Statistician cracks the scratch lottery code

Posted to Statistics  |  Tags:  |  Nathan Yau

Statisticians everywhere are squealing in delight over this story on fellow statistician Mohan Srivastava, who used his know-how to crack the code of a tic-tac-toe scatcher lottery game. After winning three dollars on a scratcher ticket that was given to him as a gag gift, Srivastava got to wondering about the process of how tickets were made. As a geological consultant who figures out if areas are worth mining for gold, he wondered if he could do the same with this scatcher.

Srivastava realized that the same logic could be applied to the lottery. The apparent randomness of the scratch ticket was just a facade, a mathematical lie. And this meant that the lottery system might actually be solvable, just like those mining samples. “At the time, I had no intention of cracking the tickets,” he says. He was just curious about the algorithm that produced the numbers. Walking back from the gas station with the chips and coffee he’d bought with his winnings, he turned the problem over in his mind. By the time he reached the office, he was confident that he knew how the software might work, how it could precisely control the number of winners while still appearing random. “It wasn’t that hard,” Srivastava says. “I do the same kind of math all day long.”

It turns out he was able to pick out winners 90 percent of the time. He eventually told the Ontario Lottery and Gaming Corporation about the flaw, simply because he did the math and he makes more as a consultant than he would scratching hundreds of tickets every day. The game is no longer in stores now, of course, but on whether other games can be cracked:

Fundamentally, he believes that creating impregnable tickets is extremely difficult, if not impossible. “There is nothing random about the lottery,” he says. “In reality, everything about the game has been carefully designed to control payouts and entice the consumer.” Of course, these elaborate design elements mean that the ticket can be undesigned, that the algorithm can be reverse-engineered. The veneer of chance can be peeled away.

I sense ticket sales spiking across the country.

The funny thing is that most statisticians I know don’t gamble at all because they know the odds are not in their favor. On the other hand, for Srivastava, it was statistics that drew him in.



  • like the story… I am feeling like it will boost up lottery sales (ok, only a little) mostly driven by the stats students :)

  • impressive…..but this was really disheartening to read that statisticians avoided this lottery because they thought the odds are not in their favor…..

  • Very interesting. There is of course one flaw. They don’t normally sell scratchers that way. You get the next one off the roll. This is clearly the case for machine sold tickets – there you have no control so you are back to the statistical knowledge that you will lose.

    I suppose in a store with a physical clerk you might be able to persuade them to let you look through the roll or stack of tickets and select the ones you want. But you’ll only get to do that once.

    So bottom line – while this is a triumph for math it isn’t going to make much difference in real life

    • I had the same thought, but the place he bought them at let him look at the tickets first. Then in that one section where he describes how he would cook up a scheme, he said they would’ve also let him return tickets.


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