'Math detective' analyzes odds for suspicious lottery wins

April 15, 2014 by Carol Clark, Emory University
Emory mathematician Skip Garibaldi (above in a classroom) helped do the math for a Palm Beach Post investigation of suspicious wins in the Florida Lottery. Garibaldi has since started eyeing data from the Georgia Lottery.

When investigative reporter Lawrence Mower decided to dig into public records for the winners of the Florida Lottery, he noticed an intriguing pattern. Over a decade, a few names kept popping up as winners of all kinds of games. The most prolific of these winners, according to the lottery data, was a man who claimed an incredible 252 prizes during six years, for a total take of $719,000.

"If you're winning like this in Las Vegas, they're going to take you into a back room and find out how you're cracking the game," Mower said.

But when Mower asked a Florida official about what seemed like a suspicious number of repeat wins by some players he was told that they could just be lucky.

Mower and his colleagues at the Palm Beach Post wanted to find out exactly how lucky these dominant players were, but they needed help calculating the odds.

"I starting looking for a mathematician who had dealt with odds and the lottery," Mower says. "That's how I found Skip."

Skip Garibaldi, a professor in Emory's Department of Mathematics and Computer Science and associate director of UCLA's Institute for Pure and Applied Mathematics, was happy to work on the project.

"It was like a dream come true," says Garibaldi, whose previous research on lotteries received the Lester R. Ford Award for mathematics and is the subject of a chapter in the popular book Brain Trust by Garth Sundem. Garibaldi enjoys breaking down complex math for the general public and has appeared on 20/20, CNN and Fox & Friends.

"I get this call from Lawrence, and he says, 'I have this huge database I'd like to feed you of everyone who has won more than a $600 prize in the Florida Lottery over a decade," Garibaldi recalls.

Philip Stark, a statistician from the University of California, Berkeley, and Richard Arratia, a probabilist from the University of Southern California, were also recruited to work with Garibaldi on the project. The three mathematicians are now writing an academic paper that will explain their lottery findings in more technical detail.

Two of the underlying principles for the lottery analysis were probability theory and the law of large numbers, which both trace their beginnings to a 16th-century Italian mathematician, Gerolamo Cardano. In fact, it was his love of dice games and other forms of gambling that sparked Cardano to work on probability questions.

"The subtle point about probability or quantum mechanics," Garibaldi says, "is that there are things that we know are possible and we can calculate the probability of them happening, but they are so unlikely that no one has seen them happen and likely no one ever will. For this lottery question, something that happens to fewer than one-in-20-trillion lottery gamblers is one of these utterly implausible events." 

Using this generous bar for random luck, the analysis identified winners who were defying the odds during the past decade, and would have had to lose prodigious amounts of money to win so many times. The most prolific winner, for instance, would have had to spend an estimated minimum of $2.07 million to have a one-in-20-trillion shot at his 252 wins and winnings of $719,051, for a net loss of about $2.35 million.

"But even if every single citizen in the state of Florida spent $2 million on lottery tickets," Garibaldi says, "the odds are less than one in a million that anybody would have won that many times."

These kinds of figures "put us in pretty safe territory with our suspicions that something was amiss," Garibaldi says.

The mathematical analysis was also able to identify winners of multiple prizes who appeared to be legitimate gamblers. "The fact that a person claims multiple prizes does not necessarily indicate that they are doing anything suspicious," Garibaldi says. "A finer analysis and more inspection can show that some people are likely just spending a lot of money on tickets and occasionally getting lucky."

"The math was the critical part of this story," Mower says of the package of investigative pieces published on Sunday, March 30. "It's been really valuable working with Skip because he'll see something that I won't."

On Monday, March 31, the state legislature called for more oversight of the Florida Lottery. On Tuesday, the lottery announced that it would adopt safeguards, such as software to track frequent winners. By Wednesday, lottery officials began raiding stores and seizing lottery equipment associated with some of the top prize winners. (Six of the 10 top winners in the lottery records were store clerks and owners who sold lottery tickets.)

Meanwhile, Garibaldi started eyeing data for winners of the Georgia Lottery. "The data from the Georgia Lottery is not as good as from Florida, because Georgia only lists winners for prizes of $5,000 or more," he says. "But just casually looking at the Georgia data since 2003, I see what may be suspicious numbers for repeat winners."

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