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A Statistician Cracks the Lottery

Lottery Scratch-off Tickets | Source: Wired.com | Photo: John Midgley

While that claim may seem pretty bold, it is exactly true. At least for the scratch off games. Check out this article for the full details, but I’ll give an “executive summary” of the story here!

A geological statistician named Mohan Srivastava was clearing his desk and found some old scratch off Ontario lottery tickets he had gotten as a gag gift from a friend. One of them was a winner. The game card he won was a tic-tac-toe type game, where 8 game boards were given, and then you scratch off to reveal “your” numbers. If any of your numbers make a three in a row on one of the boards, you win that amount of money. He had one such set, which corresponded to a $3 (Canadian) win. Being a good statistician, he realized that the results could not truly be random. A truly random game would have no way for those running the lottery to be able to predict how many winners, and how much the total payout could be.

After glancing at the card, he realized that the pattern was amazingly transparent. Numbers that appeared only once total on the 8 tic-tac-toe boards were much more likely to be numbers that were revealed when the card was scratched. His mind alternated between disbelief that it could be that simple, and a temptation to think this would make him rich. (He later calculated that he made more money consulting than he could in 8 hours a day playing the lottery.) He checked further, and discovered that his “scheme” worked with about 90% accuracy. He could pick out winning cards without actually scratching them off with great accuracy!

Here is a visual of how it works taken from the article (“latex” refers to the covering that you scratch-off to reveal your numbers):

How to Pick a Winner

1 Look over the card. You’ll be hunting for so-called singletons—numbers on the visible tic-tac-toe grid that appear only once on the whole card.

2 Make a plot of the card, marking each cell with a number that indicates how many times the numeral in the cell occurs on the whole card. If, for example, a cell has a 26 in it and the number 26 occurs one other time somewhere on the card, mark that cell with a 2.

3 All the singletons will now be marked with a 1. If any of the singletons appear in a tic-tac-toe then the ticket is almost certainly a winner: The numbers in these cells will appear under the latex coating at the left side of the ticket. Keep the ticket.

4 Scratch off the latex. You’ve got a winner!

Pretty simple, but would take some time. Sitting on this simple way to win just about every ticket you bought, what would you do? Here is what he did:

Instead of secretly plundering the game, he decided to go to the Ontario Lottery and Gaming Corporation. Srivastava thought its top officials might want to know about his discovery. Who knows, maybe they’d even hire him to give them statistical advice. “People often assume that I must be some extremely moral person because I didn’t take advantage of the lottery,” he says. “I can assure you that that’s not the case. I’d simply done the math and concluded that beating the game wasn’t worth my time.”

When Srivastava reported his finding, he was referred to Rob Zufelt, a member of the lottery corporation’s security team. After failing to make contact for a few days, he began to get frustrated: Why wasn’t Zufelt taking his revelation more seriously? “I really got the feeling that he was brushing me off,” Srivastava says. “But then I realized that to him I must sound like a crazy person—like one of those people who claims that he can crack the lotto draw because last night’s number was his birthday spelled backward. No wonder they didn’t want to talk to me.” 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.

Since then, he has found similar problems (though not all identical) with other lottery games in Canada and the US. It is likely some others have figured this out, but there are more sinister uses for this as well! It seems that organized crime is (or at least could be) using this to “clean” (i.e. launder) their money. You have illegal profits? Find winners of the lottery and pay them your money for a “share” of their winnings. Suddenly, your money is “legitimate” lottery winnings and not illegal anymore. If you figure out a card picking scheme, you don’t even need to find someone to help you. This is especially true for areas where you can return unused scratch cards. Simply buy a huge stack of cards and claim you plan to use them as gifts or rewards. Pick out the winners, and cash them in. Then simply return the likely losers to the store and say you didn’t end up using all of them. Bingo, not only do you have clean money, you also have more of it since some of the cards won more than they cost!

Of course, another shady side affect is hiding behind this. If organized crime is using the lottery in this way, or even others who want to make easy money with nothing else to hide, it means that the normal player, who is typically low income, has a decreased chance of actually winning. (From little chance to almost none.) This is ridiculous. As a Christian, and a statistician, I was already opposed to the lottery in any of its various forms. That the scratch-off games, with the appeal of instant gratification, could be even more of a rip-off to the poor seems unconscionable to me! I know that state governments make a LOT of money from the lottery, but I would honestly be willing to have them raise taxes rather than expand the lottery any further. (And please, please, don’t get me started on casinos …)

The full Wired.com article is a little long, but it is a fascinating read about the lottery, how it works, and the mindset of those that run it and play it. It is worth your time.

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