ADVERTISEMENT
See Inside Scientific American Volume 310, Issue 5

Statistician David J. Hand Shows How the Seemingly Improbable Becomes a Sure Thing

There are so many things in heaven and earth that coincidences become certainties



Matt Collins

Back in 1980, a woman named Maureen Wilcox played the Rhode Island and the Massachusetts lotteries at the same time. And she hit the correct numbers for both. Unfortunately, she picked all the correct Massachusetts numbers on her Rhode Island ticket and all the right Rhode Island numbers on her Massachusetts ticket. Shirley Jackson couldn't write a more terrifying lottery story.

Wilcox's shenanigans bring to mind a short work by Woody Allen that lampoons numerology, the search for meaning in random numbers. Its last line: “It was reasoning like this that led Rabbi Yitzhok Ben Levi, the great Jewish mystic, to hit the double at Aqueduct fifty-two days running and still wind up on relief.”

Anyway, the sad tale of the lottery switcheroo is discussed in the new book The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day, by mathematician and statistician David J. Hand. (What are the chances that the author of a book that mentions “the probability of being dealt a royal flush in poker is about 1 in 650,000” is named Hand?)

The New England states' mash-up and other oddball lottery cases are in the chapter of the Hand book entitled “The Law of Truly Large Numbers.” It opens with a quote, circa 1832, from British writer E. G. Bulwer-Lytton: “Fate laughs at probabilities.” By the way, Bulwer-Lytton is the guy who actually started a novel with “It was a dark and stormy night” and who now has a contest named for him that rewards the worst fictional sentence. The Improbability Principle is not eligible, because it is a work of nonfiction, and it is good.

“The law,” writes the learned Hand, “of truly large numbers ... says that, with a large enough number of opportunities, any outrageous thing is likely to happen.” Lotteries are wonderful examples of how events that appear virtually impossible actually become inevitable given enough time and trials. Remember, the salient feature of the Wilcox mix-up is not that it happened to her—those odds are crazy small—but that it would eventually happen to somebody. And chance happened to pluck her.

Double lottery winners illustrate the law of truly large numbers in action. For example, on April 7, 2012, a woman matched five of the six Powerball numbers in the lottery in Virginia. Twice. Her two winning tickets were each worth more than $1 million. Plus, her first name is Virginia, which is utterly meaningless but would keep Rabbi Ben Levi up for 52 nights in a row.

Then there are the lotteries themselves. In consecutive games in 2009, the Bulgarian lottery randomly picked the same set of six winning numbers. Naturally, some people suspected fraud. But Hand outs the real culprit: probability. When he works up the math, it takes just 43 years for there to exist a better than even chance for the same sets of numbers to get drawn twice (although the two-in-a-row pick was a bonus).

And that's just in Bulgaria. “When we take into account the number of lotteries around the world,” Hand writes, “we see that it would be amazing if draws did not occasionally repeat.” So it came to pass that in 2010 on September 21 and then on October 16, an Israeli lottery drew the same numbers. “Scores of people flooded Israeli radio station phone-ins,” Hand prints in the book, “to complain that the lottery was fixed.” Rabbi Ben Levi might have been among them, but chances are he hadn't paid his phone bill.

Which brings us to what comedian Dave Attell calls “God's drive-by shooting,” that is, getting hit by lightning. Hand notes the case of one Roy Sullivan, a seven-time loser in the lightning-strike lottery. Sullivan was a park ranger, so he upped his odds by being outdoors a lot. The same went for a sportsman named Major Walter Summerford, struck three times, whose gravestone took a shot four years after his death.

Yet consider that about 100 lightning bolts reach the earth's surface every second—statistically, hundreds of thousands of people are going to get hit annually, with somebody bound to take multiple zaps. And if there were really such a thing as bad luck, that somebody would be Maureen Wilcox.

This article was originally published with the title "Statistical Significance."

Rights & Permissions
Share this Article:

Comments

You must sign in or register as a ScientificAmerican.com member to submit a comment.
Scientific American Back To School

Back to School Sale!

12 Digital Issues + 4 Years of Archive Access just $19.99

Order Now >

X

Email this Article



This function is currently unavailable

X