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Should you win the jackpot, there’s a good chance you’ll have to share — and not just with family, friends and Uncle Sam.

The odds of someone winning increase as the ticket sales do. So, too, do the odds of duplicate tickets, especially for people who choose their own numbers rather than letting the computers pick.

Prefer the lucky numbers of 7 or 11? You’re not alone. How about a loved one’s birthday? It’s 31 or lower — digits more frequently duplicated than 32 and up. (There are 59 white balls and 35 red balls in the draw).

Mr. Norfolk predicts that if there is a winner, there will be multiple ones because mathematical theory shows that numbers have a way of clustering, even at much smaller sample sizes.

If you take 23 random people, there’s about a 50-50 chance that at least two will have the same birthday, Mr. Norfolk said. Throw choice into the equation — about 20 percent of players typically select their own numbers — and the clusters could be even more defined.

That played out in March, when three tickets from Kansas, Maryland and Illinois split the world-record $656 million Mega Millions jackpot.

A single ticket holds Powerball’s current record of $365 million in 2006, shared by several ConAgra Foods workers in Lincoln, Neb.

Feeling lucky in a bad economy

Gambling experts say a majority of Americans will play some lottery game at least once in a given year.

Clyde Barrow, director of the Center for Policy Analysis at the University of Massachusetts in Dartmouth, says addicted gamblers are less likely to turn to massive jackpot ticket games such as Powerball than scratch-off games.

“Scratch-off players are looking for instant gratification and an instant win,” Mr.  Barrow said. “A lot of those people don’t like playing lotto because you have to wait. You have to sit on it for a few days.”

While it may seem counterintuitive, Mr. Barrow says gambling activity often increases as the economy gets worse and people have less disposable income. However, his research — which focused mainly on New England — found the trend reversed in the latest downturn.

“The Great Recession has been so deep and so long, it’s suppressed any kind of discretionary spending across the board,” said Mr. Barrow, who added that about the same percentage of people are playing the lottery — they’re just buying fewer tickets.

Mr. Strutt, Powerball’s executive director, said sales largely stayed flat during the peak of the recession in 2008 and 2009 but have picked up since.

“Our biggest factor is gas prices,” he said. “If people go to a gas station and put 80 bucks of gas in their car, they’re not feeling happy to buy a lottery ticket.”

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