What's Luck Got to Do with It?

The History, Mathematics, and Psychology of the Gambler's Illusion

by Joseph Mazur

The book which I enjoyed reading left me with a mixed feeling. For, it reminded me of a homeschooling mother who assigned her children to learn by heart a list of words that they should not be using. The author powerfully and passionately forwards the thesis of utter unreasonableness of the expectations to win and the sense of control over one's fortunes and fate commonly proclaimed by individual gamblers. The author is quite unequivocal and outspoken about gambling being obsessive and destructive. And yet the reader gets so much information about the gambling and specifics of the games that it undoubtedly might compete with other volumes exclusively devoted to presenting particular games.

The book consists of three parts - The History, The Mathematics, The Analysis - and several appendices (Descriptions of the Games Used in This Book, Glossary of Gambling Terms Used in This Book, The Weak Law of Large Numbers, Glossary of Mathematical Definitions, Callouts).

The captions indicate the focus of each part while some discussion reemerge through the book. Real life and literary examples (anecdotes, if you will) of people addicted to gambling and the ruinous effect it had on their life and circumstances, are spread more or less evenly among the chapters. Fyodor Dostoyevsky and Leo Tolstoy are among the famous ones who suffered the consequences of their addiction. Mathematics relevant to the games of chance makes its first appearance in the historic setting of Part 1 following the names of Rabbi Abraham ben Meir ibn Ezra, Girolamo Cardano, fra Luca Pacciolli, Blaise Pascal, Pierre Fermat, Christian Huygens, Jacob and Nicholas Bernoulli, but in Part 2 and (especially in) appendices mathematics - statistics and probability - is covered at greater length. The experiments of Amos Tversky and Daniel Kahneman on decision making in the presence of uncertainty and risk are discussed in all three parts of the book.

In the first part - The History - the author traces the nature of gambling from prehistoric times through the 2008 world economic calamity. The protohumans were risking their lives to protect their kind and to provide for their families. The author treats gambling in a very broad sense. For example, on p. 4 we read

Risks are the gambles, the games, the balance of expectation and fate. And luck rarely comes without risking the possibility of loss, injury, trouble, vulnerability, ruin, or damage in a universe of opposing chances.

While I am in a complete agreement with the second sentence, I would restate the first one as,

Gambles are the risks, the games, the balance of expectation and fate.

It seems to me that taking risks due to exigency may not require the same state of mind as frivolous risking one's life, fortune, or one's family well being. This is a minor point of contention in an otherwise very plausible argument that gambling may have been germane to children playing with dry bones or adults throwing spears at their leisure.

Either way, the first part of the book presents the long history of gambling. This portion of the book reads as a chapter from the famous Extraordinary Popular Delusions and the Madness of Crowds by Charles Mackay. Edmund Burke is quoted (p. 54) to have said, "Gambling is a principle inherent in human nature." Proving this point makes only one thread weaved by author Mazur in the first part. From numerous examples, we learn that gambling in its different forms was a popular pastime all over the world of rich and poor, in peace and war, of intelligent and stupid. The author also follows the emergence and evolution of various gambling implements, like dice, of numerous forms of gambling - games, race betting, wagering of all kinds, lotteries. In this part we also learn the history of the development of counting techniques. The last chapter (Chapter 5) in Part 1 is a staggering indictment of the institutionalized gambling via stock exchanges and other forms of money manipulation by banking and brokerage industries.

Jacob Bernoulli's Golden Theorem (annunciated informally by Cardano) that is now known as the Weak Law of Large Numbers (so named by Siméon Denis Poisson) makes its appearance in Part 1. The treatment highlights its frequent misunderstanding and its misinterpretation as the Law of Averages. The Law of Large Numbers gives a justification to the statistical view on determination of probabilities. It tells us that in a sequence of success/failure experiments, the observed average of success may be expected - as the number of trials grows - to be arbitrary close to the probability of success. The law says nothing about individual trials. A common misconception is that, after a long sequence of failures, the chance (according to the Law of Large Numbers) will balance the situation by making a successful outcome more likely. This fallacy is what is known as the Law of Averages.

Mathematical aspects of the game of chance is the focus of the second part of the book. Besides the Law of Large Numbers, this part covers the binomial and normal distributions, standard deviation, the Central Limit Theorem and then applies the gained insights to the dissection of the games of chance - blackjack, lotteries, poker, roulette, slot machines, race betting, in particular. The narrative maintains the story-telling style adopted at the beginning of the book. Mathematics, as before, is introduced in a historic context. Abraham de Moivre found that the probability that the observed mean outcome in a sequence of experiments falls within a specific range around the expected value behaves as if it was governed by the binomial distribution. De Moivre's result laid the foundation of the modern statistical research. However, its significance has completely escaped his contemporaries. In the form of The Central Limit Theorem is was proved by Pierre-Simon Laplace a quarter century later.

By the end of Part 2 we learn that, all mathematics notwithstanding, the populace keeps gambling in droves. As an example, in 2005 Americans spent more than $33 billion on slot machines in casinos.

The focus of Part 3 is the gambler's psychology; the reader is treated to more examples, starting with the author's childhood experiences. Episodes from the TV show "Let's Make a Deal" and the Nigerian web swindles serve several examples of irrational behavior. The "fame effect" makes a person to savor the spotlight even when quitting would be a more rational attitude. The "house effect" pulls a fellow to continue gambling even after losing the free "house" money. There is also the "hot hand" effect which is the feeling of being on the receiving end of the fortune's largess. The author quotes from a 1985 paper by Amos Tversky and coworkers (p. 205):

People reject randomness and the mathematical(ly) expected number of runs because the appearance of long runs in short samples seems too purposeful to be random.

Outrageously, gambling establishments are well aware of gambler's weaknesses and exploit them to their advantage. But what makes a gambler?

The most recent research, using PET scans, suggests that pathological gamblers, alcoholics, and drug edicts have similar patterns of neural activity when exposed to their individual addictions. We know that just as the sight of drinks easily seduces alcoholics, lottery drawings, casinos, and Internet gambling sites strongly influence pathological gamblers.

In addition, there is a multitude of psychoanalytic theories that attempt to explain the predilection to gambling. Some theories are so bizarre that I believe their authors gambled with their scientific reputation going public. Say (p. 185)

Another prominent early twentieth-century psychoanalyst, Hans Von Hattinberg, connected gambling obsessions to the toddler years of toilet training, when unrestricted bowel eliminations (which he believed to be autoerotic pleasure) suddenly become checked under toilet protocols for the first time. This discouraged pleasure emerges in adulthood as the obsessive desire to gamble--the unconscious views this as the unrestricted flow of cash.

As the author subsequently observes (p. 186), "Testing such theories was (and still is) difficult and expensive."

Part 3 ends with the philosophical observation (p. 216) that

Life is a vast sequence of happenings and choices; happenings just happen, but free-will choices are gambles with what's ahead ... I would argue that some--if not most--gambling behavior is primarily connected to an intrinsic desire to manipulate luck ... Making choices based on scant knowledge is an essential function of consciousness. It is eating from the tree of life. ... What could be more humanly natural than to have a desire to control one's destiny? It fits the desire to believe that there is some merciful being who will oversee existence, protection, and posterity.

This seems a little far reaching, to my taste. I do not consider every situation that forces a choice even on scant knowledge a gamble. It's one thing to have to make a choice and another to seek a situation where choices are to be made. Gambling addiction is humanly natural no more than alcoholism is. This is related to the point of contention I mentioned at the beginning. But given the numbers - the popularity of gambling and the incurred risks and expenses - the author clearly has a point. The book beautifully delivers the message.

What's Luck Got to Do with It?. The History, Mathematics, and Psychology of the Gambler's Illusion, by Joseph Mazur. Princeton University Press. Hardcover, 278 pp, $29.95. ISBN 0-691-13890-7.

71544750