Mohan Srivastava, a trained statistician with degrees from MIT and Stanford, got some lottery tickets as a gag gift, and he started thinking about how the lottery’s tic-tac-toe game works:
“The tickets are clearly mass-produced, which means there must be some computer program that lays down the numbers. Of course, it would be really nice if the computer could just spit out random digits. But that’s not possible, since the lottery corporation needs to control the number of winning tickets. The game can’t be truly random. Instead, it has to generate the illusion of randomness while actually being carefully determined.”
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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.The trick itself is ridiculously simple. (Srivastava would later teach it to his 8-year-old daughter.) Each ticket contained eight tic-tac-toe boards, and each space on those boards—72 in all—contained an exposed number from 1 to 39. As a result, some of these numbers were repeated multiple times. Perhaps the number 17 was repeated three times, and the number 38 was repeated twice. And a few numbers appeared only once on the entire card. Srivastava’s startling insight was that he could separate the winning tickets from the losing tickets by looking at the number of times each of the digits occurred on the tic-tac-toe boards. In other words, he didn’t look at the ticket as a sequence of 72 random digits. Instead, he categorized each number according to its frequency, counting how many times a given number showed up on a given ticket. “The numbers themselves couldn’t have been more meaningless,” he says. “But whether or not they were repeated told me nearly everything I needed to know.” Srivastava was looking for singletons, numbers that appear only a single time on the visible tic-tac-toe boards. He realized that the singletons were almost always repeated under the latex coating. If three singletons appeared in a row on one of the eight boards, that ticket was probably a winner.
The next day, on his way into work, he stopped at the gas station and bought a few more tickets. Sure enough, all of these tickets contained the telltale pattern. The day after that he picked up even more tickets from different stores. These were also breakable. After analyzing his results, Srivastava realized that the singleton trick worked about 90 percent of the time, allowing him to pick the winning tickets before they were scratched.
Naturally he went on to make a lot of money, right?
“I remember thinking, I’m gonna be rich! I’m gonna plunder the lottery!” he says. However, these grandiose dreams soon gave way to more practical concerns. “Once I worked out how much money I could make if this was my full-time job, I got a lot less excited,” Srivastava says. “I’d have to travel from store to store and spend 45 seconds cracking each card. I estimated that I could expect to make about $600 a day. That’s not bad. But to be honest, I make more as a consultant, and I find consulting to be a lot more interesting than scratch lottery tickets.”
He took his finding to the Ontario Lottery and Gaming Corporation — and they didn’t really want to hear about it.