What’s Luck Got to do with It? – Joseph Mazur ****

Joseph Mazur’s aim in this book is to expose the “diabolical con” of the voice in the gambler’s ear that tells him he can win. To attack the “gambler’s illusion” Joseph Mazur brings out some big guns of modern science, from the mathematics of probability to the psychology of cognitive biases. Preaching is not his style, however, and there is much more in the book than arguments against gambling. The book sometimes loses its way through thickets of sociology, reportage, literary analysis and personal anecdotes. But the end results is Mazur an eclectic, personable introduction to the topic.

The first third of the book is a potted history of lotteries, casinos, shares trading, and theories of probability. Mazur takes us from eighteenth-century Bath to nineteenth-century Mississippi, from the Iliad to modern-day Monte Carlo. Inevitably some important developments are left out. For example, the rise of private life insurance in the late 18C, and its origins in a middle class anxious to protect its newly gained wealth, gets short shrift. Mazur pushes the story along with succinct scene-setting, judicious borrowing from historians of the topic, and tales of lost riches.

Modern-day gamblers will be glad to know that they are in good company–even, or especially, if they are massively in debt. Past gambling debtors include writers such as Tolstoy and Dostoyevsky, wealthy plantation owners in the American South, well-heeled dandies from the London coffee-house scene, and the entire royal court of Louis XIV. Women as well as men made disastrous flutters. Consider Francis Baddock, the accomplished 19C heiress who hung herself with gold and silver girdles after wasting her £24,000 (£2 million today) fortune in a month of high-rolling.

From history Mazur moves on to his area of expertise, mathematics. Statistical concepts are notoriously hard to get across to laypeople, and Mazur uses plenty of examples, diagrams and anecdotes to help the medicine go down. Most interesting is a chapter on the “truly astonishing” law of large numbers; most useful, a summary of the mathematics of poker, blackjack, sports betting, lotteries, and slot machines. The aims of the other maths chapters are less well-defined, but a patient reader will find colourful introductions to significance tests, normal distributions, Pascal’s triangle, the statistics of the Wall Street crash, and more.

Next up, psychology. This third of the book, like the third on mathematics, has problems of organisation. Chapter 12, sub-titled “psychomanaging risk”, seems like a chapter of left-overs, with an analysis of “Deal or No Deal” thrown together with a study of George Eliot’s Daniel Deronda and the sad tale of a minister and psychotherapist who ruins himself in a Nigerian email scam. More purposeful is a chapter on 20th century psychologies of gambling–although Mazur concludes that general theories about why people gamble, starting with the Freudian theory that gamblers have a subconscious desire to lose, are in a sorry state.

More promising is the psychology of specific errors of reasoning. Mazur draws on those darlings of popular social science writing, Amos Tversky and Daniel Kahneman, in a chapter on the so-called “hot hands fallacy”: the belief that lucky streaks are more likely to continue than not. Reports of other gambling fallacies are scattered through the third on the book on psychology, from the house money effect (gamblers take more risks with their winnings than with their own money) to the Monte Carlo fallacy (after a string of reds, bet on blue). By showing that our statistical intuitions are not to be trusted, this material is at least as powerful an antidote to gambling behaviour as mathematical arguments.

If we count all these psychological effects, there is not one gambler’s illusion but many. Mazur is never very up-front about this problem, and one consequence is that the “gambler’s illusion” he describes in the introduction (the hot hands effect) is the opposite of the “gambler’s illusion” that appears in the book’s conclusion (the Monte Carlo fallacy). Another weakness is that Mazur never properly debunks the Monte Carlo fallacy. If a fair coin has come down head 60 times in 80 throws, surely we can expect the next 20 throws to have more tails than heads? Mazur’s rebuttal is that “we all know” that coins do not have memories; the chance of heads on a fair coin is always 50/50, irrespective of past throws. But this rebuttal is no use insofar as it does not reconcile our “no-memory” intuition with the equally strong intuition–the one behind the Monte Carlo fallacy–that fair coins should give half heads and half tails in the long term. This intuition is a version of the law of large numbers, which Mazur discusses — but not in enough detail to show why this otherwise sound law is misapplied in the Monte Carlo fallacy.

Gambling is a sad topic. For every lucky winner there are many forlorn addicts, like the women Mazur meets at casinos feeding coins into one-armed bandits at 5am. And along with the jackpots there are the suicides, like the London man who sunk his life savings on 24,000 lotto tickets in one week and came away with nothing. Stories like this are perhaps the best medicine for would-be gamblers, and Mazur’s book is full of them. But the book has an upbeat tone nevertheless, thanks to Mazur’s anecdotal style and passion for mathematics.

For gamblers, What’s Luck Got To Do With It? is a non-preachy introduction to the reasons for quitting, even if it leaves open some logical loopholes. For non-gamblers it is a sweeping tour of the seedy, sad and grandiose world of games of chance, with Mazur as a well-informed (if sometimes disoriented) guide.

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Review by Michael Bycroft