Нассим Талеб - The Black Swan. The Impact of the Highly Improbable

In the group was a gentleman who ran a group of professional gamblers and who was banned from most casinos. He had come to share his wisdom with us. He sat not far from a stuffy professor of political science, dry like a bone and, as is characteristic of “big names,” careful about his reputation, who said nothing out of the box, and who did not smile once. During the sessions, I tried to imagine the hotshot with a rat dropped down his back, putting him in a state of wriggling panic. He was perhaps good at writing Platonic models of something called game theory, but when Laurence and I went after him on his improper use of financial metaphors, he lost all his arrogance.

Now, when you think of the major risks casinos face, gambling situations come to mind. In a casino, one would think, the risks include lucky gamblers blowing up the house with a series of large wins and cheaters taking away money through devious methods. It is not just the general public that would believe so, but the casino management as well. Consequently, the casino had a high-tech surveillance system tracking cheaters, card counters, and other people who try to derive an advantage over them.

Each of the participants gave his presentation and listened to those of the others. I came to discuss Black Swans, and I intended to tell them that the only thing I know is that we know precious little about them, but that it was their property to sneak up on us, and that attempts at Platonifying them led to additional misunderstandings. Military people can understand such things, and the idea became recently prevalent in military circles with the expression unknown unknown (as opposed to the known unknown) . But I had prepared my talk (on five restaurant napkins, some stained) and was ready to discuss a new phrase I coined for the occasion: the ludic fallacy . I intended to tell them that I should not be speaking at a casino because it had nothing to do with uncertainty.

The Uncertainty of the Nerd

What is the ludic fallacy? Ludic comes from ludus , Latin for games.

I was hoping that the representatives of the casino would speak before me so I could start harassing them by showing (politely) that a casino was precisely the venue not to pick for such a discussion, since the class of risks casinos encounter are very insignificant outside of the building, and their study not readily transferable. My idea is that gambling was sterilized and domesticated uncertainty. In the casino you know the rules, you can calculate the odds, and the type of uncertainty we encounter there, we will see later, is mild , belonging to Mediocristan. My prepared statement was this: “The casino is the only human venture I know where the probabilities are known, Gaussian (i.e., bell-curve), and almost computable.” You cannot expect the casino to pay out a million times your bet, or to change the rules abruptly on you during the game—there are never days in which “36 black” is designed to pop up 95 percent of the time. *

In real life you do not know the odds; you need to discover them, and the sources of uncertainty are not defined. Economists, who do not consider what was discovered by noneconomists worthwhile, draw an artificial distinction between Knightian risks (which you can compute) and Knightian uncertainty (which you cannot compute), after one Frank Knight, who rediscovered the notion of unknown uncertainty and did a lot of thinking but perhaps never took risks, or perhaps lived in the vicinity of a casino. Had he taken economic or financial risks he would have realized that these “computable” risks are largely absent from real life! They are laboratory contraptions!

Yet we automatically, spontaneously associate chance with these Platonified games. I find it infuriating to listen to people who, upon being informed that I specialize in problems of chance, immediately shower me with references to dice. Two illustrators for a paperback edition of one of my books spontaneously and independently added a die to the cover and below every chapter, throwing me into a state of rage. The editor, familiar with my thinking, warned them to “avoid the ludic fallacy,” as if it were a well-known intellectual violation. Amusingly, they both reacted with an “Ah, sorry, we didn’t know.”

Those who spend too much time with their noses glued to maps will tend to mistake the map for the territory. Go buy a recent history of probability and probabilistic thinking; you will be showered with names of alleged “probability thinkers” who all base their ideas on these sterilized constructs. I recently looked at what college students are taught under the subject of chance and came out horrified; they were brainwashed with this ludic fallacy and the outlandish bell curve. The same is true of people doing PhD’s in the field of probability theory. I’m reminded of a recent book by a thoughtful mathematician, Amir Aczel, called Chance . Excellent book perhaps, but like all other modern books it is grounded in the ludic fallacy. Furthermore, assuming chance has anything to do with mathematics, what little mathematization we can do in the real world does not assume the mild randomness represented by the bell curve, but rather scalable wild randomness. What can be mathematized is usually not Gaussian, but Mandelbrotian.

Now, go read any of the classical thinkers who had something practical to say about the subject of chance, such as Cicero, and you find something different: a notion of probability that remains fuzzy throughout, as it needs to be, since such fuzziness is the very nature of uncertainty. Probability is a liberal art; it is a child of skepticism, not a tool for people with calculators on their belts to satisfy their desire to produce fancy calculations and certainties. Before Western thinking drowned in its “scientific” mentality, what is arrogantly called the Enlightenment, people prompted their brain to think—not compute. In a beautiful treatise now vanished from our consciousness, Dissertation on the Search for Truth , published in 1673, the polemist Simon Foucher exposed our psychological predilection for certainties. He teaches us the art of doubting, how to position ourselves between doubting and believing. He writes: “One needs to exit doubt in order to produce science—but few people heed the importance of not exiting from it prematurely. … It is a fact that one usually exits doubt without realizing it.” He warns us further: “We are dogma-prone from our mother’s wombs.”

By the confirmation error discussed in Chapter 5, we use the example of games, which probability theory was successful at tracking, and claim that this is a general case. Furthermore, just as we tend to underestimate the role of luck in life in general, we tend to overestimate it in games of chance.

“This building is inside the Platonic fold; life stands outside of it,” I wanted to shout.

Gambling with the Wrong Dice

I was in for quite a surprise when I learned that the building too was outside the Platonic fold.

The casino’s risk management, aside from setting its gambling policies, was geared toward reducing the losses resulting from cheaters. One does not need heavy training in probability theory to understand that the casino was sufficiently diversified across the different tables to not have to worry about taking a hit from an extremely lucky gambler (the diversification argument that leads to the bell curve, as we will see in Chapter 15). All they had to do was control the “whales,” the high rollers flown in at the casino’s expense from Manila or Hong Kong; whales can swing several million dollars in a gambling bout. Absent cheating, the performance of most individual gamblers would be the equivalent of a drop in the bucket, making the aggregate very stable.