# How Science is Taking the Luck out of Gambling - with Adam Kucharski

Feb 27, 2020thank you all for coming now, as Tom mentioned, I am a researcher at the Lung Hygiene School of Tropical Medicine where I specialized in mathematical modeling of infectious diseases, so on the face of it my work couldn't be further from the world. of casinos and playing cards and plastic chips, but actually

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and### gambling

have an incredibly intertwined relationship in every long-standing history and that's what I want to talk about tonight and since I'm talking about### gambling

, I thought I'd start with an example of how not to gamble so this is a story from a few years back and as you can tell there's two big floors to this lady's strategy how the first one is completely illegal the second one is clearly that doesn't work and the reason why I want to show you that I think when we talk about people dominating chance and eating the system, usually these are two topics that come up quite a bit, either you make them do something a little iffy or you have them present.I'm testing a system that's clearly not going to do anything very successful and what I want to do tonight is take a look at a third approach, take a look at some of the ways that mathematicians and scientists have dealt with games. of chance and using its techniques to gain an edge over the house I also want to see how the idea of flowing the other way how actually gaming and betting has inspired many ideas that are now fundamental to modern mathematics and

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and really lotteries I think it's a good place to start, because for me it was a story about lotteries that first got me interested in the mathematics of gambling, as I'm sure any of you who have played the lottery or thought about it playing the lottery you will know that it is incredibly difficult to win even the way we do it. measuring how hard it is to win is a fairly recent development, although mathematics has been around for millennia the idea of how we quantify#### luck

how we quantify a random event is relatively recent was one that was developed in th In the 16th century in Renaissance Italy there was an Italian named Joel amo Cardno he was a doctor as a doctor he was the first to describe the clinical symptoms of typhoid fever he was also a gamer and as a gamer he was the first to mathematically describe such games he actually described what is known as the sample space So this is the combination of all the events that could happen and obviously if you're only interested in one of those that gives you an idea of how difficult it is for the UK to win right now.In the National Lottery, as it stands, you must choose six numbers from a possible set of 59, so this results in a little over 45 million possible U combinations of numbers that you could choose if you bought a card. jackpot but there is one way you can guarantee that you will win the lottery you like this weekend and that is to simply buy every number combination now which may sound a bit absurd but let's move on. Wait a minute, like I said, there are 45 million ticket combinations for the UK lottery, so if you were to buy every possible combination and line them up end to end, it would actually stretch from London to Dubai, which What's more, each ticket costs £2, so if you really want to hit the jackpot this weekend, it will cost you around £90 million to do so.

That's clearly not a feasible strategy, but not all lotteries are created equal in the 1990s. For example, with the Irish, that philosophy had a much smaller sample size. specs a much smaller combination of numbers that could come up in fact there were about 1.9 4 million combinations each ticket is 50 P so it would cost you less than a million pounds to buy each combination and indeed a syndicate headed by an accountant thought about this and it's clear that on most weeks this is a pretty bad investment because the jackpot would be maybe a few hundred thousand and if you're spending almost a million winning a few hundred thousand doesn't say much to realize it's a pretty bad investment but if a transfer were to happen, yeah maybe this could be plausible and actually rather than extend to Dubai if you lined up all these tickets and the end to end combinations in It would actually stretch from London to Plymouth so yeah you have something that's a little bit more doable and what I started to do is put these tickets together and fill out each one that I hand out to get each of these combinations and then they waited they worked for about six months until the bank holiday of May 1992 when the transfer reached 2.2 million and they put their plan into action they took all these tickets that they had filled out they started

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over the stores and buying them and in many cases , this got attention so stores would usually sell maybe a thousand tickets in a week where all of a sudden they would sell 15,000 lottery yeah maybe unsurprisingly they ran into this a little bit and tried to stop them and like result. when the lottery draw came they had only bought 80% of the possible ticket combinations so it's still a#### luck

factor as to whether they win the jackpot, luckily for them hitting the jackpot with certain numbers was within the combinations they bought so they won that week unfortunately there were two other winners that week so they had to split the jackpot but when you added up all those lower tier prizes that matched five numbers four numbers went too with a profit of 300 thousand pounds.Now for me here you are going to hear the story which was just a fantastic illustration of how you can take a fairly simple mathematical idea, a good dose of boldness and hard work and turn it into something that is profitable and yes this is not the The only case where people have focused on this type of game for the UK lottery the draw is random so really the only way you can guarantee a win is to use this brute force approach by simply buying all The c combinations but not all lotteries are created equal take scratch cards for example at first glance scratch cards are completely random if you think about it a bit they can't be completely random because if you are producing scratch cards and it wins and just randomly generates which cards are going to be winners, there's a chance that it will, by pure chance, produce too many winning cards.

If you're a company that makes scratch cards, you want some way to control and limit what prizes come out like statistics systems, we call that you need to control. randomness, you want the prizes to be distributed fairly evenly across locations, but you don't want the generation to be completely random, and in fact, in 2003, the answer from the crinkly meringue service isatis was thinking of Stratos, they had given him some as a gag gift and was wandering outside of controlled randomness, he realized there must be some way for the IFI lottery to tell which winning cars without having to scratch them off every card. e a series of digits and some of these appeared twice three times but some numbers and symbols only appeared once on the card and in fact if these unique numbers appeared in a row that card was always a winner and bought more cards and tried strategy and every time cars that had these numbers in a row were guaranteed to win now what would you do in this situation?

You're not making a few just by looking at them, would you go out and buy tons? What do you think? Going back to the slide that I showed you at the beginning. the card-buying spree was, um, figuring out how long it would take him to buy enough cards and guarantee himself a win and he was a statistician and worked on geological problems making pretty decent money and he realized that even though he had a winning lottery strategy , better to stay at your current job so what you did um when you called the lottery and told them there was a hidden code on your scratch cards and you had cracked it and knew how to win the lottery of course you didn't he took it seriously so what he did was he collected the scratch card and identified some winners some losers a lot of vitamins and he mailed them to the lottery that night he got a phone call from the lottery saying we need to talk and this story represents many areas of gambling, often not professional players, you come up with these strategies that beat the system, and often people who beat the system don't or become professional gamblers for many of these People who bet are almost a playground for ideas.

This way of testing problem solving and skills that will actually apply to many other industries. The people who talked about these problems moved to academia, to finance, to business. and as i mentioned with kadhai i know this is not a new phenomenon really throughout history many of the great thinkers and mathematicians have used gambling as a way to refine their ideas around 1900 a french mathematician named Omni prawn curry was particularly interesting to bet on was one of Watson's lost universalists as a mathematician, lost people had gone to specialize in almost every subject area that existed at the time, I hadn't expanded to the point where that it was bigger today and one of the things that interested him was predictability and for him unexpected events unexpected results were the result of ignorance he thought that if something is unexpected it is because we ignore the causes and he classified his problems by what he called the three levels of ignorance the top level was a situation where we know what the rules are, we have the information, we would have to do some basic calculations so if you have, say, a school physics test you know what the physical laws of physics are given the information so you know in theory you should be able to get the answer right it's an amazing answer then you've done something wrong at work but it is not a kind of level of ignorance difficult to escape in theory the second level of ignorance according to panco a was the one where you know what the rules are but you lack the necessary information to perform the calculations accurately and He used roulette as an example so we left you the table and you started spinning the ball around and he observed that a very small change in the ball's initial velocity could have a very dramatic effect on where it ends up because it's going to be spinning. around this table over time and today mathematicians refer to this as a sensitive dependence on initial conditions and is popularly known as the butterfly effect there is talk in the 1970s where some physicists point out that the flapping of a butterfly's wings in brazil could cause or perhaps prevent a tornado in texas these small changes that punkaway first observed could have a big effect later on and we'll say later that the results are random, it's due to chance, but it's really a problem of information, then comes the third degree of ignorance this is where I don't know the books or maybe they are so complex that we will never be able to untangle them and in this situation all we can do is look over time and try to understand some of what we're looking at and it's really this. level of ignorance when players started targeting roulette they focused on they didn't try to untangle all these physical laws they just said ok let's look at a bunch of roulette spins on one table and see if there's a bias to see if there's anything weird Continuing with this table, but this raises the question of what do we really mean by order, what do we mean by bias, and at what point was Gray thinking about roulette in France on the other side of the oh no, a mathematician named Karl Pearson was also t thinking about roulette and Pearson was fascinated by random events as he said we can't have a real sense of what nature does we can only observe and try to make inferences about those observations and he is very interested in collecting random data to test thinkers once spent their summer vacation flipping a coin 25,000 times to generate data sets for analytes and he was also interested in roulette now luckily for him at that time the lomonaco newspaper would publish the results of all new roulette spins in the casinos in monte carlo now by bits and this is a fantastic data set he wants to prove that his ideas about randomness they have all these previous roulette spins to test it and started looking for ways to understand if they were random or not and that table of course has these black and red numbers and then it has 0 if you take away the 0 over time you would expect that the proportion of that can even be read I would expect it to be kind of 50/50 over time and when Pearson looked at the data he found that red appeared 50 point one five percent of the time this was more of 16,000 spins, so based on the calculation this wasn't that implausible, so actually that kind of deviation from the expected value is reasonable given the type of data set you had, but then you continued and he looked, for example, with whathow often do pairs of numbers appear now if you have a random process of the roulette table sometimes you would expect there to be a string of the same color appearing purely by chance it may be some red some black appearing what Pearson discovered was that the numbers they were changing too often you didn't actually get the same color strings appearing as often as you would hope they would kindly change and to him this was pretty definitive evidence that the tables were corrupted with low bias and as he says, if he had been looking at the chart since the beginning of geological time on earth he would not have expected to see such an extreme result and actually suggested they close the casinos and donate the proceeds to science as there just so happened to be something a little more going on with the casinos. feet on the ground it turned out that those Philharmoniker journalists instead of sitting by the tables and coordinating the numbers instead of sitting at the bar and making them up for this idea think again think about how you put it together was the probability of observing an event as extreme as one I have observed this was the first type of four is in what those hypotheses test today nowadays you know if we work in clinical trials or in particle physics experiments we use the principles that Pearson perfected at these roulette tables and known to understand if we have enough evidence to reject or accept a certain hypothesis, so in this case, the hypothesis that the tables were random and had enough evidence to say that was not the case and actually players using these ideas throughout the Victorian style as well. times and moving to the late 1940s, for example, medical students are used to these kinds of methods to go and unlike lazy journalists actually look at the tab Les this time they collected all the data and they found their biases on these tables wore out over time and certain numbers or areas came up more often for nothing and actually turned the vada around and bet big on these tables and the exact number was never known but i bought a yacht and sailed the caribbean for a year so pretty successful strategy the problem for the players those casinos realized what they were doing and would make sure the tables were incredibly well maintained and you didn't have these biases going on but back in the 1960s and 1970s some physics students realized that this actually leaves you in second level ignorance because if you have a very pristine and well-maintained roulette table, It's not a statistics problem, it's a physics one like one of them said it's like having a planet orbiting a point where you have a ball going around and the seventies are a group of students from the University of California at Santa Cruz who actually started doing these calculations and looked at roulette spin they said ok to start with the dealer will spin the ball and it will spin around the edge of the track around the edge of the table and often a couple of turns before the dealer calls no more bets, in other words you have a window where you can collect information about what the balls are doing and act accordingly, you can place bets during this period, over time it would fall to the track and would spin freely. these deflectors and they land in one of the pockets and what did he do trying his strategy on different tables in his lab he realized that if he could calibrate his model, if he could write the equations for the physical system, he would get the ball he is slowing down and your fall is stopped, you write these equations that calibrate them into a specific table and then in that initial time you could gather enough information to improve your predictions about where th table land you'd never get exactly you didn't need it you just need having an idea of what region the table is going to land in enough to get an edge over the casino is all well and good of course doing it in a classroom and working to the locations or the equations but in a casino you have to do it in real time you have to do it on the casino floor while the ball is spinning so what these teams actually did was come up with hidden computers to do is to calculations in person now portable technologies of course all around us these days but the first Wellwood computer was designed for this purpose and since it was a new technology of course there were some drawbacks with this it would often occur electric shocks for example and on top of this amazing things are very sensitive to initial conditions so if the weather changed they would have to re-calibrate the bathroom table on one occasion they were actually losing federated money and not they could work. but what until each one lies like an overweight tourist further down leaning on the table and ruining all their predictions so really these kinds of methods were somewhat imperfect in theory they worked very well but these kinds of stories have been a bit sporadic but it was Not only roulette during this period, players started to target, they all started to target other games and in fact one of the most successful players in the world is a man named Earl Benton and when he was a student in the 70s he found himself with this. check in at an atlantic city casino that's him this sign meant one thing card counting clearly works an old idea of card counting is that if you have games like blackjack you're trying to get to some total pain , the dealer and you know the impact. you try to weave 21 but not bust so you have draw cards and you try to get close to this total and at first glance this is a random game the draw is completely random what will come up of course not for a deck. of cards because if certain cards have already turned up they can't respawn until you shuffle the deck so if you can gather information on what has already turned up this can give you an advantage over the casino it can give you an advantage against them now again. casinos started realizing that players were keeping track of what was inside the deck so they started using more decks of cards instead of one they would use a full pot and it became much more difficult than the card to come because if there are several of the same card in the deck it is much more difficult to keep track of what comes out which casinos do not have vertically giving players a very significant advantage because at that time older people tend to use what it's known as dovetail shuffling so you're probably familiar with dividing the deck into If you shuffle the cards together now or if you do it once you keep a tremendous amount of information about the cards so just to give you an example let's say we have a sequence ence of cards in order from Ace to King if we do a dovetail shuffle we split them I have colored them just to make life a bit easier and then shuffle them now they may not fall exactly on the weave which you can see here on two different colors you have to figure out what is known as ascending sequences of numbers so the cars have been shuffled but really if you know where they started at each point as you go from left to right you know there are only one of two cards that could be appearing and there's not really any other magic tricks based on this fact so if you get a deck of cards and you move one and then randomly shuffle you can detect with the move card because you don't will fit into one of these ascending sequences as mathematicians have shown that for this type of shuffling you need to shuffle the deck at least half a dozen times to get something that is as good as random and in casinos in that period people were only really shuffling once so if you can trace what happened I have a lot of information about what is going on and in many cases they would actually shred to pieces again in another application of computers and casinos to track the cards they have entered previously, whereas before, card counters would measure what is coming and then get some approximation of what is left now, in reality, at each point in time they would know that it is only one of the two cards that could have been punched. over time let's say there is one card that is advantageous and less beneficial how do you make that decision about how much to risk in that situation and what I want to do is just speak with a simple example let's say we have a coin toss and I'm going I'm going to offer you a skewed bet I'm going to offer you odds of two to one if it comes up tails so in other words you name an amount of money if it comes up heads you pay me that amount of money if it comes up tails then I wi I'll pay you double the amount that you mention so clearly that it's a pretty stupid bet on my part.

I'm giving you an advantage, but how much would you be willing to risk? After all it's a coin toss and you'd still have a chance to lose money I just got a quick sample of hands here I'd be willing to risk £1 on that bet sure pants ok so I think the Most of you will hold your hand up if you're willing to risk £10, okay? how about a hundred pounds, okay, and that's 500 one time, okay, so there are a few people left? I'm not sure if they're paying with monopoly money, but okay, if you put your hands down, that wasn't legally binding, so why, but I want to give you a chance to get a feel for it, gauge the risk of how much you're willing to listen to a situation and i know if you can see actually the hands will drop a lot between ten and a hundred pounds but this is all pretty big question for players naturally in the 50's a physicist named john kelly started thinking about this biased betting idea lets say you have inside information and you have some advantage over a sportsbook or casino how does that play out in this situation for you um even though i gave everyone the exact same bet mathematically it's the same offer your perception of the value of that was very different, some of you valued it at a pound, some at ten, some at 500, what's the optimal thing to do?

Exactly there's this concept known as utility and economics the value of something changes depending on how much money is in your wallet for example and how much you're willing to lose what Kelly did is she looked at these contrasting goals that you have if you want to get a good long-term performance so first you're trying to make money because you've got a partial bet we're also trying to avoid going bust essentially you're still flipping a coin which sets up the possibility that you're going to lose you know if I don't believe that nobody here would have bet their house on this maybe you would you could have an angry family but in this case you want to exploit it somehow but also limit your losses.

What Kelly did was she couldn't find this formula, so apologize to my handwriting, basically, you have the odds, which in this case is two. the probability that you will win this win Q: the province you will lose and this is the optimal fraction of your money to bet on a given advantage over someone in a betting situation, so the bet I just showed you was the probability of you win is 1/2 because the probability of the coin toss is also in fashion so if we plug these numbers in you get the next kind of equation a little bit of arithmetic you can end up with 1/4 so in an if situation you want to maximize your long term money growth it is optimal to risk about a quarter of your income just think about when you are raising hands if that was a quarter of you know where you are

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advantage of or not now some of you might think ok, that's what ok, you showed me a formula.Let's try it now of course I could take Carl Pearson's approach and spend the next half hour so flipping coins to convince you that's kind of boring so what I thought I'd do instead is show you some simulations if adopted different strategies, what kind of results would you get, so here along the vertical are your funds. I'm going to assume it starts with a hundred pounds and at the bottom is the coin tosses so we've played this bet again and we'll see what you'd end up with time now you could have felt a quarter of my money you know that's take no chances so i want to go big you might say well i want about 80% of my money and in this case if you just do a random sim and what might happen is you'll get a couple of big wins at first you know you're getting approaching a thousand pound blues a lot of money making a lot of money is exciting and then losing all your money and going bankrupt that's exciting if you adopt this optimal strategy of Pelley and b et 25% what will happen is it will take longer it will grow a little bit slower over time but you won't go bankrupt and in fact in the long run you'll get something that takes off I might say it's still too much for me I'm going to bet 10% of my income on each of these your salaries and in this case if you do it randomly it will take a long time to grow so you will not go bankrupt but it will take timemuch more betting your money than you notice this kind of increase is quite steep in the end and that's because you're reinvesting your money it's this kind of interest compounding over time effect again this is just a simulation it's a coin toss it's kinda random so what we could do is simulate it takes ten times instead of kind of an instance here do each of these ten times and in the case you bet 80% you end up with something that nine of these they go bankrupt one of them makes a little money, but in most of these cases you will run out of income pretty quickly if you bet 25% of this optimal amount, then it grows a little slower, but you don't go bankrupt at all moment and eventually it will increase your income and then again this 10% is just much slower growth so it just takes a lot a lot longer to build this on top of the series of bets and this is the strategy that people use to play to blackjack, playing these games a lot to manage your bankroll and actually the concept of utility and money management is obviously important in finance but it underpins the entire insurance industry because whether or not we insure something depends on how we value it, you knows if we are willing to risk the fact that we could lose it and cost us a lot of money or if we take those small bonuses that would depend on the value of the item, the implementation of the strategy, of course, for card counters, hide the apartment like a camera of letters.

I talk to students who didn't say card counting is easy. These people who are successful people like Bill Benta soon became very well known in the casinos of the world and found themselves banned all over the world so they turned their attention to a bigger game, a much bigger place to bet. Now this is the Happy Valley Racecourse in Hong Kong. If you've ever been on a Wednesday night, this is where all the action is. a typical race day they bet around 150 million dollars the game is a huge part of what's going on here all the attractions of this for the players is that it's pretty small um well first is they're pretty convincing it's an honest operation and it's a small group of horses around a thousand horses from running again again so you can generate a lot of data to look at and try to interpret which horse might have a good chance but to do that of course you need some way to convert the data into a measure of performance which horses are the best which horse is going to win and to use these teams they draw on an idea that was first put forth by this man, this is Francis Galton, a Victorian scientist and actually cousin of Charles Darwin and as and You can see that they shared some passions, particularly for ties and sideburns, but there were some differences.

Darwin was actually meticulous in shaping his research, so even evolutionary theory can see a lot of his fingerprints on this. Now I'm going to do it in kind. from thinking of himself more as an explorer, he would dabble in anthropology and psychology and biology and economics and then he would start a little bit and then he would give it up and drift off into something else and one of the things he was interested in was heredity and he asked a year on a few occasions he would send his friend seeds and grow them for him, it's sort of an early approach to crowdsourcing and being able to report and one of the things he's noticed is if he grew the season and had the subsequent generation if those were For example, taller, you wouldn't expect the next generation to be taller and taller and taller than over time you get a feature that you referred to as regression to mediocrity that surpasses By the time these types of features converged somehow and the influence of the older bloodlines could smooth out the variation, he wanted to understand this in a little more rigorous way and it is actually a horse trainer who introduced him to a figure that allowed him to frame this type of idea and it was the following it was a diagram it was a square that represented the characteristics of a horse and its trainer had proposed that approximately half of the characteristics were explained by the mother and father so we have a couple of squares for those and then for the remaining features, maybe the four grandparents explain a quarter and then the great grandparents explain another part and so on and this idea was one of the founders of what is known as the theory of regression in statistics, this idea that we can take a number of factors and determine how they influence the characteristics of a certain object or system and we could have a similar approach in horse racing. ng we could say well suppose this chart is horse performance and we have many different bits of data analysis and we could say well maybe each of these data bits explains a certain amount of horse performance of course , this is a bit simplistic, right?

Because just like with heredity features, where, for example, some of the variations explained by parents that might also be shared with the gram, the catchiest horse, these features will overlap, some of these will explain multiple aspects. so these clippings are going to be a little messier and what's more we may not be able to explain all of the performance of the horses there may be a part that we can't explain yet really the goal from a point of view statistic is try and minimize this unknown amount it was actually in the 80s but mentor visiting librarian Nevada found an article by two researchers named Roose Bolton and Amanda Chapman who work in marketing they st Actually I will do it wrong and they are not according to the outline of this method for horse racing, this approach of turning data into some kind of performance measure that you could use to make predictions and, as Bill said, it was the idea that spawned an incredibly important multi-billion dollar industry , it was actually Bolton food, it was the only paper he wrote on horse racing during his PhD and it was really kind of a side project, but it had a big impact on this industry and I'm doing the analysis that there are early unions in Hong Kong.

Certain things would turn out to be more important, for example, in one of his early investigations, the number of races a horse takes in one will tell you a lot about how it will fare. he runs more races then he'll have more experience and that will give him a better performance in the next race but they actually avoid doing it because they really know it's a jumble that all these things are kind of overlapping and explaining one thing and it's not clear that just because something is important has a direct explanation. There is a fairly common problem in statistics.

It's known as this idea that correlation doesn't always mean causation. they have at the bottom wine spending per year cambridge universities on the vertical are exam results suzy as you can see this is a pretty strong correlation across universities this online memo has better results and this is again the only thing that actually happened is countries that have higher per capita spending on chocolate tend to win more Nobel Prizes however lovely you are eating chocolate would make your Nobel Prize winner and think why we make you better in exams there's clearly something else going on there some underlying feature which explains all these things and really these syndicates so don't try to untangle it and that's one of the notable things that they have I don't wish to be experts in this kind of field for them, the question is which horse is going to win, not why that horse is going to win, so it's almost back to the idea of ignorance, they are embracing their ignorance and saying yes.

I don't really care, I can't explain exactly how it goes, I just want a method that will give me good predictions now, starting by measuring performance is a good thing, but actually when you have multiple horse races you can get some little unexpected results happen, so just an example of a simple one, suppose we have two horses, we have one that half the time does it right, half the time it does it wrong on the day you don't know which one it will be and you have the second one. horse that is a bastion of reliability in every race exactly the same performance now on average over many races they have the same type of performance because the best on average will cancel out and in one race it will be essentially lly a 50/50 because it depends completely on one race if the top world number one is having a good day or a bad day so these two horses are racing each other it's basically a coin toss it's a 50/50 chance because the top was having a good day , he will win.

If he has a bad day, he will lose. That's kind of intuitive, but if you had a third horse in the mix, something a little weird happens, so let's assume we have a third horse here, which some days performs slightly. better than the middle horse the performance on sunday is slightly worse so again on average all these horses are performing the same now by the same kind of logic the top horse here again has a 50% chance of win because half the time it will lead four and half the time it will lead last so there is still a 50% chance that the two remaining horses if the top horse does not win we can apply the same logic of these two horses in the bottom if horse number three has a good day he's going to come out on top and if he has a bad day he'll lose so if the best horse doesn't win split the odds between the two horses for the main links, you can't decide now, we'll just see what's going on. here all these horses on average have identical performance but it is the variability that is different and in fact the better horse because it is more variable in this type of race has a higher chance of winning you can actually apply the same kind of logic to other situations so say we have an election where with the absolute majority system so the person who gets the most votes wins if there are three people who on average would expect to get the same amount of votes, he's actually the most polarizing candidate, the all-or-nothing kind of guy who has the best strategy because he has the best chance of winning in this situation if you want to take the example a little further you can look into job interviews or even dating if you have a bunch of different suitors in thi In this situation, it makes more sense to adopt this kind of all-or-nothing pot strategy if the goal is to date multiple people first, and This is not a problem if there are only two in the race, but because you have multiple competitors, you get these kinds of weird dynamics that arise and really the math of games and these kinds of features of interest to mathematicians for a long time actually origins are played through the origins of games mathematics originated with poker in the 1920s a researcher named john von neumann brilliant mathematician was the youngest professor in the history of berlin university was not that good at poker although at first glance poker is a perfect game for mathematicians is the probability that you will get a certain hand the probability that your opponent will get a different one but von neumann realized that there is more to say than real life it consists of bragging about little deception tactics of asking me what the other man supposes. what I'm going to do and I wanted to study that kind of feedback between what you think, what they think and they think you think.

It looks like a simplified form of poker. A situation you see with two players each deal a single card and then they put some money in the pot at first and the first player has the toy so they can keep it, in which case they just flip their cards over and they compare them or transmit the bets and then it's over. it's up to the second player to decide whether to stick with that bet or not, so two players, one money card in the middle, what a woman found out is that in these types of games you have almost a tug of war because each player is trying to Maximizing Your Win While Trying To Minimize Your Opponents Play If you believe that in a game like poker, whatever your opponent wins comes out of your pocket, so you're trying to maximize what you get while also trying to minimize what they get which means there is this kind of balance point at a point where the two types of conflicting forces balance out and analyzing this situation for the game, he found that this situation where neither player gets would benefit by changing their strategy this point of imbalance for the first player the strategy was as follows that if they have a very high card they should intuitively raise the bets this makes sense if you have a good na card you know you might as well bet on it if they had a medium card it didn't make sense for them to raise the bets it didn't have a great chance of winning but it still had some chance so in other words they should keep goingwith our existing bet when Vannoy Minh analyzed what happened when you got the lowest type of cards he found that there is no point in holding your back if you turn over cards you are likely to lose, you should instead raise the stakes, otherwise words you should bluff and actually raise this point that players often had in poker, players often bluff in games. but it was always seen as a quirk of human psychology, some kind of innate delusion that humans come up with, but he was von Lohmann proving that it was a mathematical necessity, in other words he showed that bluffing is a necessary part of life and yes this this The idea has fundamental game theory that you can have these strategies together in this very simple version of poker, although there is almost a set list of rules that we can follow, in other words, if you hit a high card or low you raise the stakes if you get a middle card you keep what you have and any game where you got information in front of you so other games eg things like tic tac toe checkers chess all these games, in theory, have a fixed set of rules. it's known as pure strategy so you follow these exact rules and you'll get the optimal result so if someone does tic tac toe I think most people can figure it out when they're younger and realize there's a mov set is and if they always do it they always get the best possible results, of course not all games are like that. you're doing, they can take advantage of that, so it's not the optimal type of strategy if you're trying to make your opponent's decisions as difficult as possible and these types of games are what you're trying to do. make your opponent indifferent to change so you have that tug of war going on so if they can win more by adopting a different strategy you don't have the optimal approach and what paper scissors on if you want to make your opponent choices as difficult as possible what you can simply do is pick randomly if you pick completely random options among those your opponent won't be able to make any money from you in the long run so it's the best you can do then what paper sc issors are there three options it's not too hard to figure out picking at random will make your decisions difficult but games like poker are much more complex you have a wide variety of choices you can make during the game so it's not something that you can write with pencil and paper unfortunately we can fall back on a technique that one of Tom Palomas's colleagues came up with and this was a petition called Stanislaw ulam and unlike many mathem Attics, he wasn't a big fan of working with a bunch of equations at one point, he was working on a whiteboard trying to solve a quadratic, he got to the end and Ninoy was so frustrated that he went home. for the day, so it really wasn't her thing to do math with all this algebra.

One time he was playing cancam field, he is a version of solitaire and he wondered what the probability would be if he just laid out the cards. What is the probability? you would have a situation where you could win that game if the cards fell favorably. He started looking for calculations and realized that it was just a lot of effort, so he thought well, what if I j? Just spread the cards out a few times to see what happens, in other words what if I simulate this process a few times and get an idea of how likely it is and the timing?

Lamin von Neumann working on the US nuclear program. Neutron collisions and they thought the project was the hydrogen bomb and again these were random processes where you couldn't carefully write down the formulas and solve them and they realized that their method would be incredibly powerful because, being a government program, they needed a code name. that's what they called it the Monte Carlo method ulam I had an uncle who played a lot at the time and the Monte Carlo method has become a fundamental part of science I mean in my line of work where we try to look at disease outbreaks , you've got something like a bowl of Zika is an incredibly complex set of interactions, it's not something you can write down with a pen and paper in an orderly fashion, so we use these simulation-based approaches that simulate these random processes to understand these It also now appears as a sports bet when trying to understand how these kinds of complex team interactions work and it applies to poker teams as well.

Teams have used this kind of approach for poker games where you can't solve the equations, you can use a simulation-based approach to make computers learn the mischievous Alan Turing in one of the fathers of computing and when he thought for the first time on this idea of machine learning, said that actually if you are trying to build an intelligent machine. it makes no sense to build the mind of an adult it does not try to build the finished product with all the movements of knowledge it makes multiple senses to build the child's mind and let it learn let it figure out how to play these kinds of games and this is what these teams do of poker: they create these algorithms that they can learn and actually the way that they learn is perhaps a little surprising because what they do is get these algorithms over time to employ what's known as regret minimization so when they play these games billions of times against each other at each point when they've made their decision, they look back and say could that be better if I'd done something different so that each point has an artificial measure? of regrets for every decision they make, and in fact, there's a lot of evidence from some neuroscience studies on the neurological side that that ability to regret is quite important in learning gambling.

There have been studies of people who have some brain damage that is responsible. for regret disabilities now i look back and wonder how i would feel if i had done something differently and if people are often perfectly capable of playing logic games game and have to learn to play optimal strategy that is something with that they really struggle and in fact a lot of economic theories were developed not around looking back but around what's known as expectation maximization, in other words you look ahead and say if I did this, could I earn money? If I did this, could I earn more? how to employ that power of regret as you go to look back on your decisions as you take these risks and actually these teams have employed these algorithms and have gotten these computer BOTS to catch it so many times that the last year they announced that poker resolves well to be specific to two player poker where states cap these BOTS a page so many times they've laid out the strategy you're not expected to lose money long term so even if you're playing against a perfect opponent this bot wouldn't lose money over the course of a very long game um funny enough actually a lot of the players that came up with this system a lot of the computer scientists aren't very good in poker. they themselves, by their own admission, are not poker players, so it will be a kind of market illustration of the power of these algorithms: there are people who are not particularly good at poker creating poker bots that could beat any human , but they are yes this is a remarkable achievement but of course there is a downside to this and that you are assuming your opponent is perfect if you are looking for this optimal strategy that is inherently defensive because you assume your opponent is perfect and you almost i'm giving them way too much credit so if you have a flawed opponent and you're coming up with a strategy that zooms they're perfect you're potentially not exploiting them as much as you could i just thought i'd give an example of these types of failures that could happen let's go back to what Paper Scissors what you should do just turn to the person next to you and play a couple of games of what Paper Scissors with them please ok thank you Ladies and gentlemen, okay I can see there's a couple people back at UM playing best of seven or something but hey what I'd like to do just come quick show of hands who opened with rock , ok, some open quite a bit with scissors. one that opens with paper is ok not that many actually babe um so typically in these types of big competitions we play a lot of times um it's the newbies that open vaak often men sorry scissors tend to be the most popular type of people that they play a lot of these games um the roles aren't always chosen to go in also think about what happened between the first game to the second game you play because in a pretty big type of study what role scissors what happened was that people who they win the first round they usually stay the same move for the second try so this old cut, the military adage, isn't it about the generals who always fought, always fought the last war, especially if they won it, so as an idea that if you won, just stick with what saves the people who lost though and they will? it often switches to the move that would have beaten the one they lost so if they lose to rock they will often switch to paper next time which is why it always happens but in these kinds of big competitions these kinds of patterns arise , although the optimum to do what paper says is to completely randomly pave people, don't they fall into these predictable patterns?

In fact, a few years ago there was a story in Japan about an electronics company wanting to auction off their art collection and they approached Christie's and Sotheby's to hold the auction. Obviously, they were both looking forward to it, and so the head of the electronics company decided that the fairest way to solve it would be with a game of rock-paper-scissors. Now, Sotheby's thought that's perfectly random. a 71-year-old young daughter who was playing tirelessly on the playground, so she asked her daughter to teach her some rock-paper-scissors strategy and sure enough, they walked into the Sotheby's boardroom to discuss to anger. n and getting Christie's with a Christie's strategy came out a winner so in these kinds of cases exploiting those patterns and that kind of predictability and knowledge of what happened before it can be extremely valuable but there are some challenges to that and particularly if you're playing with computers one of the challenges from a human point of view is the limitation of our memory so come to this point what enlightens you now is you all trying to memorize that number for me so i'll give you a couple of moments, can I take a quick look at it, okay, but who wants to try to cut it?

Any volunteer? Yes sir, very, very close. Gavin got really close to anybody to try to build on that yeah okay so what's his name Steve Steve run report to Steve ladies and gentlemen now Steve is something pretty smart there so if he They saw, um, I spent, we did, so I asked them to memorize ten. digging is and that was actually a little torturous for me because in a lot of psychological studies, people who are presented with numbers can usually memorize around seven and recite them, um, so five digits in what, oh, sorry, yes, I have a PhD in mathematics.

You're okay, I actually made it even harder, it was cooler than I thought. I apologize, um, for what usually people can remember as a local phone number that may be UM members that they struggle with, but what Steve really did when he was kind of the numbers he didn't recite there some kind of guy said like six ten to sixty in 1091 so that's what he did he lumped the numbers he wasn't reciting temperature information he was dividing it into a smaller amount which put him below that threshold you can memorize and actually other countries so in France Vince if you go your phone numbers tend to be paired which actually makes it easier to remember the numbers because it's so much easier for you remember member of these curved chunks of numbers instead of a single sequence.

I can't guarantee that all of you will remember this number when you get home tonight and that's actually if you take it apart and add a little punctuation and then flip it over that's just the time and date of this talk for everyone you know that number and can recite it and the reason is that you have gone from ten bits of seemingly arbitrary information to one that clearly has some meaning to you and this the ability to shred is something card counters employ because clearly memorizing an entire deck of cards is incredibly difficult so what they do is they use what's known as grouping, they'll group into, say, low cards, medium cards, high cards and then more than having to memorize a whole deck that only has these three cubes to remember and besides it's kind of opposites no memory you don't have to remember everything you can justkeep track of these three values, of course there are some people who can memorize the first numbers of the cards, you know, the best memory champions can memorize about a thousand cards in an hour, now thousands of paper cards can be marked and the way they do it is they actually add characters to the cart this will turn them into a person an object and they'll attach a story to it that's similar while everyone will remember this because they're not remembering a number they're remembering an event they remember one single thing that is much more memorable and that is you really humans can get around this idea of memory limitation but there are some downsides to learning about your opponent and remembering things and trying to take advantage of it and that if your opponent is incredibly might teach you the wrong image of themselves, which is why it's known as the problem of getting caught and exploited if you're playing poker, for example. lo, your opponent could pretend to be very passive and pretend to be very timid and then once you learn that notion of how they play they might actually change their behavior and exploit the fact that you've learned the wrong perception of them, it's not just the poker that happened a couple of months ago you may have seen is a Microsoft released a bot for Twitter to learn - you can see where it will try to learn the language with no ideas have conversations and improve your ability to learn tips for Twitter users and for Chile decided to teach him some unfortunate tricks what really happens in 24 hours had to be removed because he was coming out with so many horrendous opinions.

I think that's an example of you having a pretty smart algorithm, but if it's being given the wrong picture of what it should be doing, it can actually go a long way off. very quickly and at this point if you have talked about poker bots you would pay billions of winnings to find your strategy. I have talked about these BOTS of these languages in many situations these bots are not see and complicated in finance for example the programs are designed to be fast if you are trading if you want to get compensation do it quickly so having that lots of complexity and nuance and latinity in your algorithm is not going to do the job you know you really want to keep it as simple as possible in many cases these high speed algorithms you may only have a few lines of code and there is a researcher from economy you might as well put it where there are ten lines of code that isn't even bug level intelligence it has no rationality or nuance it just tries to run trades as fast as possible in some situations this means you may run into problems recently there was a case in Norway where two traders noticed that a US stockbroker had an algorithm that fed trades into the market and the algorithm always reacted to a trade the same way, in other words if you traded with it it would change its price by the same amount no matter how big that trade was so what these um though I did was teach the algorithm what to do so it made many small trades so it would go up in price and make one big trade and profit from the difference now this ended up in court these two exchanges were charged with market manipulation and received suspended sentences, but then there's some kind of Robin Hood's reputation in the media for his annoyance went to appeal and his appeal centered around that if they had been trading against a stupid human that was doing this that wouldn't be a problem, the problem it's that they were trading their stupid algorithm. presumably created by a human being who hadn't been thinking about what he was doing and what should be different how was the notion of skill and responsibility different because there's kind of a one step and actually this argument held up in court and in this situation they were actually in you know this distance was revoked and it's a first as very simple algorithms have problems um similar points actually to the US the stockbroker was introducing a new algorithm to feed orders across four markets you have a lot of client orders coming in to the broker and you would like to feed them they had eight servers doing it what they had was a counter to keep track because obviously if you get a lot of orders and also send them to the market you want keep track of how many you've completed you don't want to accidentally do too many and they had one of these tips on each server and then actu they alized their software but by all accounts they didn't add the counter to the 8th server so seven servers knew what they were doing the 8th which is doing its thing and when this went live what happened was the 7th they were behaving as they were supposed to, the 8th just filled the market with high speed trades and in fact when they found out what was going on and shut it down in 45 minutes he lost about 450 million dollars so that's a hundred hundred thousand dollars a second for this runaway algorithm because it was acting so fast and way beyond what consumers could control and you could attract that bad luck you could call it a skill bug and I think those cases around these types of games and opportunities events that are currently unfolding in the US in recent years there has been a major crackdown on poker, particularly online, and also in 2012 there was a The crackdown on New York poker rooms and the gentlemen who ran a poker room were taken to court and charged with operating a betting operation now many games in federal law are defined as gambling, but poker isn't one of them, so it was actually disputed whether or not it was gambling, and if federal law gambling is defined as anything that is predominantly due to chance, then any predominant game will be dissolved. chance is defined as gambling so what happened is this whole legal case was based on their poker game of chance or game of skill and they got mathematical economists and pointed out that in a single poker game of course as a element of luck because you have this deal, but equally in baseball it's someone throwing a single bull, there's going to be an element of chance involved, but over the course of a game of poker it's usually more skillful. l players won and this is the first time a US court has ruled whether poker was a game of chance or a game of skill and ruled it a game of skill there is a footnote to the story the following year when he went to the state appeals court now in new york state law, gambling is defined as anything that has a material element of chance, so think about that this is a much narrower definition of gambling, it's not predominantly chance like anything with a material element which clearly poker does have and under this condition it's defined as gambling and your debate is ongoing if you know any kind of fantasy sports in the US and many of these systems where we have something which is luck we have some skill where we really define these things as gambling I think there is often a temptation to put things in boxes actually with the situation we like to say box by a lot and there is a ca ha of skill I think generally if we're good at something, it goes in the box on the right, but bad is something that goes in the box on the left and that's really a bit tempting, but I don't think that's a realistic notion. necessarily. roulette and lotteries are much more of a spectrum actually games that we might think of as the archetype of luck things like roulette actually if you have a skillful approach you can master that chance and you can turn it into some element of a game of skill and Even games that we might think of as incredibly almost exclusively games of job skills like chess can have amazing results. blue made a move that was so unexpected and almost so subtle that it threw him off and everything convinced him that he was playing something there just beyond what it was. yeah, I've never seen anything fully about this ability before, it turned out what happened there is that Deep Blue had run into a situation where it couldn't identify the best move and in that situation it had been programmed to pick randomly, so that this this set of games that is one of the milestones in artificial intelligence over humans in a game that is thought to be purely skill was actually shaped by this chance event and I think these kinds of illustrations show why to bet and why what these types of games Chance is very important because, whatever your views on casinos and sportsbooks, gambling is an inherent part of life.

Gambling is an inherent part of what we do. to make decisions with hidden information we have to deal with uncertainty we have to balance risks with rewards i think that is why historically there has been so much research on us and gambling and continue to do so because really if you want to understand luck and chance decision making and risk, then there is arguably no better way to start than with a bet. What is your opinion? We are investing in the stock market. Should I pay someone a 2% fee for their ability to invest my money or should I just trust buying the market?

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