Randomness and the roll of the dice: Meditations on Yudhishtra, Probability, and Black Swan events.

(Note: this picture is an AI-generated image. It took several interactions with the Dall-E engine to get this scene right. It is fascinating how, with a slight change in the specification, the AI engine was able to modify the rendering and paint the appropriate emotion and body language I prompted it to follow. This image could be further improved, but I felt, for the purpose of this essay, this picture was good enough.)

It is remarkable how the Indian epic Mahabaratha speaks to every human type and character. It is not an exaggerated claim when scholars say that within the pages of the Mahabaratha, there are answers to every human conundrum – moral, ethical, social, or spiritual. Personally, I can’t agree more. No other epic – at least in my study of epics – including Homer’s Iliad and the Odessey, has the scope, depth, and range of characters and situations that Mahabaratha packs into its meticulously crafted Escher-style narrative of stories within stories. I have never got tired of them. Since my childhood, I have read different versions of the Mahabaratha. From abridgments to modern full-length renditions, I loved reading these stories through the lens of different perspectives. Give me a copy of Mahabartha anytime, and I will gladly reread it. I have always gleaned something new, a fresh take on a character or an event that has eluded me. Every story and each character of this epic is worthy of independent study and exposition – and, more importantly, relevant even today and prescient of the times we live in. Think of someone you know in your life, and I assure you, you will find an equivalent sketch of such a character in the Mahabharata. If only Carl Jung, the great Viennese doctor of the mind, had the time to study this epic thoroughly, he wouldn’t have claimed the idea of collective human archetypes as his own. Vyasa had unearthed that idea millennia ago.

Recently, I have been looking at the Mahabaratha from a different angle. All of us know that the main narrative of the epic hinges on the incompatibility between the Pandus and the Kurus. The epic takes a pivotal and irrecoverable turn for the Pandus when Yudhishtra, the eldest brother of the Pandavas, accepts the teasing challenge of his uncle Shakuni to play a game of dice with him with enormous stakes. Vyasa portrays Yudhishtra as a man of profound wisdom but still an imperfect man. ( One of the things I love about the Mahabaratha and the reason I think it resonates with most readers is that there are no perfect characters in this epic. Even the best of characters have weaknesses, and the worst of them have some positive traits. Even Krishna, the god in human form who masterminds the drama in favor of the Pandus, does a few things that are quite unacceptable.) Yudhistra accepts the invitation knowing well that Shakuni is a better gambler than he was, and the dice always fell in his favor. At least, that is the wild reputation that Shakuni carried in his circles. There is something inexplicable, unpredictable, and exciting about the throw of a dice or a toss of a coin. It encapsulates the most elemental form of uncertainty. If you have ever played any game that involved the throw of a dice, you will remember the breathless tightening of the body and a foolish sense of confidence each time you rolled the dice. And how we unconsciously exert our will, hoping to control the direction of the tumble and outcome of the roll and the cry of exultation or a sigh of disappointment that usually follows the outcome. It is difficult not to feel these emotions. Human nature hasn’t changed over the millennium. We may have vastly improved upon the understanding of the art of gambling and playing with risk, but the tingling thrill and misplaced optimism of a gambler haven’t gone away.

The history of Mankind can be best interpreted as an attempt to control uncertainty in every sphere of life. From the discovery of fire to the invention of the steam engine to the institution of marriages to the democratization of electricity to weather prediction algorithms to Global positioning systems to buying and selling insurance to stock market trades to yearly health checkups to boarding a flight or waking up in the morning – in every domain, we have tried to manage and control the uncertainty that pervades our lives. Peter Bernstein, in his book “Against the Gods,” a marvelous one-volume survey of the evolution of risk management, wrote: “The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature.” Every age in human history is punctuated by technological and material progress. Therefore, that does not define modernity. However, what has changed in the last three hundred years is our ability to handle risk and uncertainty. We have become less dependent on oracles and superstitions in living our lives and more confident in our ability to quantify and manage risks. This improved capacity for managing risks is both a boon and a curse. On the one hand, our lives were simple when we attributed the uncertainties we faced to unknown powers, to the Gods, beyond our control. On the other hand, today, our sophisticated quantitative measurements of uncertainty, and our belief that we have somehow mastered risk have largely stripped us of that simple faith we had earlier. From a time in our history when uncertainty was the norm to modern times when we largely sleepwalk through life without ever thinking of uncertainty at all, we have come a long way. Today, we are again puzzled by uncertainties in a different form. We considered it funny that life is uncertain, and aberrations to the “normal” are often met with surprise as if it shouldn’t be happening at all. We have come a long way from our primal ancestors, who, I presume, would have woken each morning with nothing but uncertainties looming in front of them, to the modern man, who likes to live his life totally indifferent to randomness. Think about it. We blame the weather if it is contrary to what our weather app says. We blame the world if our quantitative predictions about finance, medicine, election, economics, and ethics go wrong ( and not the other way around). We try hard to abstract away randomness and believe it is not there. We derive sophisticated mathematical arguments to insure ourselves against uncertainties, but no matter what we do, uncertain outcomes have a way of hitting you when you least expect it. Randomness rules our lives every moment. Wise men understand this and live accordingly; the otherwise suffer, complain, and fume.

The first reference to the nature of probability was made by an Italian scholar, Luca Paccioli ( Accountants will know him as the father of the double-entry bookkeeping system). In his mathematical work ” Summa de Arithmetic,” he poses a curious question, which is the official beginning of the study of uncertainty. The question is worth quoting in full: ” A and B are playing a fair game of balla ( dice); they agree to continue until one has won six rounds. The game stops when A has won five and B three. How should the stakes be divided?” This question is the first formulation of the problem of probability in mathematical literature, and a variant of this question would appear in subsequent centuries in the works of many influential scholars and thinkers. The rift between the old world and the new began with this investigation. Can Man predict and control uncertainty? If the investigation of this puzzle could lead to a method of quantifying gains and losses, then we don’t have to look to the gods for help. Paciolo’s puzzle is a momentous stride in our intellectual history. Pacioli himself did not attempt to answer the question he posed, but his question opened the doors to one of the daring pursuits of man – how do we quantify and control uncertainty? The challenge remained unsolved for another two centuries until, in 1654, when the Renaissance was in full bloom, a Frenchman Chevalier de Mere challenged Blaise Pascal, one of the original thinkers in the history of science, to solve a puzzle about dividing the stakes of an unfinished game of chance between two players when one of them is ahead. This is, as you will notice, a classic reformulation of Pacccioli’s problem two centuries ago. Unlike Paccioli, Pascal was a practicing mathematician and a genius at that. He loved intriguing problems. He and Fermat, another towering name in mathematics, together attempted to solve this puzzle. Their solutions and epistolary exchanges between them on this problem were an intellectual dynamo. Two sharp and brilliant minds cutting their way to find an answer that no one had ever dared to seek before. The numerical approach they proposed to solve this puzzle laid the foundation of the theory of probability, which is the essence of risk-taking. After Pascal and Fermat broke open the shell of the problem, other great minds over the centuries, such as Leibnitz, Abraham de Moivre, Bernoulli, and many others, stepped in. They widened, deepened, and developed this idea of managing risk into a refined science.

Yudhistra could have saved his kingdom and the wrath of his wife if he had paused to ask the question that Chevalier de Mere posed to Pascal. Is it worth continuing when I have lost my kingdom and wealth? What are the odds of my winning the remaining rounds? It is easy to sit in judgment over a character from two thousand years ago. It is not Yudhistra’s fault that he didn’t think along these lines. Thinking requires a prior foundation of thought, and during the time of the Mahabharata, risk and uncertainty were still the province of the gods and oracles and not something men and women pondered about. They prayed, and that was the best they could do. Thinking about risk or randomness was not even an option. And, of course, Yudhistra couldn’t stop himself from rolling the dice and staking one thing after another. It must have been a bad rush of adrenalin ( a typical gambler’s problem). However, it is interesting to meditate on what could have happened if Yudhishra had access to the tools of measuring randomness, say something like Pascal’s triangle, an elegant construction of probabilities of winning or losing in a given number of attempts. Yudhistra could have stepped aside for a moment, consulted the table, and figured out the best options for him. Even a casual glance at the table would have informed him that his chances of coming out tops were non-existent. Armed with this knowledge, he may have gracefully bowed out of the challenge ( much to Shakuni’s chagrin, of course) and salvaged what he had left of his family and wealth, and who knows, Vyasa would have written an alternative version of the Mahabaratha, and we would be talking about Yudhistra in a different vein altogether. Unfortunately, Pascal’s computation came in a thousand years late for Yudhistra. He believed in righteousness as his tool to win the game of dice. Not a bad idea, but that didn’t help roll the dice in his favor. Alas!

One of the most influential series of books I have read in my life is Nassim Nicholas Taleb’s five-volume study of randomness, written between 2001 and 2018. I began reading the first books of the series in 2015, and I continue to engage with them. Though Nassim prefers to refer to these books as lengthy meditative essays – in the style of the great French essayist Montaigne – and not serious technical books, they have been the most profitable and healing reading I have done. Some books educate, some entertain, some explain, some books are to be read for the sheer beauty of their style, and there are those few rare books that transform one’s outlook. The “Incerto,” as the five volumes are collectively called, is not easy to read in the sense that Nassim’s vibrant mind constantly jumps from one idea to another, tackling, illuminating, and unsettling deep-seated opinions and ideas and continually challenging the reader to stay with in sync with his penetrative mind. But it is worth the trouble and focus and extremely profitable reading, especially for those who like to meditate and introspect about what they have read. His books changed my worldview; I mean it, not just because the force of fanciful theories carried me away, but because it profoundly and positively vindicated and clarified my own life experiences. There are only a few books that can do that, and Nassim’s work has the potential to shatter and reorient the mind to a new way of thinking and understanding. Nassim is a controversial man. I would be surprised if he isn’t. Anyone who goes against conventional and accepted wisdom is bound to be treated indifferently. However, over the years, many of Nassim’s observations have come to make sense and become mainstream. During the formative years of Amazon, Nassim’s second book in the incerto, ” The Black Swan,” made a deep impact on Jeff Bezos. Of all the books in the series, the Black Swan is perhaps the best-written book and one in which the idea of randomness and its pervasive influence in everything clearly comes through.

Yudhistra had a contrary view of the whole affair. He had already had a couple of bad runs in which he lost pretty important things, but he firmly believed that his run of luck would change for the better after the significant losses he had experienced. The biological nature of the mind is not properly wired to understand the nature of randomness. That success doesn’t have to follow failure or failure; success – is the essence of randomness. Good gamblers and risk-takers understand this and draw their limits well. They know when to get in and when to get out. Does that mean human effort, commitment, hard work, and preparation mean nothing? No! That is the point. We have to do what we have to do, but that doesn’t guarantee anything. Our efforts increase our chances of being in the pipeline to success – which is a good thing. You don’t want to be left out of the race. But there is no causal relationship between what you do and what you get. My take of that famous verse in the Bhagavad Gita ( embedded in the Mahabharata, as we all know), ” to action you have the right, but not to the fruits thereof,” is a perfect explanation of randomness. This verse is popularly explained away as words of solace to those who work hard but don’t see success. We tell people: “Look, keep putting in the effort, but don’t expect results. But know for sure that your efforts will yield the right fruits”. What we don’t explicitly make clear ( which will then make it non-spiritual) is that the ” right result” may not necessarily be a successful one. That there is randomness everywhere, and all that one can do is to keep at one’s job. We see all around us really smart and hardworking people nowhere near the limelight, and some people are pasted all over the media for no apparent reason. Well, Gita’s message is, “Hey, look, there is enough randomness to elevate someone with no talent to a position of success, so don’t fret; just keep doing your job, and there is a chance you may find yourself in a position you deserve.” This interpretation is not pessimistic at all; on the other hand, it is the most liberating and truthful message to live a good life.

Nassim popularized the term Black Swan event to refer to those events that are considered impossible but suddenly happen or are spotted or discovered. For centuries, people believed that Swans were invariably white because of the white color of their feathers (even today, you will rarely find a painting or a picture of black-colored swans). Black swans were first spotted by Europeans in 1697 when the Dutch explorer Willem de Vlamingh and his crew sailed into Western Australia and beheld a black-colored swan, thus disproving the long-held “truth” that swans were only white. Since then, Black Swan events and thinking have entered the echelons of philosophy and finance. The key point behind the principle of the Black Swan is that most of what we call common sense is nothing but a collection of inductions based on what we know. The sun has risen every day in the morning since the day I can remember. Therefore, the sun will rise tomorrow morning as well. Simple induction! In fact, in the Mahabharata, there is a story about how Krishna, in order to misle the Kauravas from choosing the correct day for starting the great battle, disturbs the regular orbit of the planets to create “Amavasya” or a new moon event. In other words, he precipitates a black swan event that confuses the pundits because, according to their calculations based on past data, Amavasya was not yet due. Faced with an unexpected Black swan-like event, the pundits readjust their explanation to fit the facts and observe the rituals appropriate to that day. This is what we do all the time. We tend to induct from past patterns and meet the future, and we derive the causes and effects of these patterns. Biologically, the capacity of induction is essential for our survival. Primitive man must, within a moment’s notice, based on patterns of black and white stripes, figure out whether it is a zebra or a tiger he is looking at. Even if he is wrong, the ability to form such a narrative is important. As long as we understand this capacity for creating stories for what it is and not be fooled by randomness ( Nassim’s first book in the series is called “Fooled by Randomness”), we are fine. The problem is that we are so deeply invested in not perceiving randomness around us that when an event takes us by surprise, our immediate reaction is to explain the event based on what we know rather than see it for what it is – sheer randomness.

This essay has turned out to be a long one, and I do not wish to prolong it any further. The study of probability and randomness in the last four centuries has come a long way in harnessing risk in human life. The fact that we live a fairly secure life is because we have a sophisticated understanding and quantification of risk and are, therefore, able to plan for unexpected outcomes. Each time I drive my car, there is risk: the gears could fail, the brakes can stop functioning, and the fuel engine could give up – a million things can happen, but the fact that it doesn’t as often as it should is indicative of how much thought we have put into manufacturing these vehicles. Automobile manufacturers will tell you that they don’t ( cannot) make cars that will never fail. Instead, they can only make cars with tolerable limits of failure, and therefore, we are safe with it most of the time. That is the key to managing and facing risk. I started off this essay with Yudhistra’s folly of gambling with Shakuni without understanding the laws of probability. The question is; Are there any such laws?. The answer is yes, and the funny thing is that we can, to a remarkable extent, account for the probability of an event happening, providing the events are discrete ( like the throw of dice or the toss of a coin) and we have a large enough sample population. In 1703, Jacob Bernoulli wrote Leibnitz questioning him about the sample sizes to calculate the odds of, say, six or seven appearing on the throw of dice. Leibnitz’s response sums up the essence of probability, black swans, and the whole study of risk. He wrote: “Nature has established patterns originating in the return of events, but only for the most part. New illnesses flood the human race so that no matter how many experiments you have done on corpses, you have not thereby imposed a limit on the nature of events so that in the future they could not vary”.

In this single sentence, Leibnitz captured the truth and the ambiguity present in probability studies. Nature does repeat herself; we are thankful for that; however, that does not mean the past can always be a guide to the future. Covid’ 19 struck us out of nowhere. Was it a black swan event, or a conspiracy, or both, we dont know, but the fact is, we are totally unprepared for it. Tsunamis and earthquakes happen despite our best efforts. The essence of the Mahabharata, to me, is all about being prepared for anything, in other randomness. The fact that Vyasa placed a game of dice at the heart of the epic is, to me, indicative of how much he valued the power of uncertainty in man’s life. In the five rounds that Yudhistra played, he gambled everything, and when the audience ( including his brothers) thought that he would gamble no more, Yudhistra created a Black swan event by staking his wife, Draupadi. The ripple effect of the terrible decision would haunt the five brothers throughout the story. Generations of scholars have debated the moral and ethical impacts of Yudhistra’s decision. The nature of Black Swan events is that they happen, and sometimes, they are significant enough to change the course of human history.