Cracking the Scratch Lottery Code: a good Wired article

Jonah Lehrer wrote an article for the February 2011 edition of Wired called "Cracking the Scratch Lottery Code." It's about Mohan Srivastava, a statistician with degrees from MIT and Stanford who has been looking into ways to beat the scratch ticket lottery system, a $70 billion a year business in North America.

Srivastava examined some tic-tac-toe lottery tickets published by the Ontario Lottery and found a defect. The visible numbers on the tickets could be used to figure out information about the numbers hidden under the scratch off material.

2781216199_1d6fd7b3dd.jpgThe 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.
Cracking the Scratch Lottery Code

Photo by Moacir P. de Sá Pereira. Creative Commons Attribution 2.0 Generic license.