Chances Are

by Michael Kaplan

  When the young Paul Mellon admitted that he was interested in owning racehorses, his father—Hoover’s very frightening Secretary of the Treasury—fumed that “any damned fool knows that one horse runs faster than another.” Most damned fools also know that a horse runs more slowly under extra weight, and that the longer the race, the more distance lost. Younger horses and fillies, being naturally of a lighter build, feel the effects of weight more keenly than older horses and colts. A horse’s performance on a given day seems the opposite of random: it is the unique solution to an equation in many variables, including form (the who-beat-whom-when relationships that all serious horseplayers know by heart); the condition of the racing surface; the likely run of the race and its implications for speed against stamina: Who will be pacemaker? Who has a finishing kick? Is the jockey bright enough to realize that the inside of a curve is shorter than the outside? Finally, there is the behavior of the bookies themselves: are the odds shortening fast for one particular horse? Does that horse have an owner or trainer known to bet, hoping to clean up today? Each of these is an essential element in the science of picking winners. This variability makes horseracing addictive to the gambler. Failure is always explicable: negative results are as intellectually satisfying as positive ones. True, there is that stinging sense of losing money—but there is also, always, the satisfaction of finding a rational explanation.

  For years, the science of betting on horses was a little like high-school chemistry: certain combinations, certain procedures produced a satisfying result sometimes, but there was no unifying sense of why they worked. So many variables cluttered up the calculations that a small discrepancy in any of them could distort the whole result. It was only when an ex-math teacher named Phil Bull brought his stopwatch to the races, that one variable stood out above all others: time. A horse that has carried a given weight over a given distance in a shorter time than other horses have in other races will probably beat them, no matter how the form lines connect them or what the trainer tells the press. Bull’s stopwatch supported him as a professional gambler for two decades, giving the world the unusual sight of a math teacher in a Rolls-Royce, smoking a cigar. Eventually the bookies, too, resorted to timing; then the race courses published official times, and when the government decided that something as lucrative as betting should be taxed, Bull moved on to create a publishing empire, Timeform, supplying fellow betting scientists with the same raw data he used himself.

  Timeform still operates from Bull’s hometown. The current chief executive, Jim McGrath, joined the company in his teens after attempting to break into racing as a jockey. Dark-suited, solemn, he has far more of the seminary than the stable yard in his manner. He also bets as a “serious hobby,” making, he says, a profit of around 15 percent on his turnover—enough to have brought him into the ranks of racehorse owners.

  “It’s an art as well as a science,” explains McGrath. “You apply your skill—judgment of form, ground, trainers, and jockeys—to select horses with potential, but then you need discipline: ‘I think this horse has got a very good chance of winning, around three-to-one, but he’s trading at eleven-to-four. Is that good value? Do I back him or do I leave him out?’ Everybody can pick winners—give your granny fifty bets and some will win. It’s eliminating losers that’s difficult. Not every person has the strength of character to walk away from a bet . . . but if you can’t, you won’t win.”

  The science of uncertainty is fascinating—but fascination is no reason not to bet on a certainty, if you can find one. Photo-finish cameras came to Britain in 1948; but a traditional photograph takes five minutes to develop—how should bookmakers and gamblers pass the time? By betting on the result of the photograph, giving all those eager scientific minds twice the exercise for each close race. The professional gambler Alex Bird saw potential here; stationing himself as close as possible to the winning post, he closed one eye and, alone among all spectators, refrained from watching the approaching horses. While all others remembered the race as an unfolding story, seen by its end through the tears of joy or sorrow, Bird saw only what the camera saw: one nose ahead of another at one vital moment. For five minutes, he was in the position of a man with tomorrow’s newspaper. It made him very rich.

  If, in London, you are short of something to say to a taxi driver or a duke (after exhausting the weather), you can always discuss betting on horses. The stock market, though, is a tricky topic, seen as either vulgar or crooked. In America, the weighting is reversed: mention you’re studying probability, and the first question will usually be whether it tells you what stocks to buy. Horses and investments share the fascination of an immature science: there are lots of reasons for any event, and some other person—pundit or tipster—knows which is most important.

  “When I was young,” said Sir Ernest Cassel, banker to King Edward VII, “I was called a gambler. As the scale of my operations increased, I was known as a speculator. Now I am called a banker. But I have been doing the same thing all the time.” Someone who cannot stay off the phone to the bookie is a compulsive gambler. Someone with a dedicated line to his broker is a committed investor. We allow financial markets a degree of comparative dignity because they reflect the economy of the nation and the livelihoods of us all. But then roulette demonstrates the eternal laws of physics, and horseracing those of genetics; these aren’t, however, the reasons for our following any of them. Ball, card, odds board, or ticker, we stare at them because they promise us the twin pleasures of excitement and unearned gain.

  Earth, this lone orb hanging in space, gains from the sun each year enough energy to justify between 1.5 percent and 2 percent economic growth. In gross terms, making anything more than that involves playing the odds: anticipating red when all around shout “black”; knowing the deck holds more high cards than usual; backing the stable that’s coming into form. This brings out the same patterns of behavior in brokers and investors that you will see recurring, slightly more loudly, in Las Vegas. “Chartists” and other formal analysts treat market indicators much as the febrile crowds with their little pencils follow the progress of the wheel: they see the numbers as encoding pattern, reflecting the driving forces of some hidden generator. You can find an analyst to champion almost every complex randomizing mechanism as the secret begetter of market change: Markov chains, fractal curves, spin glass algorithms, simulated annealing—all the ways nature shakes order into phenomena through random nudges. The appeal of the financial markets to pattern seekers is not just that someone will pay them to exercise their dark arts, but that the jagged traces of financial indices seem significant at every scale, from the great waves that roll under the monetary cycle to the hectic ticking of this day’s trading. Choose your algorithm and there will be a time-scale it fits best; and if it fits, there must be a reason.

  The problem for chartists is that they lack the probability information that any roulette player has: despite the efforts of generations of economists, there is only the meagerest sense of how a market should behave “normally.” This means that, even where a pattern seems to be forming, the analysts will have to guess at the function that generates it—and one awkward truth of mathematics is that many different combinations of functions, many superimposed generators (or, indeed, pure randomness), can produce the same trace over a finite range of input: in this case, over finite time. Of these many possible generators, some may continue the apparent trend into the future, in which case the analyst gains a handsome bonus; but some will introduce large, unpredictable variations immediately after the period analyzed—ending in a curt interview and a cardboard box of personal effects at the security desk.

  As well as pattern-chasers, there are also wheel-watchers and card-counters in the market: people who believe that in the midst of randomness there are sudden moments of order, pockets of smooth flow in the surrounding rapids. Indeed, the people behind the shoe-mounted roulette computer later moved into doing the same thing for financial trading, advising Swiss banks on how to s
pot and exploit the market’s brief Newtonian spells. Their contracts forbid them to say how well they’re doing—but their clients have not yet won all the money.

  Gambler’s swank is never far away in the financial district. Trading selects for the aggressive, not just because they want to win, but because they can create fear of gambler’s ruin in the other party. Mergers and acquisitions may be framed in terms of “synergies of the business” or “streamlining processes”; but the real question is, again, the size of the bankroll each player brings to the table. Companies, too, have gambler’s swank: at the moment when the dotcom bubble reached its maximum of globularity, start-ups were bragging competitively about “burn rate”—how much of their backers’ money they were getting through each month. In a game with no edge, you have to play as if your pockets are bottomless.

  Of course, swank has a distorting influence in markets where predictions can be self-fulfilling; if enough people believe in your IPO you win, although no amount of crowd desire will force the favorite first across the line. And there is a further major difference between investment in financial markets and any other form of gambling: it is unbounded, both in time and result. The wheel stops, the slots eat or regurgitate change, the raise is called—but the markets carry on. So, yes: if you had invested ten dollars in the Dow in 1900 you would now be able to hire Donald Trump as your butler—assuming you sold RCA on October 28, 1929. Moreover, you cannot lose more than you put on the table during this turn at blackjack or roulette; but in the markets, your winnings so far—all those comforting paper gains in your pension report—remain in play, at risk throughout the term of investment. It is as if, on the rare occasion when the roulette wheel stops at zero, the house also had the right to everything in your pockets. Most financial markets operate this way, offering a drip-feed of little gains to compensate for the potential deluge of loss.

  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 win
king 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

  There was a man in the land of Uz, whose name was Job; and that man was perfect and upright, and one that feared God, and eschewed evil.

  —Job 1:1

  Of 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, unlucky—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.