# Cracking the Lottery

Using statistics to crack the lottery.

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 story contains a few more examples, as well as informed speculation that several state scratch games have been "broken" without detection.

And then there’s Joan Ginther, who has won more than \$1 million from the Texas Lottery on four different occasions. She bought two of the winners from the same store in Bishop, Texas. What’s strangest of all, perhaps, is that three of Ginther’s wins came from scratch tickets with baited hooks and not from Mega Millions or Powerball. Last June, Ginther won \$10 million from a \$50 ticket, which is the largest scratch prize ever awarded by the Texas Lottery.

As a computer scientist with knowledge of pseudorandom number generation algorithms, I can add to the discussion slightly: obtaining tickets in the same sequence they are generated would also give insight into the number sequence. The tickets I've seen are printed in perforated rolls (like toilet paper). The best way to crack the lottery would be to get access to these rolls.