How A Statistician Beat Scratch Lottery Tickets

In North America, the lottery is a $US70 billion-a-year industry, bigger than movies, music and porn combined. But it's not infallible. That's what Mohan Srivastava, a geological statistician, found out when he took a closer look at scratch lottery cards.

WIRED tells Srivastava's story in this month's issue. As a geological statistician, he's responsible for looking at samples from potential gold mines and determining how much gold might lie therein. It was the same type of math that helped him discover a simple trick for predicting winning tickets of a Canadian Tic-Tac-Toe scratch lottery game with 90 per cent accuracy:

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 realised 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.

After determining that scamming the lottery would ultimately be less profitable (and less enjoyable) than his consulting job, Srivastava alerted the Ontario Lottery and Gaming Corporation to the game's flaw and they pulled it a day later.

But the tic-tac-toe game wasn't the only one that was vulnerable. Srivastava found that a variation of his singleton trick at least doubled his chances of picking winners on several other similar games, his keen eye for patterns and probabilities seemingly the key to unlocking the scratch off games. Ross Dalton, president of leading lottery game producer Gtech Printing, told WIRED that "breakability" is a main concern and that they're "always looking at new methods of encryption and protection". But with minds like Srivastava scrutinizing tickets, it's hard to imagine keeping that vast $US70 billion industry completely watertight. [WIRED]