code name for this new kind of method. So as Ulam had a heavy gambling uncle, they nicknamed it the Monte Carlo method.
And this has now become a really important part of science. We use it in disease analysis for things like Ebola and Zika. The transmission dynamics are incredibly complex.
It’s not necessarily something you can solve mathematically. And it makes its way into a number of other fields as well, including analysis of games. Many of the top game-playing algorithms now use these kind of simulation-based approaches to refine their strategies. And in poker as well, one team at the University of Alberta adopted this kind of approach and refined their strategy so much over time that, last year, they announced that poker is solved.
So for two-player poker, in which the potential stakes are limited– so known as limit poker– they had essentially, through this kind of iterative approach, found a situation or a set of strategies which are such a good approximation to the equilibrium that it wouldn’t expect to lose money over a kind of human lifespan. So they hadn’t found this exact solution like we can write down for rock-paper-scissors, but they found one which was such a good approximation that they wouldn’t expect to lose money over time. It’s obviously a tremendous achievement. But it does have the limitation that you’re assuming that your opponent is perfect. If you design an equilibrium strategy, you’re assuming you’re facing the optimal potential opponent. And that makes it quite defensive, because essentially you might be facing someone with flaws.
And if you’re following the equilibrium strategy, you’re essentially deciding that you’re trying to minimize your losses. You’re trying to make sure that, no matter who you’re facing, you’re not going to lose money over time. Of course, people do have flaws. And just to illustrate what happens when people play games, what I’d like you to do is just pair with the person next to you and play a couple of games of rock-paper-scissors. So I’m sure you all know how this works– one, two, and then show what you do. So just a couple of games and see what happens.
[SIDE CONVERSATION] ADAM KUCHARSKI: OK. So I think everybody’s had a go at it. OK. OK, great. So there were a few of you, I think, who were playing a best of seven or something. But what I’d to do– OK, so can you just raise your hand if, on your first go, you picked rock.
OK. Who picked scissors? OK, and who picked paper? A lot of people didn’t play, it seems.
[LAUGHTER] So generally– I don’t know if you can see that– but the split there was most people were picking rock or scissors. And actually, in many large-scale games where people played a lot of times, that tends to happen. Papers isn’t a very popular opening option. And often what will happen is novices and particularly men will pick rocks.
So it’s not that a hard and fast rule. But that’s generally what happens is scissors comes out as the most popular option amongst experienced players. So I told you about five minutes ago what the optimal strategy was for this game.
And yet, you kind of still fell into certain patterns. I think as well between what happened between your first go and your second go. So in one large study done about two, three years ago, what tended to happen was the person who won on the first go would stick with the same one on the second go. And the person who lost initially would switch to the move that would have beaten them.
So if you lost to rock, you’d switch to papers afterwards. So again, doesn’t always happen. But people often will fall into these kind of predictable patterns. There’s actually a story about 10 years ago where the head of an electronics firm in Japan wanted to sell an art collection. And Christie’s and Sotheby’s were interested in holding the auction.
And the head of the electronics firm decided the fairest way to settle it was with a game of rock-paper-scissors. Now, Sotheby’s were like, great, that’s random, that’s fine. Christie’s, however, he had a daughter– the CEO of the company– who played it relentlessly at school.
So he got his daughter to teach him the basics of rock-paper-scissors strategy. And sure enough, they walked in to play this game of rock-paper-scissors. Sotheby’s treating it randomly. Christie’s with a strategy. Christie’s walked out the winner. Because in these kind of situations, if you’re viewing it as a completely random game and you’re playing this [INAUDIBLE] opponent, it makes sense potentially to deviate from your strategy and take advantage of that.
But there’s a downside in these kind of games if you try and adapt what you’re doing. If you move away from this equilibrium strategy to try to exploit an opponent. And that’s what’s known as the get toward an exploited problem, because if you’ve got a very smart opponent, they could teach you a false appearance of what their strategy is. So in poker, they could initially pretend to be quite passive, maybe indecisive. And you would adjust your model of your opponent to that. And then they would adapt their strategy and take advantage of the fact that you’ve learned an incorrect version of themselves.
And there was actually an example not just with poker. In other industries, you have this problem. So finance is another situation where big increase in the role of algorithms, unlike poker, where you have these very detailed strategies.
In finance, obviously if the aim is to be quick, you want as little code as possible. You want to execute it as fast as you can. And a couple of years ago, there was a situation where two Norwegian traders had noticed that a US stockbroker had an algorithm which would always react to a trade in the same way. So no matter how big the trade was, the algorithm would change the price by exactly the same amount.
So what they did is they trained it. They got it, made lots of small trades to nudge up the price, and then made a huge one and profited from the difference. Now, that went to court, obviously. And they were charged with market manipulation. And they were handed suspended sentences. But on appeal, their lawyer made the point of, if they’d been trading against a stupid human, there wouldn’t have been anything wrong.
The issue that apparently was the problem was they were trading against a stupid algorithm, who presumably was designed by a human who was lacking in a few skills. [LAUGHTER] And that appeal was seen as justified, actually. It didn’t make sense that if you’re trading against a human there should be different rules for if you were trading against an algorithm.
How can one be skillful and yet the other not? And similar arguments have developed in other fields. For example, a few years ago– and is continuing to happen– that the US are cracking down on poker, particularly online poker but also real games.
And in 2011, a person who was offering a poker room in New York was actually taken to court for operating a gambling operation. Now, in federal law, many casino games are explicitly defined as gambling. But poker isn’t actually one of them. So poker is kind of open to debate a bit as to whether it is gambling. And in federal law, gambling is defined as a game that is predominantly down to chance, predominantly the result of chance.
So this whole legal case rested on, is poker predominantly a game of chance or predominantly a game of skill. A lot of economists and mathematicians weighed in, obviously making the point that in a single hand you got this element of luck. But over a realistic course of a poker game, skill can prevail. And this is actually the first time that a judge in the US has ruled on whether poker is predominantly a game of chance or a game of skill and ruled that it was a game of skill. It was not gambling under federal law. But there’s a footnote to this case, because under state law, gambling is defined as anything that has a material element of chance.
Now, it’s very hard to deny that poker has an element of chance. And so in this case, it was defined as gambling under state law, and this decision was overturned. And then you were seeing it increasingly with things like fantasy sports as well in the US. Where do we draw this line between something that’s a chance and something that’s skill?
And I think there’s often this temptation to almost put things in boxes. We like to say, this is a box full of luck, this is box full of skill. And I think this also tends to, if we’re good at something, we tend to put it in the box on the right. And if we’re bad at something, we put it on the box on the left. But really, I think, history and looking at these games and gambling has shown that it’s much more of a spectrum than that. Some of the stories that I’ve shown you and many other situations and things like card counting as well have shown that a lot of games that maybe we think of luck actually with sufficient skill and efforts can be overtaken with mathematical and scientific thinking as well.
And actually, games that we think of purely dependent on skill perhaps may have an element of luck as well. So back in the ’90s, when Garry Kasparov was playing Deep Blue, IBM’s chess computer. There was a point in the game where Deep Blue made a move that was by all accounts so ingenious and so subtle that it threw Kasparov a bit. And actually, a lot of the commentators said it changed the course of the game, because it was so unusual what he had done that it convinced Kasparov that he was playing something that was simply beyond what he had encountered before. He was playing an entirely new class of player. As it happened though, Deep Blue hadn’t chosen that move because it was clever.
It had run into a situation where it couldn’t make a decision about which move was best. And in that situation, to avoid a dead end, it had been programmed just to pick randomly. So this game, which is really held up as one of the landmarks of artificial intelligence versus humans, one of the most significant moves was actually made purely by chance. So again, games of skill potentially might be closer to luck than we think.
And I think that’s why gambling is a really interesting field of study, even if you never visit casinos or bookmakers. I think whatever industry you’re in, gambling and betting and chance play a role. I mean, I work in health, in business, and finance. The situations where we have to try to make decisions with hidden information.
We have to try and deal with uncertainty. We have to try to balance risk against potential payoffs. I think historically that’s what has been so interesting to a lot of people who are quantitatively minded and continues to do so today. But I think there’s another reason as well, which is why these games are so interesting.
And I think Alan Turing put it well when he was working on games to understand thinking machines a bit better. As he said, it would be disingenuous of us to try and disguise the fact that the principal motive for the work was the sheer fun of it. So thank you. [APPLAUSE] MALE SPEAKER: Thank you very much.
We’re now opening up to questions. I have the first and obvious one. Do you gamble? And how many casinos are you banned from?
[LAUGHTER] ADAM KUCHARSKI: Actually, I mainly play poker. And I think one of the things this book has kind of taught you is how many games– just the sheer amount of effort required. So there are syndicates out there taking on a huge amount of sports.
But essentially, that would just be doing my full-time job on a different data set. So I think poker’s a nice one, where a relatively small edge can play quite a big role. Unfortunately, most of my friends refuse to play with me now. [LAUGHTER] AUDIENCE: So you mentioned Kasparov and Deep Blue. And we’ve just had– or we– DeepMind and AlphaGo. What’s your opinion on the work that you see DeepMind doing in terms of changing games from– rather far more to the scale element and kind of the way computers are working on games?
ADAM KUCHARSKI: I think one of the things with Go that stands out, and it’s similar with poker, is just the speed at which these developments are happening. So I think Go for a lot of people was safe from computers for a few more years and, similarly, with a lot of the more complex forms of poker. So no-limit, hold ’em, and these kind of things. I think people had this idea that humans would be dominant for a lot longer. So I think that’s quite interesting in the time scale. Also with Go, just the way it’s tackling it, because obviously it’s a game that you can’t find this optimal solution.
So from what I understand, it’s much more about understanding the shape of the board. So adopting almost more human approaches to learn these games rather than simply crunching the numbers, as you might do for a very simple game. So I think that’s quite interesting of having to reproduce human learning techniques. And actually, for poker, a lot of the algorithms they use to try and solve these are based on regret minimizations. So they have a kind of regret function within their learning component. So I think that’s actually quite interesting, just coming out as a side issue, of what the efficient ways of learning these kind of games are.
AUDIENCE: Hi. Can you tell us a little bit about how this works in the disease spreading part, and if you tried that with any diseases, like maybe Zika or something? ADAM KUCHARSKI: Yes.
So as I mentioned, many of the ideas that came out of games and gambling we use in our work. So an obvious example is things like Monte Carlo simulations, that generally if you try to infer what disease does, you need some way of combining a simulation process with inference of data. And so actually, in this kind of situation, it’s much more efficient to just do lots of simulations and then kind of refine them to what the data is.
But there’s a number of other ideas as well. So in some situations, people using game theory. Again, these kind of strategies that came out of betting to understand how different countries may be interacting to make vaccine decisions. Because in many situations, you have almost like a tragedy of the commons, from something where you’ve potentially got a vaccine that has a side effect or has a problem.
From an individual point of view, your priorities and your risk profile is very different to what a population does. So if you have a whole population making a decision, you might have some effective herd immunity. But if enough individuals ignore that, you can end up with a different outcome. So it’s the push and pull between what’s good for a population and what’s good at individual and how those things interact. So I think that’s where a lot of the ideas come into.
I think it’s also just good sometimes when you’re working with these ideas day in, day out, to understand where they come from. And I think as well just the fact that these kind of games are very nice situations. If you work in disease data, it’s pretty murky. There’s a lot of unknowns, a lot of uncertainty, whereas for something like a simplified version of poker, it’s a sort of well-defined problem to work on.
So I think you do in any industry, you work on kind of cartoon problems, because they’re simple to analyze. I think it’s just interesting to see how the history has developed in these kind of things. AUDIENCE: The disease data, I’m quite interested. And we hear a lot about immunization– sorry, the way that antibiotics will affect us on a global population and that we might not globally be prepared for outbreak of a pandemic or similar. And that often feels like it’s a governmental problem– governments communicating with each other and so forth.
So as a mathematician, as a scientist, how do you look to communicate your findings onto a kind of political and to a human level and try to impact the system that is often quite messy? ADAM KUCHARSKI: That’s a good question. Doing Ebola, we did quite a lot of work with government agencies. And I think one of the things they say is it’s better to be 80% right today than 90% right in two years’ time.
And it’s really kind of working on– there’s never a single piece of research that defines a policy. It’s always that kind of aggregation. But I think there’s often situations that there’s a lot of options. It’s not clear what’s even reasonable. I think modeling and a mathematical approach is a good way of essentially taking things off the table and refining it down. I think, especially doing these kind of real-time outbreaks, the Zika’s another example.
There’s a huge amount of uncertainty. And ideally, you’ll get in and do all kind of field studies and do everything properly. But in the absence of that, we need to make decisions now. I think these kind of analysis are quite a useful way of doing it. I think policymakers appreciate having things there very quickly as an evidence base to make decisions on. AUDIENCE: I was just thinking about your [INAUDIBLE] a bit like roulette moving from more into a skill mode than a luck mode.
Do you think the insurance industry is actually going to be– because at the moment, it’s just down on this huge population, and you’re roughly going to die or roughly going to have a car crash. But actually, as you have increasing levels of data about everything you do in a car or every bit of genetics, then it becomes calculable potentially. Do you see that shift in the insurance industry? ADAM KUCHARSKI: Yeah.
I mean, it’s already happening. I don’t know the details, but I know there’s been a few test cases in recent years of that trying to refine it into certain parts. So the split between males and females, for example.
And I think there’s been some legal disputes as to whether you can actually do that. And you’re right. It makes sense if you had that large set of data, because you can really refine the risk based on a particular individual. But there’s that kind of conflict between people wanting a uniform policy.
So again, that’s the kind of interesting thing of where what the model says is best conflicts with what’s actually acceptable. AUDIENCE: So if you’ve got an opponent that you know is playing a perfect strategy, is there any way to use that information to game that opponent? And are there some games which are, because of this, intractable?
ADAM KUCHARSKI: So if you’re playing a perfect opponent, then I suppose by the definition of that strategy, your best response is to play an equilibrium strategy as well. One of the things that’s interesting, actually, talking to people who are working these poker games is, in two-player situations, it’s pretty obvious that, if they’re playing an optimal strategy, you need to do the same. But the definition of an [INAUDIBLE] equilibrium is on unilateral behavior. So it’s no player has anything to gain by individually changing that strategy.
But when you have multiplayer games, you have the potential for collaboration and coalitions. And actually, some of the people working on poker, particularly on the versions of the game that are intractable, have found that you can have these kind of equilibrium strategies. And when people put them together, potentially two players could gang up on a third.
And the third can’t do anything about that. So in that situation, where they all are playing pretty good strategies but not perfect ones, it doesn’t necessarily make sense for that person who’s being picked on to rely on that as a defense. And it might make sense to look for flaws in what they’re doing instead.
So I think there’s just a lot more to be seen for when you have these multiplayer games, that it’s not so clear that these kind of equilibrium strategies are useful. Hopefully that answered your– AUDIENCE: It did, thanks. AUDIENCE: I’m very curious as to what brought you down that path. Why did you write this book? ADAM KUCHARSKI: So I’ve said, these kind of stories have always been hovering in the background for me.
And it was actually, it was during my PhD– so I did PhD in maths. And we’d often get emails from usually the standard crowd, just tons of investment banks, generally. But you’d often get a few different ones appearing. And it was actually firms who are essentially betting hedge funds got in touch about possible recruitment. And for me, that was something that I just wasn’t aware of as an industry that had developed. And actually, as you start to look into it, it was only in the last decade or two that in the UK on, say, football that people have been able to make consistently good enough predictions to make that a viable business model.
And that kind of started for me. That was quite interesting. That was something I was completely unaware of as an industry. And then when you start to dig down into the history, you realize that not only there are a lot of other people doing these things that potentially aren’t reported a lot. Actually, you’ve got a lot of quite major developments in science that– I don’t know about you, but I was just completely unaware that a lot of these ideas had originated with games like roulette and gambling.
I thought it would just be really interesting to have a book that explores not only the history but also some of the modern efforts and, again, with some developments in AI. I think that’s coming on frustratingly almost when you write a book, that it’s coming on so quickly, because it kind of updates. But I think that’s fascinating looking at what’s happening in the modern day. And it’s just the fundamental question of, if you’re going to put money on the line, what evidence do you need to make a decision? And it’s the same of whether you’re deploying a vaccine or whether you’re making a business choice. It’s what evidence convinces you that that risk is worth taking.
I think gambling is a really interesting industry to look at in that context. AUDIENCE: So we work at Google, and we love data sets and big data sets. We had a speaker recently who spoke of understanding whale noises and that it’s a problem where, if we had a larger data set, we could actually make some progress trying to understand how they speak to each other. So in terms of your industry and what you’re dealing with, what would be your fictional ideal big data set that currently you can’t collect or is too expensive to collect and you would love to play, be it a game or health or similar? ADAM KUCHARSKI: So in terms of my day job, I think one of the big questions that we don’t know– generally, we focus on things we can measure easily.
You know, a disease case is been diagnosed. That’s the thing. If we for Ebola put in a treatment center, that’s something you can quantify.
I think the thing that’s really hard to measure is behavior and attitude and how they change during outbreaks. And I think they change a lot, particularly for Ebola. We see it in some areas, the epidemic would tail off.
And anything you could shove in a model would not explain that. There was clearly some feedback process happening, and people were seeing what was going around and changing their behavior accordingly, and I think just in reaction to a lot of other of these outbreaks. And that’s something that’s quite hard to– I think often we try to measure stuff as proxies. You can do surveys of people and their behavior.
But if I ask you what you’re doing today and there’s a huge outbreak next year, can’t guarantee you’re going to behave in the same way. And I think that’s something that would be really interesting to try and understand actually what people really do versus maybe what they say they do or what they think they do and how that has an effect, because I think that’s a big gap in our understanding of outbreaks certainly. AUDIENCE: In the beginning, you were talking about the group that found the hole in the lottery system. Did you, while doing your research for the book, also find some fault, some flaw in a system that you could have potentially exploited? ADAM KUCHARSKI: So one example is, if you remember back in January, the UK National Lottery. So they introduced this rule.
So they upped the number of combinations. So I think it was previously about 9 million possible combinations, and they upped it to 45 million. And unsurprisingly, this meant they didn’t have any winners for ages, which is incredibly bad publicity, because actually, for lotteries, they like winners.
It gives them people smiling with checks. It’s good. An interesting rule– if it hit 50 million as a rollover, they would redistribute the prizes to lower tiers. So that was one thing actually I sort of chatted with a few people about, of in that situation, if you don’t necessary have to win the jackpot to net 50 million, that gives you a positive expectation on the lottery.
So actually, the value of a ticket on average is worth more. But then there’s the issue of, is expectation of good way of judging an investment? Because you’ve got a tiny, tiny chance of winning a lot. And then again, from ideas from the book, if you actually looked at that kind of investment, if you looked it from a utility point of view rather than, if I played this game an infinite number of times, I might make a profit, think of it of, how much is this worth to me?
How big a bankroll do I need to make it worth buying a 2-pound ticket. And actually, in that case, with these kind of lottery rollovers, buying a single ticket is only worth it if you’re a billionaire, basically, from a utility point of view, which is not a great message. But I think there was a lot of focus on people saying, well, you know, it’s expected value.
It’s a great week to play. But the nuance of actually how do you make those decisions, I think, was a quite interesting thing to think about. MALE SPEAKER: You’re talking about obviously the strategies for playing games and stuff but also in relationship to banking, investments, and stuff. Obviously, that’s an area where different people are competing with different strategies. But as soon as one strategy starts to take hold, then that changes the environment in which the strategies are behaving. So are there any interesting things happening in trying to predict not only when you introduce a strategy and how it will do, but how it will change the environment?
ADAM KUCHARSKI: Yeah, that’s a very good point. And that’s one thing that people are starting to work more actively actually is– I think there’s a lot of focus on finance from an individual point of view. You’ve got a single investor, a single strategy. But of course, it’s basically an ecosystem. And a few people compare it to an evolutionary dynamic, that if you come up with a good strategy, other people adopt it.
And then it becomes less successful, and then you have to kind of evolve what you do. And they’re saying the bigger the advantage, the quicker it’s going to decay in terms of effectiveness, because it’ll be easier for people to spot. And I think for these high-speed things in particular, that time scale is quite short, because if you speed up what you’re doing, you have such a big edge over other people that there’s a big incentive for them to come in. And in one case, for example, the people are building a hardwire from– I don’t know if you heard about this– from London to New York, underneath the flight path, because it would give them a fraction of a second quicker information on the market. And building that cable is sufficiently valuable to actually get that edge. So I think in particular, as the speed increases, that evolutionary process is increasing a lot.
And I think there’s a lot we don’t understand. I mean, you can take some of the basic ideas from ecology, about what happens when you put lots of people together. And one of the classical results actually from chaos theory in the ’70s was, if you have something following simple rules, it can do very weird, complicated things. I think we’re seeing similar things in finance, that you have a load of algorithms written with 10 lines of code sitting together, and they don’t necessarily do what you think they’d do.
So I think that’s quite an interesting, important field, but one that hasn’t been fully explored. So it’ll be nice to see what happens in the future. AUDIENCE: Going back a bit to the disease outbreaks, you mentioned that that data is sometimes not complete. So I was wondering, where do you usually get that data? And once you get the results, how does that data turn into action?
Do you just give it back to the government? How does that work? ADAM KUCHARSKI: So it varies depending on the outbreak.
I mean, so with Ebola and these kind of things, ideally you have data on the cases as they’re being collected at the time. We’re working directly with agencies as well as WHO. You had Medecins Sans Frontieres, and these kind of groups and actually kind of converting the data back into a potential forecast for them. So I think with all these things, it kind of works best if you work with the people who created the data, because they understand how it’s collected, and it’s potentially useful. But I think one of the things that was surprising with Ebola, for example, is that in many cases, people collecting data in one district didn’t actually have the data for the next district. So we had a situation where we were synthesizing it and visualizing it and giving it back, so they kind of knew what the border picture was.
And it’s quite a basic data analysis, because it’s essentially just cleaning it and visualizing it. But I think in some of these situations, that’s almost the most important thing– that you can do fancy modeling in the long term. But really the fundamental thing on the day is, what’s the situation? Is this the kind of idea of nowcasting for a disease? You’re always looking into the past, because you have these delays in terms of how the data come through and under-reporting and those sort of stuff.
So the data that comes in today might actually be representing what happened a few weeks ago. So even just making those adjustments and giving them back to the people in the field can be quite a useful exercise. AUDIENCE: You’ve discussed how in chess, Go, poker, roulette– these kind of games– there’s been sound kind of breakthrough in which someone could be pretty much all the others.
What kind of game do you see next, where this could happen, where somebody could develop a new strategy or get more data than anyone else and beat the system? ADAM KUCHARSKI: So which game might fall next? I think poker, certainly no limits. We’re kind of at that point.
So there’s a tournament last year, where bots kind of played humans. And they played a vast amount number of hands. The humans came out with a very slightly smaller pot on average. So naturally the researcher said that wasn’t statistically significant and the human said that they had won. [LAUGHTER] So I think we’re reaching that point where, if you talk to professionals, these games are still safe.
If you talk to the guys working the algorithms, it’s only a matter of time. And I think it’s particularly interesting we have these strong feelings about games that are seen as an art. So a lot of these poker kind of games are scene as very experienced players with intuition and instinct. I think that’s their realm. So it’s quite interesting as computers start to come into it and challenge those notions.
So yeah, I think that’s going to be the one to watch in the next couple years. MALE SPEAKER: All right. If there are no more questions, I think we’ll wrap it up here. Thank you all for coming. Thank you, Dr. Adam Kucharski, for being here. It was a pleasure.
Thank you so much. [APPLAUSE]