Beyond Coincidence (14 page)

Richard Wiseman points out that the risk of believing too much in one's own luck is not limited to adrenaline junkies.

“Research being done by psychologists has revealed a growing body of people who are relying totally on the prospect of good luck on the lottery as a means of progressing in life. Rather than trying to get a job or seek promotion, they are just sitting back and waiting for their lucky numbers to come up. They are convinced it will happen, so see no point in making an effort in any other areas of their life.

“Putting trust in superstitious beliefs in luck is disastrous. Luck simply doesn't work like that. Research shows that unlucky people tend to be more superstitious than lucky people. Lucky people are generally more constructive about the problems in their lives. Unlucky people invest all their optimism in an outside agency. They have a magical viewpoint of luck. The problem is that all these superstitious rituals, touching wood, and lucky charms, don't work and these people just end up getting even unluckier.”

Professor Chris French says research proves that people who are psychologically healthy and think of themselves as lucky people are actually less in touch with reality than depressives.

“The truth is that life really is pretty awful,” he says. “The depressives have got it right. The people who don't suffer from depression are the ones who have what we call ‘unrealistic optimism.' We give people questionnaires to fill in and ask them what are the chances of certain negative things happening to them—of being run over by a bus or contracting a particular illness. Most people assume that the bad things won't happen to them and the good things will. And the truth is that they are being overly optimistic. The depressives tend to be much more accurate. But by living your life as if you were a lucky person, good things will tend to happen to you because you will be willing to take risks. By not living in an overcautious, worried, anxious way, you will get more out of life. This is a nice example of a situation where an irrational belief can be psychologically healthy.” In the final analysis, whether we go to luck school and learn to control our luck, carry lucky rabbit's feet in the hope of warding off bad luck—or simply leave ourselves open to whatever luck is handed down to us from on high (literally in the case of forest ranger Roy Sullivan), Dame Fortune can be very mischievous.

In June 1980, Maureen Wilcox bought tickets for both the Massachusetts and Rhode Island lotteries. She had the winning numbers for both but didn't win a penny. Her Massachusetts numbers won the Rhode Island lottery and her Rhode Island numbers won the Massachusetts lottery.

What on earth could she have done to deserve that?

7

DOES COINCIDENCE ADD UP?

Mathematicians are not fanciful people. They are rationalists, using numbers to understand life's mysteries. Where others see coincidences as evidence of magic or divine intervention, they see the laws of probability in action.

So how unlikely would something have to be, how long the odds against it, before a fusty old mathematician was prepared to accept that it was beyond coincidence—that something really rather strange was going on?

What's the most unlikely thing you could imagine happening? Winning millions on the lottery—twice? Being struck repeatedly by lightning? These things happen, as we have already seen. They don't happen very often, of course, and not usually to us, but they do happen. Mathematicians tell us that if a thing can occur it will occur—eventually. Only impossible things don't happen—like discovering icebergs in the Sahara or taxis in the rain.

How does the mathematics of probability—of coincidence—add up? What would be the odds, for example, of being struck by a meteorite just minutes after discussing the odds against such a thing happening? And if it happened, would a mathematician be prepared to believe that it was just coincidence? The answer to this a little later.

Meanwhile, at the other end of the probability scale, how surprised should we be when we meet someone at a party who happens to have the same birthday?

With odds of 365 to 1 against, it doesn't seem like this should happen too often. When we find someone who shares our birth date, we tend to think something a bit special has happened. Fancy that, of all the dates in the year, we have the same birthday. What a coincidence!

Surprisingly the (rather complicated) mathematical formula dictates that you only need twenty-three people in a room for there to be a better than 50 percent probability that two of them will share the same birthday.

It seems an absurdly low figure—one worth putting to the test. We looked for an average sample of people. Where better to find one than on the street?

In the event, we had to ask twenty-nine people before we found a match—a young girl waiting for a bus was born on 24 July, the same day as the sixth person we spoke to. The girl at the bus stop was not remotely surprised that we had only had to stop so few people. In fact she thought it odd we had had to ask as many as twenty-nine. Her boyfriend, and four of her friends, all shared her birthday!

Eminent mathematician Warren Weaver once explained this at a dinner attended by high-ranking U.S. military men and then started around the table to compare birthdays. To his disappointment, he reached the last officer without turning up a single coincidence. But he was rescued by the twenty-third person in the room. The waitress, who had been listening, announced that she had been born on the same day as one of the generals.

Mathematical truths are often counterintuitive. The reality can surprise and delight us—or, at times, disturb us. We have a natural tendency to think the likelihood of something happening is either much greater or, indeed, much smaller than it really is. Our underestimation of the odds against winning the lottery keeps us buying tickets, and our overestimation of the odds against a road accident keeps us driving our cars.

Let's look at some other improbable things. If you were playing bridge and received a hand containing thirteen cards of the same suit, you would be amazed. And yet that eventuality is no more likely, or unlikely, than any other combination of cards. The likelihood of receiving any
predicted
hand of cards is, of course, another matter. The odds against being dealt all thirteen spades, for example, has been calculated as 635,013,559,600 to 1.

So the average bridge player shouldn't expect this sort of thing to happen too often in a lifetime, unless he happens to live on the planet described by evolutionary biologist Richard Dawkins in his book,
The Blind Watchmaker.

If on some planet there are beings with a lifetime of a million centuries, their spotlight of comprehensible risk will extend that much farther toward the right-hand end of the continuum. They will expect to be dealt a perfect bridge hand from time to time, and will scarcely trouble to write home about it when it happens.

When Dawkins says “dealt a perfect bridge hand,” he means when someone receives a “perfect deal,” such as thirteen cards of the same suit. A “perfect hand” in bridge would be one that cannot be beaten, and involves quite different mathematical calculations. In case you are interested, the odds against being dealt a perfect hand in bridge are 169,066,442 to 1.

Anyway, even on a planet where people live for countless millennia, the prospect of
all four
players in a bridge game receiving perfect deals looks a little unlikely. Dawkins calculates the odds against this happening as 2,235,197,406,895,366,368,301,559,999 to 1.

As mind-boggling as those odds may seem, such an extraordinary event has, apparently, happened—at a whist club in England, back in January 1998. As reported in the paper:

Eighty-seven-year-old Hilda Golding was the first to pick up her hand. She was dealt all thirteen clubs in the pack. “I was amazed. I'd never seen anything like it before, and I've been playing for about forty-odd years,” she said.

Hazel Ruffles had all the diamonds. Alison Chivers held the hearts. The spades were with the dummy. Alison Chivers insists that the cards were shuffled properly. “It was an ordinary pack of cards. They were shuffled before they went on the table, and Hazel shuffled them again before they were dealt.”

The elderly members of the whist club had just beaten astronomical odds. It was actually more likely that each would win the jackpot in the national lottery and the football pools in the same week. Unfortunately it didn't win them a penny.

So just how astonished should we be by such an event? That we know about it at all is a product of “selective reporting.” The newspapers printed the story because they had decided that it had been a remarkable thing. The perfect hand of bridge is more likely to make headlines than an imperfect one. We don't get headlines saying “Bridge Players Are Dealt Random Shuffle of Cards.”

William Hartston, author of
The Book of Numbers,
believes we get too excited about coincidences. For example, he was less than impressed by the story of two golfers who hit a hole in one with successive shots. The players had the same surname but were not related. Wasn't this rather extraordinary?

Not a bit of it, says Hartston, “First of all, let's dispose of the little matter of the golfers having the same name. The tournament was in Wales and their shared surname was Evans.”

But Richard and Mark Evans had both hit a hole in one at the third with successive shots. What are the odds against that?

Hartston estimates that the chance of a hole in one varies from 1 in 2,780 for a top professional to 1 in about 43,000 for a club-swinging amateur. In the latter case he calculates that on any given hole, the chance of two players acing the ball with their tee shots, one after the other, would be 1.85 billion to 1.

But isn't that pretty staggering?

Apparently not, Hartston explains, “If 2 million golfers play an average of two rounds of golf a week each, that's more than 200 million rounds of golf a year, amounting to a total of 3.6 billion holes. That 1.85 billion to 1 shot doesn't look so unlikely anymore, does it?” In fact, if Hartston's calculations are correct, we should expect this sort of thing to happen somewhere about once a year.

He argues that stories and statistics like these show two things: first, that we are bad at assessing probabilities and second, that we tend to err in the direction of optimism. “Encouraged by stories of holes in one, royal flushes, and jackpot wins, we swing our golf clubs in blind hope and gamble our spare cash on impossible odds, hoping to catch the eye of Dame Fortune. Yet at the same time we play sports, where the injuries send millions to the hospital every year, we travel by car, which kills many people every day, and we smoke, which causes hundreds of thousands of deaths a year.”

In the fifty years following the first conquest of Everest by Sir Edmund Hillary and Sherpa Tenzing in May 1953, 800 people climbed the world's highest mountain. Of those, 180 died in the attempt. William Hartston points out that the ratio of successes to deaths is roughly 5 to 1—the same odds as Russian roulette.

Accidents and misfortune, we like to think, happen to other people. Acts of incredible good fortune, we hope, will happen to us. Certainly our general inability to fully grasp the subtleties of the laws of probability can lead to some very strange attitudes toward risks in life.

A paper produced by the Said Business School points out that we all regularly run the risk of being killed in a road accident. Almost 1 man in 100 (though many fewer women) dies that way. How much, therefore, would we pay for extra safety features that would halve the risk, such as airbags and crumple zones? A thousand dollars, or perhaps as much as $2,000? But how much would you want to be paid before you would agree to cross a minefield in which there was a 1 in 100 chance of you being killed? Almost certainly more than $2,000, suggests the paper.

Anyone seriously attempting to understand the significance of coincidences (and who wants to be clearer about the relative risks in life) might find the following statistics helpful:

• The odds against winning the U.S. Powerball jackpot with one ticket: 80,089,128 to 1

• Being dealt a royal flush at poker: 649,739 to 1

• Hitting a hole in one with any one shot: 42,952 to 1

• All four players drawing perfect hands of bridge: 2,235,197,406,895,366,368,301,559,999 to 1

• Being murdered in the next year: 18,141 to 1

• Being struck by lightning: 600,000 to 1

• Dying in a railway accident: 500,000 to 1

• Dying under the wheels of a bus: 1,000,000 to 1

• Dying in a plane crash: 10,000,000 to 1

• Choking to death on food: 250,000 to 1

And the odds against two Welshmen having the same surname: 15 to 1.

What are the odds against dreams coming true? Accounts of prophetic dreams have been reported through the ages—by the ancient Assyrians and Babylonians and throughout Egyptian, Greek, and Roman civilizations. There are numerous accounts in the Bible. And they still happen.

Sharon Martens of Milwaukee, Wisconsin, was fourteen when she met and became firm friends with a boy named Michael. About a year later she had a disturbing dream—that she and Michael were at a basketball game and he told her he was leaving town the following Tuesday. Later that week, Michael approached her at school and told her his family had made the sudden decision to move to Colorado. When was he going? The following Tuesday, he told her.

Did young Sharon have some sort of psychic premonition? Or was this just coincidence? And if it was just coincidence, what would be the odds against such a thing happening? In an article published in the
Washington Post
in 1995, Chip Denman, a statistics lecturer at the University of Maryland, worked it out.

He made a series of complex mathematical calculations, involving various assumptions about how often we dream and the odds against any individual dream coming true. He eventually came to the conclusion that the average person, simply as the result of chance and without the help of special psychic powers, will have a dream that accurately anticipates future events, once every nineteen years. “No wonder so many of my students tell me that it has happened to them,” says Chip.