Chances Are (15 page)

This state of affairs reflects an innate imbalance in our view of risk. We like to see our statement get bigger, month after month. Our brokers and their analysts are paid by the year; they like to match the mean growth of their industry, since their bonuses depend on it. When the wheel hits zero and the money disappears, the brokers and analysts are fired, only to be replaced by new people who think just the same way. And unless we are made completely destitute, we also soon forget the lesson of our loss; tomorrow is a new day and we have survived the unthinkable—or, at least, like Dostoevskian heroes, we have shown the world that we know how to lose well.

It makes you wonder: are, say, hedge fund investors intrinsically more rational than the old lady in the visor and one glove, feeding her favorite machine with quarters from a paper cup? She, at least, gets the pleasure most gamblers pay for: perpetual expectation. Making money is only the medium; the message is being singled out for favor, taking a brief vacation from the
quid pro quo
of work and cost. Church halls still fill with devout bingo players, although the house edge there gives a pretty good idea of God's omnipotence. People mark their lottery cards every week, although the chance of striking it lucky in most 6-out-of-49 games is about one-eighteenth the chance of being struck by lightning.

Almost since they first began, lotteries have been criticized as a tax on the poor. That may be so; but we should consider the alternative uses for the money. Five dollars will make little difference to a family's weekly spending; putting it away in the bank at a 2 percent real return means that fifty years of savings might add up to enough for an extra three years of penury in old age—$34,970. Yet the possibility, however remote, of winning real wealth provides its own rate of interest in dreams and hope. Will you buy the Ferrari first or go to Tahiti? Set up your children in houses or, as one lucky trucker did, drive around the highway system for a month, waving to your ex-workmates from the open sunroof of a limousine? In fact, looking at the lives of so many who have suddenly become rich, lotteries may actually do more for those who do
not
win than for those who do.

If you insist that sudden wealth will not spoil you, there is—although no way to improve the odds of winning—at least a technique to increase the amount you would win if your numbers came up: think randomly. People not only see patterns, they cannot resist them. They draw diagonals, choose dates—so any winning sequence with 19 or 20 in it is more likely to have multiple winners sharing the jackpot. If you can switch off the gambler's belief in significance, and revel in the randomness of choice, your numbers are more likely to be yours alone.

 

Paradox, like the pun, is a debased form of art—but there's one paradox that shows nicely how you can win from losing games, all through the power of randomness. It's called Parrondo's paradox, and was devised in 1997 by a professor at the Universidad Complutense in Madrid. Imagine that the Buddhist casino owners have been corrupted by their chosen trade and now offer two games, each with a house advantage. Game A is like their previous coin-tossing game, but now involves a slightly biased coin, so that you have marginally less than a 50 percent chance of winning. Game B is more complicated, to inveigle the unwary. You usually get to toss a coin that
favors
you (giving you about a 75 percent chance), but each time your total capital is a multiple of 3, you have to toss the Coin of Doom, on which you lose 90 percent of the time. Over the long run, this more than balances out the advantage from the favorable coin: Game B is as much a mug's game as Game A.

Now, though, paradox comes in: imagine you can switch from one game to another—at set intervals, or even randomly. Suddenly, your total capital begins to increase. Why? Because Game B involves winning often but losing big, while Game A involves near-stasis. Being able, occasionally, to duck out of Game B increases your chances of missing the obliterating blow when your capital is a multiple of 3. The best way to imagine it is in the form of the Cornish Man Engine, a nineteenth-century device for getting workers up and down the shafts of tin mines. It had two ladders: one fixed permanently to the shaft wall, and one that moved up and down with the six-foot stroke of the steam engine at the top. Neither ladder
went
anywhere, so staying on either one would leave the miner permanently down the pit. But switching to the moving ladder, either at the top or bottom of the stroke, allowed miners to be shunted up or down six feet, before switching again to stand pat by the wall as the stroke returned, and thus make their way to the seam or the surface in a series of pulls. Parrondo's Game B is a jerky engine, with a slow upstroke and a sudden downstroke; his Game A is close to motionless, a fixed ladder. A miner who switched between them, even randomly, even blindfolded, would spend more time going up than down.

Ingenious people are currently trying to find ways to apply this to stock markets, switching, say, between high-volatility shares and cash—but, as yet, it looks as if you would do better by searching out corrupted Buddhists.

 

In Pushkin's
Queen of Spades,
all the young officers gamble and all lose—because their interest is pleasure. Herman the engineer, however, is “not in a position to sacrifice the essential in the hope of acquiring the superfluous.” He touches no cards until he hears the story of the old Countess Anna Fedotovna, who was given a magic method, those many years ago in Paris. She had only used it to get herself and—once—a friend out of embarrassments; Herman now wants it as a sure path to riches. He threatens the Countess with a pistol, and she dies; on the night of her funeral, she appears to him in a dream and reveals the secret: play 3 on day one; 7 on day two; ace on day three. Herman wins and doubles his money the first two days, but on the third, instead of the ace, the ill-fated Queen of Spades is turned up and—as Herman's fortune is scooped into the banker's bag—winks at him. He goes mad. The others marry well; for them, gambling was a prelude to more important things.

Bet your shirt on a horse, your retirement on GE, your premiums on disaster, your tuition on a college . . . your energy on a book. Birth is just anteing up; every action thereafter is a bet. We need betting to remind us of our habit of drawing conclusions from insufficient evidence; we must remember that being too sure of anything is likely to end in a winking queen and a sudden surge of blood to the head. The lesson of the tables comes when we push back the chair, stride out through the hushed, shadowy palace, and enter once more the world of people, with their habits and quirks, biases and secret patterns. That is when the true gambling begins.

5

Securing

—Job 1:1

 

 

 

 

 

 

 

O
f course, if Job could have taken out insurance, the whole point of his story would be lost. Job's comforters had the practical, modern view: nothing, good or bad, occurs without a reason. The poignancy of genuine misfortune, though, is that it is in the realm not of practicality, but of probability: it just happens. If God turns out to be behind it, He rarely gives us a glimpse of His reasoning—and if He did, would He still be God?

All a man's piety will not make him proof against disease, fire, and war. Who could be so pure as to avoid all misfortune, to merit only contentment and delight? “Too many fall from great and good for you to doubt the likelihood,” as Robert Frost crisply put it. So, if we cannot control our local fates by making ourselves deserving of divine favor, what is left? Many—most—societies, at this point, leave the big idea of Goodness at the temple threshold and turn to the thousand little household shifts of ritual and superstition.

Rubbing against an adulterer will cure warts; a cork under the pillow relieves cramp. We divine and conjure by fire, hair, dogs, salt, mirrors, or the new moon. In Ireland, the week's first day has been particularly lucky—and in Scotland,
un
lucky—for more than a thousand years . . . long before Stormy Monday had a name. The Romans of the Republic elevated superstition to a point where it almost defined them as a people. Minucius the dictator immediately resigned because a shrew squeaked in the Forum at his proclamation. Flaminius was stripped of office after his great victory over the Gauls—because he had ignored the omens that predicted defeat.

The more hazardous or unpredictable the work we do, the more magical the precautions we take. Sailors (though their touch brings luck to others) are hemmed in by objects of ill fortune: stormy petrels, crossed eyes, eggs, rabbits, swans. Fishermen dare not mention ministers, wash scales from their boats, or utter the true name of the Red Fish. Baseball players put their right shoes on first, and actors must never wish each other luck or mention
Macbeth
. Do you walk under ladders? Probably not without a feeling of defiance, at least.

Sense and superstition are not entirely separate kingdoms, though, and not all traditional mitigators of misfortune are matters of omen and taboo. Some are intelligent anticipations of risk—such as the practice among many hunter-gatherer societies of leaving behind a little of all found treasures, from berries to buffalo. This is effectively insurance: paying a premium into an environmental policy to tide you through the bad times.

The other traditional form of insurance is having many children. “Blessed is he who haveth his quiver full of them: they shall not be ashamed, but they shall speak with the enemies in the gate,” says the Psalmist (euphemistically describing a practice still, sadly, current in his country). Each child is a separate policy, diversifying our genetic risk over time and space, increasing the chances our line will survive any one disaster. Somalis grade and name their famines by how much of this investment must be written off: “Leave the Baby” is the first degree, followed by “Leave the Children,” “Leave the Wife,” and “Leave the Animals.” The logic—and the cold-bloodedness—parallels the advice a consultant would give a failing company: last hire/first fire, slash the workforce, default on the backers, shut the plant.

 

In the United States, non-life insurance claims average close to a billion dollars every day, and cover the whole range of human misfortune: the predictable winds of the Gulf of Mexico and the uncertain ground of California; Nebraska hailstones the size of golf balls; roaring Arizona brushfires; defaulting New York debtors. Physical, moral, or financial collapse, explosion, subsidence, combustion, consumption, and rot—no matter what the disaster, you'll find a company somewhere willing to bet it happens less often than you think it does.

That bet is a curious one when reduced to its essentials: a parceling out of the world's misfortune into individual bags, one of which you can buy. Take out fire insurance and your premium is, in theory, your fair share of the loss from all the world's insured fires this year. In 2001, that total loss was roughly $36 billion. Like all global numbers, it's so large as to be meaningless; but it is the equivalent of the entire gross domestic product of Ecuador having been blasted to smoking ruin in a single fireball.

Seen in that blazing light, your premium might appear relatively small—especially when you know that it also includes your share of the salaries of thousands of sleek executives and rent on impressive offices in a host of busy cities. So if the ratio of your premium to the value of your house is really an accurate reflection of the probability of your losing everything in a fire, perhaps the world, seen as a whole, is less dangerous than it seems. This apparent discrepancy between premium and loss reflects a deep, old, and natural psychological imbalance. We think we are more prone to misfortune than simple probability suggests—because the evil thing that happens to us is intrinsically worse than the same thing happening to someone else. “Who has a sorrow like unto my sorrow?” When misfortune strikes me or those I love, it ceases to be a statistic and becomes a unique tragedy, too imaginable in all its terrible detail. It is no longer Chance—it is Destiny.

 

Put in purely probabilistic terms, insurance is no more than the even redistribution of risk: dividing unbearable trouble into bearable doses. In legal terms, it is the substitution of corporate responsibility for personal loss. In emotional terms, though, it will always appear as something more complicated, which may explain the typical grandiloquence of its advocates. In the 1911 edition of the
Encyclopaedia Britannica,
the contributors Charlton Lewis and Thomas Ingram wrote:

 

If we strip away the Edwardian veneer and look at the solid woodwork underneath, what do we see? Laplace's 8th, 9th and 10th Principles and, binding them together, Bernoulli's Weak Law of Large Numbers.

Like their near-contemporaries the Bach family, the Bernoullis were a constellation of professional talent: twelve made significant discoveries in mathematics and no fewer than five worked on probability. Staring out, ruffed and ringleted, from his portrait of 1687, Jakob Bernoulli looks self-assured, even arrogant. But there is also something in that flat eye and downward-turning mouth of the “bilious and melancholly temper” mentioned by his biographer. Bernoulli spent his life as a professor at Basel; after his death, his papers revealed he had been puzzling for twenty years over the problem of uncertainty, or
a posteriori
probability—that is, how to assign a likelihood to a future event purely on the basis of having observed past events. For Pascal, probability had been an
a priori
game, where we knew the rules if not the flow of play: all those coin tosses and card turnings expressed simple, preexisting axioms recognized by us, the players. But what if, as in most natural sciences, we do
not
know the rules? How and when do repeated observations or experiments, each with its own degree of circumstantial error, tell us whether Nature is playing with a full deck or a fair coin?