Zero or Two Thousand?

Would you pay $1000 for an unbiased coin toss that gives you $2000 if heads and nothing if tails? Tomorrow you can have zero or $2000 in your pocket, each with a 50% probability. Surely you don’t feel neutral about it. You would either take it or not. But mathematically, you should be neutral about it. Since the fair value of a bet is given by the linear combination of the two states (mathematical expectation), which in this case is just (50% * $0) + (50% * $2000) = 1000. So where is the discrepancy?

Fooled by Randomness by Taleb talks about how we can conjure up one and only state at a given time—zero or two thousand. The fear of ending up with nothing or the excitement of another thousand. One dominates the other, and that’s how you decide whether you’ll take this bet. If something as simple as a coin toss can split people, imagine adding a pinch of randomness in life. Taleb gives an example:

“Imagine a waiting room full of actors queuing for an audition. The number of actors who will win is clearly small, and they are the ones generally observed by the public as representatives of the profession. The winners live a life of luxury; the others (the great majority)–we can imagine their fate, a lifetime of serving foamed caffe latte at the neighbouring Starbucks, fighting the biological clock between auditions.

One may argue that the actor who lands the lead role that catapults him into fame and expensive swimming pools has some skills others lack, some charm or a specific physical trait that is a perfect match for such a career path. I beg to differ. The winner may have some acting skills, but so do all the others, otherwise they would not be in the waiting room.

It is an interesting attribute of fame that it has its own dynamics. an actor becomes known by some parts of the public because he is known by other parts of the public. The dynamics of such fame follow a rotating helix, which may have started at the audience, as the selection could have been caused by some silly detail that fitted the mood of the examiner on that day. Had the examiner not fallen in love the previous day with a person with a similar sounding last name, then our selected actor from that particular sample history would be serving caffe latte in the intervening sample history.”

All this is trying to demonstrate is that randomness and timing matter, outcomes do not linearly move with skill. And it applies to matters of wealth as well.

Consider the stories of Raamdeo Agarwal, Chairman of Motilal Oswal Group, who back in 2012 purchased Eicher Motors on the back of its truck sales, and believed in Royal Enfield, its bike segment, only as a backup. “In case the bikes do not sell, Royal Enfield will not allow us to sink,” he said while explaining his investment rationale. After they bought, due to the rise in sales of Royal Enfield, the EBITDA margins of the company had grown to 30% from 17-18%. He had estimated that in the worst case, the stock would double in five years or else it will go on to be a multibagger growing 10 times. The bet paid off for the veteran as the stock has returned much more than that, with 10-year CAGR returns of 57.81%. He bought the stock as a truck company, but the upside was given by the Royal Enfield business, which he thought would barely affect the returns.

Earlier, Agarwal also shared a funny incident about how luck favored him in a multibagger investment. In 1991, he bought Vysya Bank for Rs. 20 based off the suggestions of one of his clients. The price increased to about Rs. 2000 in the next 1-2 years; later fell to Rs.500, so he tried to sell his shares and sent the delivery to Bangalore. But somehow the parcel got lost so he had to get duplicates, and by the time it came back to him after 6 months, it was again Rs.2000. In fact, he sold it at Rs.2250 (>100x return). This he purely attributed to luck, and he recounts this as a pivotal moment in his investment career, shaping his understanding of wealth creation in the stock market.

Limits of Rationality?

Okay, skill alone doesn’t dictate outcomes, luck plays a large role, is there an explanation? Herbert Simon, talks about how if we were to optimize at every step of our life, then it would cost us an infinite amount of time and energy. So rather than optimizing, we ‘satisfice’ (satisfy + suffice): we stop when we get a near-satisfactory solution. Otherwise it would take us an eternity to reach the smallest conclusion or perform the smallest act. We are therefore rational, but in a limited way: boundedly rational. He believed that our brains were a large optimising machine that had built-in rules to stop somewhere.

Enter KT—Kahneman and Tversky:

KT went ahead, and showed that our decisions don’t just fall short of perfect rationality; they are systematically biased. They looked for rules in humans that did not make them rational—they called them ‘quick and dirty’ heuristics; the dirty part being that it came with biases as its side effects.

In fact, the stories we’ve already seen reflect these systematic departures from rationality. Take the coin toss: most people shy away from it, even though the expected value is neutral. This is risk aversion, a cornerstone of prospect theory, where the sting of losing outweighs the thrill of gaining. Taleb’s actors waiting in the audition room illustrate survivorship bias. We see only the few who make it to the screen and assume their success was inevitable, forgetting the many equally skilled faces who never got noticed. Raamdeo Agarwal’s investments reveal another bias. In hindsight, his Royal Enfield bet looks like a masterstroke, but at the time he viewed it as a truck company hedge. The narrative of genius only emerges after the fact—classic hindsight bias.

What all these stories make clear is that outcomes in life and markets are never a simple function of skill. Chance intervenes, and our minds, wired with biases, often misread that randomness. We underestimate luck, overestimate foresight, and build neat narratives after the fact. The lesson is not to dismiss skill, but to stay humble about its limits. In investing, as in life, success lies not just in making the right choices, but in recognizing the silent hand of luck and the noisy shortcuts of our own thinking.

This is one of my articles on the Bodhi newsletter, find their substack here.