Beyond Coincidence (11 page)

Thirty-five-year-old pharmacist Trupti Patel denied killing her sons Amar and Jamie and daughter Mia between 1997 and 2001—none of them survived beyond three months. She denied she had smothered her babies or restricted their breathing by squeezing their chests.

In Britain, approximately six hundred children each year die suddenly and unexpectedly at some time between their first week of life and their first birthday. In half of these cases, a clear medical reason for the death is found at postmortem—the remaining, unexplained cases are recorded simply as sudden infant death syndrome.

At the trial of Trupti Patel, the pediatrician stated that “two crib deaths is suspicious, three is murder—unless proved otherwise.”

The members of the jury, this time, were not convinced. On June 11, 2003, at the end of the six-and-a-half-week trial, they found her not guilty on all three counts of murder. The jury had decided that the deaths of the three babies, as in the case of Sally Clark, had been a tragic coincidence. Whatever the odds against something happening, the fact that odds can be calculated means that it can, and, given enough time, will happen.

Odds of 73 million to 1, although inaccurately applied in the case of Sally Clark, will, eventually, come up. Even if those had, in fact, been the odds against the deaths of her three children being coincidence, it would not have pointed unerringly to her guilt. A 73 million to 1 chance occurrence isn't an unimaginable likelihood. If one in every seventy-three million people were green, then there'd be eighty-four green people in the world. Shouldn't be too hard to spot.

Judges and juries are regularly asked to weigh up odds of 1 in 3 million—in cases where DNA samples are presented as crucial evidence.

And, of course, they get it wrong.

In 1990, Andrew Deen was sentenced to sixteen years in jail for raping three women. The main evidence linking Deen to the attacks was the close match between DNA samples found at the scene of the crimes and those from Deen. At the trial, the forensic scientist presenting the DNA evidence said that the match was so good that the probability of the samples having come from someone other than Deen was 1 in 3 million. In his summing up, the judge told the jury that so large a figure, if correct, “approximates pretty well to certainty.” There could be no coincidence.

But on appeal the court quashed the conviction, declaring the verdict unsafe. It decided that both the forensic scientist and the judge had fallen into a trap known as the “prosecutor's fallacy.” They had assumed that the DNA evidence meant that there was only a 3-million-to-1 chance that Deen was not guilty. But they were mistaken.

For the true picture, the appeal court judges turned to a mathematical theorem constructed by a nineteenth-century cleric. Bayes' Theorem addresses the laws of “inverse probability.” It provides a formula for working out the impact of new evidence (like DNA samples) on the existing odds of guilt or innocence prior to the introduction of the new evidence.

If “prior probability” of guilt is small—if there is little other evidence to corroborate the DNA evidence—then even the impressive probabilities of genetic fingerprinting can be dramatically diminished.

Researchers at the Institute of Environmental Health and Forensic Sciences in Auckland, New Zealand, use crime statistics and “Bayesian reasoning” to estimate typical prior probabilities. They found that even a DNA match with odds of millions to one can be cut down to final odds against innocence of just 3 to 1—leaving plenty of room for “reasonable doubt.”

So if you are currently stuck in an intractable legal dispute over the probability of something or other having happened, or not happened, as the result of pure coincidence—help is at hand. Try applying Bayes's handy mathematical formula.

Good luck.

6

LUCK OR COINCIDENCE?

It's the day of the Kentucky Derby and you grudgingly hand over your hard-earned $20 for the office pool. Your horse, which has begun with a moderate chance of success, mysteriously chooses to stop half way around the course to admire the stamina and athleticism of its four-legged friends. Your colleague George Robertson wins the jackpot. His horse, a rank outsider, confounds the bookies' pessimistic expectations. This is the seventh time George has won the sweepstake in ten years.

Do you say, “Well done George, it's good to see that the rules of probability are still functioning and that your chances of winning this year were not materially diminished by the fact that you have won so many times before.”

Like hell you do. You say, “You lucky s.o.b., George. The drinks are on you.”

It's hard not to conclude that someone or something is smiling down on the likes of George Robertson, singling them out for good fortune—leaving the rest of us to muddle along the best we can.

Everything George touches turns to gold. If a nice business trip to Bermuda is in the offing, George gets to wear the shorts. If a promotion is up for grabs, George grabs it. As we know, he wins the Derby pool every year. He won a tidy sum on the football pools a few years back and has even picked up a couple of thousand on the lottery. He's got a beautiful wife, two well-adjusted, respectful kids, a terrific house (bought outright with an unexpected inheritance) and a luxury car. Yes, George is, indeed, among the luckiest of lucky s.o.b's.

But not the luckiest.

Donald Smith of Amherst, Wisconsin, won the state's Super Cash game three times. On May 25, 1993, June 17, 1994, and July 30, 1995. He won $250,000 each time.

Joseph P. Cowley won $3 million in the Ohio lottery in 1987 and retired to Boca Raton, Florida. Six years later he played the Florida Lotto on Christmas Day—and won $20 million.

In 1985 Evelyn Marie Adams won $4 million on the New Jersey Lottery. Four months later she entered again and won another $1.5 million.

Why isn't luck more evenly distributed? What special qualities or mysterious powers are possessed by those few, those lucky few, upon whom Dame Fortune invariably smiles? Is the inordinate amount of good fortune experienced by these lottery winners the result of simple coincidence, or were they born lucky?

What on earth made gambling-mad Mick Gibbs think he could ever pull off the outrageous wager that finally netted him $912,000 in what has been described as the greatest betting coup of all time?

Fifty-nine-year-old Mick of the UK, placed a 50 cent stake on a fifteen-part accumulator bet on who would win a long series of games across four different competitive sports.

The first fourteen parts of his accumulator all came good, defying staggering cumulative odds. The final part of the wager—that the German team Bayern Munich would win a European soccer championship at odds of 12 to 1 looked like a long shot. When the game was played on May 23, 2001, Bayern's opponents, Valencia, looked set to upset the apple cart when they took a 1–0 lead. Victory for the Spanish side would have meant Mick earned nothing. Bayern managed to tie before the end of the match and the teams had to play extra time.

Mick was on the edge of a nervous breakdown, pacing up and down in his garden, unable to watch the match. The game—and Mick's bet—was finally won in the last minute. Bayern won the cup, and Mick won close to $1 million.

Mick doesn't put his success down to luck or coincidence. He believes he won the money because of science. He says he spends hours poring over the latest sports news and working out his complicated bets.

But if all it takes to win a small fortune is a bit of hard work and the appliance of a little science, why aren't the rest of the world's habitual gamblers driving around in flashy sports cars, instead of cycling to collect their unemployment checks?

Can science explain the apparent extraordinary luck of Englishman Charles Wells, the man who broke the bank at Monte Carlo?

Wells's legendary success did not appear to have involved the use of any system. He walked into the casino in July 1891 and began putting even money bets on red and black, winning nearly every time. When his winnings passed the one hundred thousand francs mark, the “bank” was declared broken, the table was closed and a black “mourning” cloth placed over it. Wells returned the next day to repeat his extraordinary achievement, to the amazement of the casino attendants.

The third and last time Wells appeared at the casino, he placed his opening bet on number five at odds of 35 to 1. He won. He left his original bet and added his winnings to it. Five came up again. This happened five times in succession. The bank had been broken yet again.

Extraordinary things do happen in gambling casinos. Evens once came up twenty-eight times in succession at a Monte Carlo casino—against odds of 268 million to 1. But was Wells's good fortune simply the laws of probability kicking in? Was he the world's luckiest man? Or was something else going on?

Wells did not get to enjoy his winnings for long. His luck, or whatever it was, dried up. He got involved in a number of shady deals, was arrested by the French police and charged with fraud. Extradited to Britain, he stood trial and was discovered to have had twenty aliases—his real name was never discovered. He was sentenced to eight years in prison. After his release he went to live in Paris where “the man who broke the bank at Monte Carlo” died in poverty in 1926—a broken man.

The secret of Wells's amazing achievements at the roulette table was never discovered. It seems unlikely that his gambling feat was the result of pure luck or, indeed, guided by some supernatural force. Although inspiration for gambling success can come from some pretty strange sources.

On September 15, 1948, a New York—bound commuter train plunged into Newark Bay killing a number of passengers. Front page newspaper photographs showed the train being winched back out of the water. The number 932 could clearly be seen on the side of the rear coach. Dozens of people took this to be a sign that the number had some sort of significance and chose it in that day's Manhattan numbers game. The number 932 duly came up, winning hundreds of thousands of dollars for the people who had bet on it.

The good luck experienced by fifteen members of the church choir in Beatrice, Nebraska, didn't bring them fame or fortune—it saved their lives.

Choir practice at the West Side Baptist Church in Beatrice always began at 7:20 on Wednesday evening. At 7:25 P.M. on Wednesday March l, 1950, an explosion demolished the church. The blast forced a nearby radio station off the air and shattered windows in surrounding homes.

But by an incredible coincidence every one of the choir's fifteen members escaped injury. Normally punctual, that evening they were all, and for different reasons, late for practice.

The preacher, Walter Klempel, lit the furnace at the West Side Baptist Church and then went home for dinner. His return to the church with his family was delayed when his daughter's dress was soiled and his wife had to iron another for her.

Ladona Vandergrift, a high school student, was having trouble with a geometry problem. She decided to solve it before leaving for choir practice.

Royena Estes couldn't get her car to start, so she and her sister called Ladona Vandergrift and asked her to pick them up. But Ladona was still working on her geometry problem, so the Estes sisters had to wait.

Marilyn Paul, the pianist, had planned to arrive half an hour early, but fell asleep after dinner …

And so the list of delays went on. The entire choir, all of whom were normally punctual for practice, were late that evening.

At 7:25, the church blew up. The walls fell outward, the heavy wooden roof crashed to the ground. Firemen thought the explosion had been caused by natural gas that had leaked into the church from a broken pipe outside and been ignited by the fire in the furnace.

A major tragedy had been averted by the narrowest of multiple squeaks. The grateful Beatrice church choir members put their amazing good luck down to an act of God. But you don't have to be in a church choir to narrowly escape death.

John Woods, a senior partner in a large legal firm, left his office in one of the Twin Towers of the World Trade Center in New York seconds before the building was struck by a hijacked aircraft. It wasn't his first close brush with death. He had been on the thirty-ninth floor of the same building when it was bombed in 1993, but escaped without injury. In 1988 he was scheduled to be on the Pan-Am flight that exploded above Lockerbie in Scotland, but canceled at the last minute in order to go to an office party.

Unlike John Woods, Yugoslavian flight attendant Vesna Vulvic failed to avoid traveling on a plane destined to explode.

A terrorist bomb was thought to be the cause of the massive explosion that ripped apart the DC-9 aircraft traveling over the former Czechoslovakia on January 26, 1972.

Rescue workers who came upon the tangled wreckage on the ground didn't believe anyone could still be alive. Then they found flight attendant Vesna Vulvic inside part of the fuselage. She was badly injured, but still breathing. She was the only person to survive.