Srivastava speaks quietly, with a slight stammer. He has a neatly trimmed beard and a messy office. When he talks about a subject he’s interested in—and he’s interested in many things, from military encryption to freshwater fossils—his words start to run into each other.
As a trained statistician with degrees from MIT and Stanford University, Srivastava was intrigued by the technical problem posed by the lottery ticket. In fact, it reminded him a lot of his day job, which involves consulting for mining and oil companies. A typical assignment for Srivastava goes like this: A mining company has multiple samples from a potential gold mine. Each sample gives a different estimate of the amount of mineral underground. “My job is to make sense of those results,” he says. “The numbers might seem random, as if the gold has just been scattered, but they’re actually not random at all. There are fundamental geologic forces that created those numbers. If I know the forces, I can decipher the samples. I can figure out how much gold is underground.”
Srivastava realized that the same logic could be applied to the lottery. The apparent randomness of the scratch ticket was just a facade, a mathematical lie. And this meant that the lottery system might actually be solvable, just like those mining samples. “At the time, I had no intention of cracking the tickets,” he says. He was just curious about the algorithm that produced the numbers. Walking back from the gas station with the chips and coffee he’d bought with his winnings, he turned the problem over in his mind. By the time he reached the office, he was confident that he knew how the software might work, how it could precisely control the number of winners while still appearing random. “It wasn’t that hard,” Srivastava says. “I do the same kind of math all day long.”
That afternoon, he went back to work. The thrill of winning had worn off; he forgot about his lunchtime adventure. But then, as he walked by the gas station later that evening, something strange happened. “I swear I’m not the kind of guy who hears voices,” Srivastava says. “But that night, as I passed the station, I heard a little voice coming from the back of my head. I’ll never forget what it said: ‘If you do it that way, if you use that algorithm, there will be a flaw. The game will be flawed. You will be able to crack the ticket. You will be able to plunder the lottery.’”
The North American lottery system is a $70 billion-a-year business, an industry bigger than movie tickets, music, and porn combined. These tickets have a grand history: Lotteries were used to fund the American colonies and helped bankroll the young nation. In the 18th and 19th centuries, lotteries funded the expansion of Harvard and Yale and allowed the construction of railroads across the continent. Since 1964, when New Hampshire introduced the first modern state lottery, governments have come to rely on gaming revenue. (Forty-three states and every Canadian province currently run lotteries.) In some states, the lottery accounts for more than 5 percent of education funding.
While approximately half of Americans buy at least one lottery ticket at some point, the vast majority of tickets are purchased by about 20 percent of the population. These high-frequency players tend to be poor and uneducated, which is why critics refer to lotteries as a regressive tax. (In a 2006 survey, 30 percent of people without a high school degree said that playing the lottery was a wealth-building strategy.) On average, households that make less than $12,400 a year spend 5 percent of their income on lotteries—a source of hope for just a few bucks a throw.
Mohan Srivastava, a geological statistician living in Toronto, realized that the logic he used to find gold deposits could also crack lottery cards.
Photo: John Midgley
There was a time when scratch games all but sold themselves. But in the past two decades the competition for the gambling dollar has dramatically increased. As a result, many state lotteries have redesigned their tickets. One important strategy involves the use of what lottery designers call extended play. Although extended-play games—sometimes referred to as baited hooks—tend to look like miniature spreadsheets, they’ve proven extremely popular with consumers. Instead of just scratching off the latex and immediately discovering a loser, players have to spend time matching up the revealed numbers with the boards. Ticket designers fill the cards with near-misses (two-in-a-row matchups instead of the necessary three) and players spend tantalizing seconds looking for their win. No wonder players get hooked.
Srivastava had been hooked by a different sort of lure—that spooky voice, whispering to him about a flaw in the game. At first, he tried to brush it aside. “Like everyone else, I assumed that the lottery was unbreakable,” he says. “There’s no way there could be a flaw, and there’s no way I just happened to discover the flaw on my walk home.”
And yet, his inner voice refused to pipe down. “I remember telling myself that the Ontario Lottery is a multibillion-dollar-a- year business,” he says. “They must know what they’re doing, right?”
That night, however, he realized that the voice was right: The tic-tac-toe lottery was seriously flawed. It took a few hours of studying his tickets and some statistical sleuthing, but he discovered a defect in the game: The visible numbers turned out to reveal essential information about the digits hidden under the latex coating. Nothing needed to be scratched off—the ticket could be cracked if you knew the secret code.
Intriguingly more at:
http://www.wired.com/magazine/2011/01/ff_lottery/all/1