## MATHEMATICA!

# Statistician cracks scratch card system.

by Wired

Mohan Srivastava, a geological statistician living in Toronto, was working in his office in June 2003, waiting for some files to download onto his computer, when he discovered a couple of old lottery tickets buried under some paper on his desk.

The tic-tac-toe lottery was seriously flawed. 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. 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.

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.

When Srivastava reported his finding, he was referred to Rob Zufelt, a member of the lottery corporation’s security team. But, instead of trying to get Zufelt to return his calls, Srivastava decided to send him a package. He bought 20 tic-tac-toe tickets and sorted them, unscratched, into piles of winners and losers. Then, he couriered the package to Zufelt along with the following note:

In the enclosed envelopes, I have sent you two groups of 10 TicTacToe tickets that I purchased from various outlets around Toronto in the past week… You go ahead and scratch off the cards. Maybe you can give one batch to your lottery ticket specialist. After you’ve scratched them off, you should have a pretty solid sense for whether or not there’s something fishy here.

The package was sent at 10 am. Two hours later, he received a call from Zufelt. Srivastava had correctly predicted 19 out of the 20 tickets. The next day, the tic-tac-toe game was pulled from stores.

The funny thing is that these flawed scratch cards were on the market fro quite a while before Srivastava’s discovery which leads to me think that the professional scratchers (yes martians, there are professional scratch card players on earth) were already wise to the flawed system.

And they say you never use math in real life

😡

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