Thursday, February 3, 2011

And you thought statisticians were just good for counting cards

We're also handy if you have a handful of scratchers.

From Wired (via Felix Salmon):
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.

For example the ticket below has one winning row. If you're having trouble spotting it the article has a step-by-step solution.

To make things even more interesting, there's evidence that Srivastava may not be the only one to have spotted the pattern.

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