Better Living Through Applied Statistics: Cracking Scratch-off Lottery Games

Michael Giberson

In WIRED, Jonah Lehrer reports on how Toronto geological statistician Mohan Srivastava discovered a flaw in a lottery scratch-off game.

As a trained statistician with degrees from MIT and Stanford University, Srivastava was intrigued by the technical problem posed by the lottery ticket. In fact, it reminded him a lot of his day job, which involves consulting for mining and oil companies. A typical assignment for Srivastava goes like this: A mining company has multiple samples from a potential gold mine. Each sample gives a different estimate of the amount of mineral underground. “My job is to make sense of those results,” he says. “The numbers might seem random, as if the gold has just been scattered, but they’re actually not random at all. There are fundamental geologic forces that created those numbers. If I know the forces, I can decipher the samples. I can figure out how much gold is underground.”

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…

Andrew Gelman comments at his Statistical Modeling, Causal Inference, and Social Science blog:

“Ticket designers fill the cards with near-misses…”: This doesn’t sound like they’re just slapping down random numbers. Instead, the system seems to be rigged in the fashion of old-time carnival games in order to manipulate one’s intuition that the probability of near-misses should be informative about the underlying probability of hits. …

In this sense, the story is slightly more interesting than “Lottery designers made a mistake.” The mistake they made is directly connected to the manipulations they make in order to sucker people into spend more money.

If Gelman’s view is right, it suggests that scratch-off games companies will continue to produce and sell games that can be cracked. Quasi-randomized games can be made more interesting than a truly randomized game, so more tickets will be sold, so more money made by the lottery, so they will keep doing it. Presumably now, however, they watch their payout rates a little more closely and shut down their quasi-randomized games when it appears that someone has figured it out.

2 thoughts on “Better Living Through Applied Statistics: Cracking Scratch-off Lottery Games

  1. So a presumed game of chance may not a game of chance, but a contrived, non-random game meant to hook unsophisticated players. Interesting.

    Do casino slot machines and other gambling devices have similar non-random characteristics? I’ve always thought that people who identified paterns where none should exist were fooling themselves, but the idea tickets could be created through an algorithm would certainly change my views.

  2. Don’t know anything about slot machines, but at the least they would seem to reveal much less information – just three/four/or five digits or symbols – which would seem like very little information to base a prediction on for the next result (assuming they are non-random just for sake of argument). Of course you can buy more information by paying the machine….

    Clearly slot machines are contrived to be “hooky”, with lights, color, sound and all. In theory it seems like programming a machine to show more near misses rather than just random spins would make a machine hookier still. If they are made that way, then maybe there it information in the series of results. I’m guessing the game is still rigged in the house’s favor.

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