The Paradox of "Hitting It Big"

January 8, 1998

Philip J. Davis

This article is a reaction to a letter sent recently by a high school teacher of mathematics to a local newspaper. The teacher was complaining that, as regards gambling, the math teachers of the country have not done their duty. They have not driven home the brute fact that people who go into casinos or play the lot, on average, lose money.

I have a somewhat different opinion. People know very well that, on average, they lose money when they gamble. The public knows that the casino owners or the state governments are raking it in; that if they weren't, the slots and the wheels and the little scratchaway slips would rapidly be junked, that the stock of the big suppliers of mathematical gambling systems and hardware would plummet. It is not a question of knowledge; something else is at work.

Mary Y. and John Q. Public say to themselves: "Averages be damned! I'm not going to run my life by averages. I'm going to really hit it big next time." And if they hit it, by God, 50 million power ball dollars walk into their checking account over a period of years, to make them ecstatically happy or miserable, as the case may be.

What is the relation between the received mathematical theories of probability and people's actions? Is the former an adequate description of the latter? Is it possible to set dollar value on the entertainment implicit in gambling, on the expectation of "hitting it big," and to factor the adrenaline into our theories? (Some psychologists have written that in numerous cases, the adrenaline comes from losing, not from winning.) Well, you might say that the market automatically does just that, and its answer seems to have resulted in the largest mania for gambling and the production of the largest legalized gambling industry that has ever flourished in this country.

Moving away from gambling conceived narrowly as The Lot, The Wheel, or the chances that kids sell to enable the High School Band to buy uniforms, we are all fundamentally gamblers. When we cross the street we take chances; when we have children we take genetic chances. The pop-philosophers even assure us that life is a worthwhile gamble, and so we indoctrinate our children into our personal perception of the common sense of living in a chancy world. And what role does mathematics play in all this?

I recall going some years ago to a scientific meeting held at the National Cancer Institute in Bethesda. A noticeable number of the participants, including the local statisticians, were puffing away. I wonder how it would be now that the antismoking campaign has intensified considerably. What has resulted from the bumper stickers that read "Say no to X, Y, and Z"?

Consider the gambling aspects of book publishing. There are many, many reasons why a person might want to have a book published. Desire to inform, to amuse, to warn, to confess; desire to appear wise, to achieve fame or notoriety, to praise, to smear, to amass power; desire to perform a public service. Despite the large salad bar of possible motivations, only a relatively few people go the route of commercial publication. And there is one additional motive, lurking behind all the others: the desire to hit it big as regards royalties.

We have all heard of books in the scientific field that have hit it big. All kinds of books: textbook popularizations, even books that only a half dozen people in the world would claim to have understood. Out of the hundreds and hundreds of manuscripts submitted in these categories, many have been called but Lady Luck has chosen few to hit it big.

I have not seen any statistics on the subject, but my personal estimate is that, on average, book writing pays less than minimum wage. You have written, say, a short monograph on an advanced mathematical topic. How many copies will you sell? 1500 (2000, in the palmy days before libraries were computerized), all over the world? So at $25 a copy and a royalty of 10%, you will get $3750, which is 750 hours at a wage of $5/hour, or three months' work at eight hours a day. Do you think you could knock off a monograph in three months? Could a novelist knock off a novel in three months? No way, Josť, unless your name happens to be Georges Simenon or Barbara Cartland of Harlequin fame. And I've heard that the average first novel sells fewer than 2000 copies.

Of course, all kinds of objections can be raised to these computations. Nonetheless, on the basis of the stats, I would advise the would-be author: Get out of the writing game and into lecturing or op-ed'ing, where the hourly return can be greater. Yet the flame lit by the expectation of "hitting it big" burns brighter than you might think, and I know numerous scientists who have taken up the pen in this expectation and been gravely disappointed.

How does the matter look from the publishers' side? If the author is a gambler risking his/her time, then the publishers are the casino owners, who will tend to diversify their portfolios of authors. What they lose on monographs, they may make up on wildly successful textbooks or popularizations. So, we might say: Weep no tears for the publishers.

But that would be an inadequate perception of a complex situation, where the competition of other distributive modes has cut into the book market; where increasing manufacturing costs and slashed library budgets have upset old guidelines; where takeovers have been rampant and have resulted in publishers who now want only block-buster manuscripts that will hit it big; where the very act of reading is perceived to have been threatened by the public's whole-hearted joining with the computer mouseketeers.

Enough about writing. After all, relatively few people write and get paid for it. Let's talk about travel. A larger fraction of the population travels. Now there we may experience the reverse phenomenon, in which a single disaster sets off a chain reaction in excess of what might have been deduced from a calm consideration of the probabilities. I recall that about ten years ago, in response to terrorist action in London, the tourist business experienced a terrible slump. So much so that when my wife and I showed up in London as we had planned months in advance, our British friends expressed surprise: "You didn't cancel out?"

Or, please tell me what is the prudent course of action to take when you read in the papers that a certain airline has had a disaster and you are holding space on one of their flights.

Yes, one day we say, "Damn the stats. The weather in an average life is a light drizzle. All honor to the individual life!" And the next day we succumb to the insurance peddler who points out some corner of our lives that is not covered by our current policies or by the government. Reader: Does your homeowner's policy cover you against power blackouts and spoilage of the contents of your freezer?

Conclusion: it is very hard to move from mathematical theories of probability to moral or economic advice for the individual. Whether or not such advice will be taken seems itself to be a random variable.

Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island.

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