The practice of wagering money (or something valuable) on an uncertain event is as old as our history gets. From dice to blackjack, a lot of the big names in science have eventually been fascinated – or even involved personally – by the connection between risk, reward, and probability. Yet, the economic incentive has not been the only reason why it was important to decode the laws of probability. Instead, they have been driven by the quest to tame randomness using maths, intuition and the scientific method.
In hindsight, gambling has been a laboratory in which many ideas have turned out to have practical applications in the financial world. As we walk down the road that connects Las Vegas to Wall Street, we will learn how they have shaped quantitative investing and led many legendary investors to success. However, we will see that knowledge is not enough to make it through. We need to take one step further and ask ourselves: what does it take to play the odds?
At The Beginning Was Chance
Gambling is by far one of the world’s favourite – and oldest – hobbies. Whether we talk about commercial casinos, bookmaking, lotteries or online betting, gambling definitely plays a relevant role in the global economy. Only in the US, the revenues for 2018 have soared to the record-high $41.7 billion dollars, according to the data gathered by the American Gaming Association.
However, even without the perks of modern casinos, it is true that humans have always found it appealing to wage valuables on the outcome of uncertain events.
It also seems that this behaviour has been somehow instrumental to the evolution of the audacious – yet complex – relationship between men and probability. For example, in ancient times it was not uncommon to believe that betting outcomes reflected the whims of gods or, in general, were influenced by external forces that depended on one’s fate.
In this sense, the earliest concrete evidence that we have about forms of betting dates back to 2300 B.C. in which a game of chance with wooden tiles is described in the famous "Book of Songs" – the oldest existing collection of Chinese poetry. Later on, around 200 B.C., the Han dynasty organized a state-funded lottery to finance major government projects like the Great Wall of China. In Europe, the earliest records of lotteries were held during the Roman Empire, at first as amusement at dinner parties and occasionally to raise funds for the city of Rome.
However, it was not until recently that the properties and nature of random events have been formalized and become well-known.
Although gamblers can rightly claim to be the first movers in the field of probability theory, it was thanks to the works of many well-known scientists – Bernoulli, Fermat, Poincaré, and Laplace to name a few – that gambling slowly turned from art to science. Randomness was discovered not to be an indomitable force but instead to obey the complex rules of maths and statistics. Along with this, the scientific method was introduced to manage and measure risk, calculate probabilities, and determine the optimal strategies to follow to decide under uncertainty.
When we put things together, we understand why it appears useful (and fascinating) to retrace the footsteps of the history of betting.
It is because it has been the laboratory for many brilliant minds of our time to develop ideas that have gone far beyond their initial scope (e.g. think about random number generation and the development of the Monte Carlo simulation method) and have radically changed the way we see the world, contributing to advancing our knowledge in many other fields.
Finance has drawn heavily from all the knowledge acquired in the field of gambling. Indeed, although they are very different, they both involve making decisions under uncertainty and – as we will see – it did not take long to figure out how concepts such as risk, money management, and behavioural biases could be transferred from one domain to the other.
Start integrating AI into your investment process with the most advanced no-code solution.
Book A Custom Demo
The famous 1985 book co-authored with Ralph Leighton "Surely You're Joking, Mr. Feynman!" is a must-read book and a collection of the incredible stories about the life of Richard Feynman, the American Nobel-prize winner theoretical physicist that is widely recognized as one of the fathers of quantum physics. His life was undeniably extraordinary. Aside from being part of the Manhattan project – the US military programme that led to the first atomic bomb – he contributed massively to the fields of quantum mechanics, quantum electrodynamics and particle physics.
Yet, to the general public he is remembered as a man of sharp wit, biting sarcasm and curious mindset, qualities that have brought him to embark into many ventures, from playing music to betting at the casinos.
One story tells us about what he learned during his PhD at Princeton University. In the late 1940s, he visited Las Vegas with the purpose of calculating the probabilities for each casino game. After all, as one could guess, there is a long list of men of science – from Girolamo Cardano to Edward Thorp – that eventually tried to apply (or leverage) their advanced mathematical and statistical knowledge to get some advantage over the house.
Soon he confronted himself with the house edge – the mathematical advantage that the casino has over the players as they play overtime. So, for example, in the American roulette, despite there being 38 possible outcomes (i.e. the numbers from 1 to 36 plus 0, and 00), players can only win 35 times the initial bet.
Indeed, as players can only bet on the numbers (and not on the zeros), the casino expects – on average – to win the stake bet by the gamblers 37 times out of 38, while it expects to pay out 35 times the initial pot only once out of 38 times. So, from the casino’s point of view, the house edge can be calculated using the following formula:
So Feynman started going from table to table and worked out how much he could expect to win (or more likely to lose) from each game.
He decided that craps – in which players wage on the outcome of the roll of a pair of dice – was a good deal: for every dollar bet, he could expect to lose 1.4 cents on average. So, the story tells, he started playing and – as the game went by – he ended up losing five dollars (a little less than what is now a one-hundred-dollar bill) and that it was enough for him to quit the idea of gambling.
As he concluded there was no optimal strategy to get a systematic edge over the casino, one thing puzzled his mind: he had learned about a gambler called Nick the Greek (i.e. the nickname given to the famous high-roller Nick Dandolos) that was known to win consistently and he could not figure out how this was possible given that, in the long run, the house always wins.
When Feynman asked him how he managed to make a living out of gambling, he answered "I only bet when the odds are in my favor".
As Dandolos further revealed to Feynman, he was well aware of the edge that casinos had. Yet, this was the reason why he did not bet at the tables but instead made wagers with the people surrounding them, as they had biases and prejudices that he could exploit.
For him, to work out the numbers and probabilities of games had not been the hardest part. What made him successful at gambling was that he did not only know the game and its rules, but he knew players as well and this made him able to convert his knowledge into an effective strategy – something that seems to be true also in the world of investing.
Les Jeux Sont Faits: Lions, Roulettes and The Brain
The previous story is helpful because it puts into perspective many elements that, as we will see, come up frequently when we talk about making choices under uncertainty. Especially, it gives us some critical insights:
- Probability is not subjective;
- People have biases and do not think like computers;
- The house edge makes gambling a negative-sum game;
Indeed, as explained in the best-selling book by Nobel-prize winner Daniel Kahneman "Thinking fast and slow", our brains have a very peculiar way of dealing with uncertainty. In this sense, we tend to think in frequencies of events (i.e. how many times something happens) rather than probabilities (i.e. its relative likelihood).
Biologists, on their side, have a good explanation on why this happens.
During our evolution it has been more convenient to develop a close-to-optimal way to take gut decisions instead of carefully analyzing data to extract probabilities (e.g. if we observe a lion dying after having drunk from a lake, it is easier to switch lakes instead of determining the probability of getting ill). This may be one of the reasons why we subconsciously use shortcuts – generally known as heuristics– that help us cut through complexity and assist our decision-making.
In this sense, probability-weigh decisions are a rather new feature that our human brain has developed over the millions of years of evolution. On the contrary, as widely documented by the recent literature in the fields of biology, neuropsychology and behavioural economics, the mechanism that is hard-coded in our brain seems to be quite the opposite: be always ready to take quick fight-or-flight decisions and be reflexive and analytical only if needed.
Yet, those mechanisms get in our way when we are asked to evaluate probability. For example, using past outcomes to forecast future behaviour (known as the representativeness heuristic or as gambler’s fallacy) has been what turned an ordinary gambling night into a memorable – and very expensive – spin of roulette at the Monte Carlo casino in 1913.
One night, at the roulette table some gamblers noticed that the ball had fallen on black for quite some time. Believing that it meant that the probability of a red was higher, they started increasing their stakes.
However, the strike of blacks continued for as long as 25 times with them losing millions looking for a red number. They had to learn the hard way that – unlike humans – roulettes forget the past, and each time they spin the probability does not change but it is (as statisticians say) independent.
Eventually, as we dig deeper into the world of probability, we feel to end up with more questions than answers. Why do our instincts fail to provide a correct representation of probability? On top of that – even if we know our biases – what can we do to fix them?
One thing is sure: we need to pay more attention to the things we take for granted and instead consider carefully what is true and what it is not. Again, although with different names, science and experience seem to agree on which is one of the first principles to turn to for more rational decision-making. In the words of arguably one of the greatest investors of all time – nicknamed the Oracle of Omaha – Warren Buffett: "In order to succeed you must first survive. You need to avoid ruin. At all costs". Let's see why.
The No.1 Rule Is To Survive
Lobbies are one of the most important locations in a casino. In a sense, they are the place where the desire, the temptation and ambition is subconsciously built into gamers. To a certain extent, each person walking by a casino lobby can figure himself stacking chips over chips and living a very long strike of winning games.
Ironically, they are built to make us forget the exact opposite – that surviving in a casino is anything but easy.
In the book "Skin in the Game", Nassim Taleb – author of the "Black Swan" and "Antifragile" – gives us a clear example of what we mean by that.
Imagine you invite one hundred people to go into a casino to gamble. As we expect, at the end of the day some may lose, some may win. Imagine that eventually player number 99 is served a terrible hand and goes bust. Will gambler number 100 be affected? Of course not, because the two events are independent from each other.
Now consider the case in which we go to the casino a hundred days in a row. If we go bust on day 23, what is the probability to play on day 24, 25, or even day 100?
Of course, zero. Unlike the previous example, now the two outcomes are not independent anymore and we will stop playing as soon as there is no money left to gamble. Those examples emphasize an important remark: the difference between ensemble (i.e. group) and time probability (i.e. also known as the risk of ruin). When we are constantly exposed to a source of uncertainty – instead of facing it once – the risks we incur are indeed very different as they grow exponentially over time.
Indeed, as the following image shows, while in the first example we can expect the proportion of people that go bust overtime to remain almost the same, in the second example every player will eventually face ruin as he plays repeatedly over time. Simply put: if there is a small chance of ruin, we can expect to observe it if we wait long enough.
Zooming In and Out of Random
As we have seen, decisions under uncertainty or with partial information are quite a complicated subject to deal with. Hard not only because we cannot trust completely our instincts, but also because the answers we get can appear counterintuitive at first. We need to discard the idea that things happen by chance and embrace the notion of probability. After all, as the statistician Chip Denman said once: "Luck is probability taken personally"
On the contrary, we should focus on another interesting consideration that emerges as we move forward: are things really random or do we just not know why they happen? In this sense, what we see as random may only be due to the fact that we are not aware of what causes it.
Although provoking, this question – originally posed by the famous French mathematician Henry Poincaré – seems to open the door to a deeper level of understanding, that he used to call the three levels of ignorance.
He suggested classifying a problem according to what we know about data and the laws that describe its behaviour. So, we may fall into one of the following degrees of ignorance:
- We know the law it follows and have all the necessary information
- We know the law but are not able to measure the problem correctly
- We do not know the law (or it is too complex to decode) and do not have all the necessary information
For each level, Poincaré suggested a different way to orient problem-solving. However, if the solutions to the first and second level problems were attained by solving equations or by limiting the extent of the forecasts respectively, the third and most extensive level required a totally different approach.
It meant to shift the perspective and back-engineer the underlying laws out of their outcomes, that is, by collecting, analyzing and making sense out of a massive amount of data – an approach very similar to the one which is used today in the fields of artificial intelligence and machine learning.
For instance, many financial problems seem to belong to the latter. We not only lack a general formula (or law) that precisely describes why every security changes in price, but also the data that we get is often huge, noisy and complex.
This approach hints at a possible solution: searching for answers by zooming in and out of what appears at first to be a chaotic and random process.
Eventually – as we can imagine – finance is not the only field in which the third degree of ignorance occurs so extensively, but it is recurrent for many problems of physics, engineering and math.
This is why, during the years, scientists have developed several methodologies to shed light on their true nature, like the so-called Monte Carlo simulation.
The Road to Monte Carlo
It was while working on the project to build the first hydrogen bomb that the Polish physicist Stanislaw Ulam found himself in the third level of ignorance: he needed to determine the collisions between the atoms inside the bomb to predict the magnitude of the explosion.
Since it appeared like a never-ending task to exactly calculate each of them, he soon shared the problem with two fellow colleagues, John Von Neumann and Nicolas Metropolis. Eventually they came up with a solution: why not simulate the random collisions on a computer and study the results instead?
What they did was actually one of the first times in which the laws of probability and technology seemed to work together to decipher (or crack) the code of physics. Instead of directly solving equations, they used a computer to run millions of simulations and then studied what happened to get a probabilistic answer to their questions.
Eventually, the process to describe phenomena in probabilistic terms, simulate their behaviour and deduce information became known under the name of Monte Carlo simulation method and turned out to be one of the most useful cross-border techniques to solve problems that are difficult analytically.
For example, we can use it as an alternative way to approximate the value of Pi – the ratio between a circle’s circumference and diameter – running a very simple experiment.
We can imagine drawing a square and putting a circle into it. Then, we could tell the computer to draw two random coordinates and place it over, counting how many points fall in or out of the circle, as shown by the following image.
Since the side and the diameter of the circle are the same, we can approximate the value of Pi by using the following formula:
Eventually, as we generate more points and let them fall inside or outside the circle, both the circle and the square’s areas get filled and we can get a more precise estimation, as we can see from the following plot.
However, this simple experiment is just the starting point to the many applications the Monte Carlo method has found. Since it allows to run controlled simulations, it has found large applications in Finance where it can be used both for risk management or for pricing purposes.
For example, a portfolio manager could be interested in performing a stress test to evaluate the sensitivity of his portfolio to a given risk factor. So, he could run a simulation to generate many random scenarios and see how the portfolio would perform under those circumstances.
Alternatively, a bank may want to use it to price a complex option by discounting the average payoff it would pay from the thousands of possible price paths that the underlying security could take.
Investing Is Not Gambling
Although we could glimpse at some similarities between investing and gambling, we should remember that the two are very different. Indeed, if on the one hand gambling has built-in rules to make it an unfair game at the advantage of casinos, on the other hand investing is a complex activity to allocate money efficiently across assets to meet investment goals. However, as we will see, there are many other differences that emerge when we compare investing and gambling.
Investing Involves Ownership
When you invest you always become the owner of something, may it be something physical (e.g. a commodity), virtual (e.g. rights to buy or sell) or dematerialized (i.e. shares). For instance, when you buy a stock you are effectively buying a unit of ownership of a firm’s capital. This gives the right to vote at the company’s meetings and to be rewarded with a portion of the earnings of the company when they occur. On the contrary, when you gamble you are only buying the right to receive compensation if an uncertain event occurs, a right that expires as soon as the wager is over.
Investing Is Time-Rewarding
Although financial markets do not climb in straight lines (but instead experience many periods of ups and downs) if we observe carefully the last century of the global stock market we see they all have grown significantly.
This hints at a key concept of investing: there is a reward from taking risks that investors can exploit by being invested (i.e. the so-called equity risk premium). Besides, investing is time-rewarding also because of the long-term benefits of compounding that makes any additional interest earned to increase the original capital. Conversely, time seems to play the opposite role for gamblers. As betting is designed to have a built-in house edge, in the long run players can expect to lose money if they keep on betting.
Investors Have Many Tools To Hedge Risk Effectively
Although the probabilities that gamblers face when they bet are static (i.e. they do not change over time), casino games are not designed to diversify risk. This makes players often put all the eggs in one basket and have very few risk management tools.
On the contrary, although investors face dynamic probabilities (i.e. that change over time) they have plenty of techniques to hedge or reduce risk effectively.
Among these, the most effective is diversification: adding inversely or low-correlated securities into the portfolio reduce its volatility, as their co-movements tend on average to balance out the gains and losses
Knowledge Is Power
Even though gamblers can have some knowledge if a certain table is hot or cold, it is very difficult for them – or even useless – to use that knowledge to have a real edge on the house. In contrast, when people make investment decisions, they use a wide array of information: from past performance or volatility to a company’s fundamentals. Ultimately, although noisy, information-gathering and processing is an essential part of a profitable investment strategy.
From Las Vegas to Wall Street
As we have seen, throughout the years we have been able to develop several techniques to manage uncertainty and make better decisions. Similarly, it did not take long for many famous investors to understand how this gambling-related knowledge could be beneficial for investing.
As we will see, even though each of them has his own style, their investment strategies can be traced back to concepts like statistical arbitrage, odds mastering and exploiting behavioural biases. To a certain extent, they have all taken this knowledge out of Las Vegas to conquer Wall Street.
Ed Thorp
Edward O. Thorp & Associates
Edward Thorp is a mathematician, gambler and author of the famous book entitled "Beat the Dealer" in which he exposed to everyone the way cards could be counted at blackjack. After having taught maths at MIT, it did not take him long to redirect his knowledge to the world of Finance and to launch the first quantitative, computer-driven and market-neutral hedge fund.
Its strategy consisted of hedging mispriced securities and pocketing the difference, while maintaining a neutral exposure to market-wide swings. In his words, "We asked ourselves: In what ways and to what extent is the market inefficient? And how can we exploit this?". From these statistical arbitrages, Thorp’s hedge fund went on to earn an annualized 15.1% rate of return from 1969 to 1989, without scoring a single losing quarter.
Jim Simons
Renaissance Technologies
James Simons is a mathematician who worked in the mid-1960s for a government agency as a top-secret codebreaker. There he learned about computer science, algorithms and statistical modelling, concepts that led him in 1982 to found Renaissance Technologies – one the best-known quantitative hedge funds in the world. His investment strategy does not focus on the subtleties of financial markets or on which theoretical framework is responsible for generating anomalies. Instead, he looks for inconsistencies in data that could help him get a statistical edge. With this technique his flagship fund – called The Medallion Fund – has generated returns of about 40% a year since its inception in 1988.
Warren Buffett
Berkshire Hathaway
The Oracle of Omaha built his fortune through value investing, that is, buying securities that the market currently trades under their intrinsic value. The idea is that – like humans – financial markets tend to overreact to news and thus make some securities expensive and others cheap, which can be identified through an extensive analysis of their fundamentals (i.e. their balance-sheet implied value).
As the long-term prices will tend to align with the intrinsic value, one can profit from this convergence. During his 54-year investment activity, Buffett pooled his own capital with that of his investors into a single limited partnership, Berkshire Hathaway, recording a compounded annual return of 20.5%.
Carl Icahn
Icahn Enterprises
Similarly to Buffett, Carl Icahn also thinks that the consensus is generally wrong and so he performs thorough due diligence looking for undervalued firms. However, if Buffett waits for prices to converge in the long-term, Icahn acts fiercely. He first accumulates a significant position in the company and later demands for severe changes in its board.
Once he can influence the firm’s decisions, he starts restructuring the business cutting costs, divesting loss-making activities or buying back stocks with the goal to increase the stock price in the short-run. Eventually, although he bets against the odds, he changes the rules of the game forcing them to come on his side. Even if this strategy may sound hazardous, his hedge funds performed an average annual return of 15% for the last 18 years.
Ray Dalio
Bridgewater Associates
After some years floor-trading at the NYSE, Ray Dalio started Bridgewater Associates in 1975, what is now the world’s largest hedge fund with assets under management of about $120 billion. His fund makes bets based on macroeconomic factors, but its success is not the only interesting thing about it. Indeed, Dalio’s radical truth and radical transparency philosophy accounts for a great part. He believes that humans tend to make decisions on emotions or skewed views about the past, causing biased investment choices.
Instead, investment ideas should rather be data-driven and unbiased, looking not for the idea with maximum consensus, but the best probability-weighted one. Through 2018, Bridgewater recorded $57.8 B in net gains since its inception, making it the most successful hedge fund of all time.
The Lessons We Learned
Eventually, investing seems to be quite a fertile playground in which many ideas that have originated in other fields – especially gambling – have later cross-fertilized. Indeed, they not only seem to be intrinsically risky endeavours, but also activities in which one has to face uncertainty constantly. Yet, for each of them, the introduction of the scientific method has been of crucial importance to decode and tame into its apparent randomness.
As Feynman, Ulam and Poincaré suggested, we should be able to zoom in and out of what we think happens by chance and rather build intuition and insights combining keen observations with data analysis and the most advanced technology – like Artificial Intelligence and Machine Learning.
Eventually, being rational, unbiased and scientific has become the new language of modern investing and what it really takes to play the odds. Indeed, given the high availability of data, investing has rapidly become a unique field in which this new technological and data-driven landscape is taking place to the point that – as quantitative hedge funds surpass the $1 trillion assets under management mark – it does not seem like a distant future, but instead something happening right now.
