Chances Are (14 page)

“Once, in Atlantic City, someone offered me a bet based on the Monty Hall problem.” Zia Mahmood is one of the most skillful players in world bridge, combining an uncanny card sense with an intuitive, bravura style of play. “I knew the answer
had
to be to switch. We use the same probability argument in bridge: we call it the Principle of Restricted Choice, where someone playing
any
one card of two suggests that he had no choice—two-thirds of the time.”

Such is the human capacity for obsession and competition that the mere quarter-million possible five-card poker hands rapidly lose their intrinsic interest. Fortunately for those whose desire for complexity goes deeper, there is bridge. It offers 635,013,559,600 different possible hands. All are equally probable, although some are considerably more interesting than others; being dealt all the spades is just as
likely
as getting ♠ Q 10 9 5 4 2 ♥ 4 ♦ J 10 9 2 ♣ 9 2—the difference is that you feel the former is a sign of divine favor while the latter is “my usual lousy luck.”

We have come far enough together for you to be entitled to ask: “My chance of drawing all spades is one in 635,013,559,600? Just how do you come up with such a precise figure?” Well, spades are 13 out of the 52 cards, so your chance of taking a spade on the first draw is 13/52. If you
did
draw a spade, there will be 12 spades left out of 51 cards. So the chance of drawing two spades in succession is 13/52 × 12/51. Continue like this and you find your chance of drawing all and only spades is
which when simplified is one in 635,013,559,600.

Many odds calculations in bridge are similarly mechanical; the sort of deductive reasoning at which computers are particularly good—and there are, indeed, excellent bridge-playing computers now operating. Zia is convinced, though, that there is an intrinsic difference between the human and machine apprehension of probability in bridge because the uncertainties differ depending on exactly who is around the table. “Some players are machines, some Rottweilers, some are sensitive artists and some seem psychic. That means there is no one best play for a given situation; I could have the same hand and bid three hearts today and bid three spades tomorrow against different opponents—and have done the right thing both times.”

 

The running horse seems to waken an old memory in all observers: roused by hoofbeats, the most prosaic soul resonates to the ancient themes of saga and romance. Horses are
genuine
—athletes who know neither transfer values, endorsement contracts, strikes, or silly hairstyles. The equine victor stands shivering in the winner's circle, coat dark with sweat and veins bulging, gazing above our heads at something on the horizon; and we see the isolation of the hero, the being who has done what is beyond us—for us.

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 spot 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.