Ludic Fallacy

Non-Brooklyn John

I found the perfect non-Brooklyn in someone I will call Dr. John. He is a former engineer currently working as an actuary for an insurance company. He is thin, wiry, and wears glasses and a dark suit. He lives in New Jersey not far from Fat Tony but certainly they rarely run into each other. Tony never takes the train, and, actually, never commutes (he drives a Cadillac, and sometimes his wife’s Italian convertible, and jokes that he is more visible than the rest of the car). Dr. John is a master of the schedule; he is as predictable as a clock. He quietly and efficiently reads the newspaper on the train to Manhattan, then neatly folds it for the lunchtime continuation. While Tony makes restaurant owners rich (they beam when they see him coming and exchange noisy hugs with him), John meticulously packs his sandwich every morning, fruit salad in a plastic container. As for his clothing, he also wears a suit that looks like it came from a Web catalog, except that it is quite likely that it actually did.

Dr. John is a painstaking, reasoned, and gentle fellow. He takes his work seriously, so seriously that, unlike Tony, you can see a line in the sand between his working time and his leisure activities. He has a PhD in electrical engineering from the University of Texas at Austin. Since he knows both computers and statistics, he was hired by an insurance company to do computer simulations; he enjoys the business. Much of what he does consists of running computer programs for “risk management.”

I know that it is rare for Fat Tony and Dr. John to breathe the same air, let alone find themselves at the same bar, so consider this a pure thought exercise. I will ask each of them a question and compare their answers.

NNT (that is, me): Assume that a coin is fair, i.e., has an equal probability of coming up heads or tails when flipped. I flip it ninety-nine times and get heads each time. What are the odds of my getting tails on my next throw?

Dr. John: Trivial question. One half, of course, since you are assuming 50 percent odds for each and independence between draws.

NNT: What do you say, Tony?

Fat Tony: I’d say no more than 1 percent, of course.

NNT: Why so? I gave you the initial assumption of a fair coin, meaning that it was 50 percent either way.

Fat Tony: You are either full of crap or a pure sucker to buy that “50 pehcent” business. The coin gotta be loaded. It can’t be a fair game. (Translation: It is far more likely that your assumptions about the fairness are wrong than the coin delivering ninety-nine heads in ninety-nine throws.)

NNT: But Dr. John said 50 percent.

Fat Tony (whispering in my ear): I know these guys with the nerd examples from the bank days. They think way too slow. And they are too commoditized. You can take them for a ride.

Now, of the two of them, which would you favor for the position of mayor of New York City (or Ulan Bator, Mongolia)? Dr. John thinks entirely within the box, the box that was given to him; Fat Tony, almost entirely outside the box.

To set the terminology straight, what I call “a nerd” here doesn’t have to look sloppy, unaesthetic, and sallow, and wear glasses and a portable computer on his belt as if it were an ostensible weapon. A nerd is simply someone who thinks exceedingly inside the box.

Have you ever wondered why so many of these straight-A students end up going nowhere in life while someone who lagged behind is now getting the shekels, buying the diamonds, and getting his phone calls returned? Or even getting the Nobel Prize in a real discipline (say, medicine)? Some of this may have something to do with luck in outcomes, but there is this sterile and obscurantist quality that is often associated with classroom knowledge that may get in the way of understanding what’s going on in real life. In an IQ test, as well as in any academic setting (including sports), Dr. John would vastly outperform Fat Tony. But Fat Tony would outperform Dr. John in any other possible ecological, real-life situation. In fact, Tony, in spite of his lack of culture, has an enormous curiosity about the texture of reality, and his own erudition—to me, he is more scientific in the literal, though not in the social, sense than Dr. John.

This difference in answers illuminates one of the most vexing problems about the connections between two varieties of knowledge, what can be dubbed Platonic and a-Platonic. Simply, people like Dr. John can cause Black Swans outside Mediocristan—their minds are closed. While the problem is very general, one of its nastiest illusions is what I call the ludic fallacy—the attributes of the uncertainty we face in real life have little connection to the sterilized ones we encounter in exams and games.

The ludic fallacy arises from the misuse of games and their probability models to describe real-life randomness. It is the error of assuming that the same statistical distributions that govern simple setups—coin flips, dice throws, random walks, the digital “heads or tails” expressed as 0 or 1—apply to complex systems like financial markets, political events, or historical shifts. In games, the randomness cancels out quickly; the casino can be certain that in the near long run the house edge will prevail. This is what might be called protorandomness—a controlled, tame version of uncertainty that has none of the wild, scaling properties of genuine randomness. Theories built around such setups ignore a deeper layer of uncertainty. Worse, their proponents often don’t know it.

Nowhere is this fallacy more dangerously institutionalized than in the world of business schools, economics departments, and risk-management firms. Several hundred thousand students from Singapore to Urbana-Champaign are taught “scientific” methods grounded in the Gaussian distribution, despite the fact that these tools belong to Mediocristan—the placid province of mild, thin-tailed variation—while they are being turned loose on Extremistan, where outcomes follow fat tails and huge deviations are not only possible but defining. It is like developing a medicine for plants and applying it to humans. I have a wall of statistics books in my house that I find largely useless outside of their academic applications; not one of them deals with Extremistan. The few that do are written by statistical physicists, not by statisticians. The entire enterprise runs the biggest risk of all: handling matters that belong to Extremistan but treating them as an “approximation” to Mediocristan.

A vivid illustration of the ludic fallacy played out at a think-tank symposium held in a Las Vegas casino. The casino’s management, obsessed with monitoring cheaters and card counters, had invested millions in high-tech surveillance to combat risks that resemble the sterilized randomness of their games. Meanwhile, they were utterly blind to the real Black-Swan threats: a performer’s tiger who mauled his trainer, a disgruntled employee who set fire to the premises, an economic downturn that kept high rollers at home. They saw the trees—the known, game-like risks—and missed the forest.

The same pattern recurs in high finance. In 1997 the Royal Swedish Academy of Sciences awarded the Nobel Prize in Economics to Myron Scholes and Robert C. Merton for refining the Black-Scholes option-pricing formula. That formula, and the elegant edifice around it, relied heavily on the Gaussian distribution, assuming market returns were tame and well-behaved. It was compatible with existing economic theories but ignored the possibility of large deviations—the very events that blow up portfolios. The following year, Long-Term Capital Management (LTCM), a hedge fund that used these models as its intellectual backbone, collapsed spectacularly, threatening the global financial system. When practitioners or skeptics challenged the Gaussian assumptions, many economists responded with ad hominem attacks or invoked Milton Friedman’s dictum that models need not have realistic assumptions. Yet these models were neither realistic nor predictive; they were the embodiment of the ludic fallacy, mistaking a neat mathematical framework for a faithful map of a messy world.

The ludic fallacy also manifests in everyday reasoning. Like Dr. John, someone might insist that after ninety-nine heads, the odds remain 50:50, fixating on the given assumption of a fair coin while ignoring the overwhelming evidence that the assumption itself is faulty. This is the sterile quality of classroom knowledge that can blind its holder to the actual texture of reality. Fat Tony’s instinct—to question the premise rather than compute within it—is more “scientific” in the literal sense, even if it lacks academic polish. Similarly, the fallacy can appear in any domain where a person clings to a statistical abstraction (like an assumed probability distribution) while disregarding the real-world processes that generate the data. It is an insistence on treating uncertainty as if it were a game with fixed rules and known probabilities, a Platonification of randomness that gives a false sense of security and systematically underestimates the probability and impact of Black Swans.

The consequences are severe: overconfidence in models that assume normal distributions, blindness to tail risk and systemic fragility, and a proliferation of risk-management practices that are worse than useless because they embolden decision-makers with the illusion of control. When we teach people methods from Mediocristan and then release them into Extremistan, we are not just making an error; we are actively manufacturing disasters.

These distinctions are not merely intellectual. They go to the heart of who we trust with positions of responsibility. Dr. John is predictable, meticulous, and safe within the narrow confines of his box; Fat Tony is unruly, intuitive, and far more attuned to the ways the world can truly surprise us. In a complex, Extremistan-filled reality, the Fat Tonys of the world may be the ones who actually understand risk—while the Dr. Johns, for all their credentials, are the ones who unwittingly invite catastrophe.