How to use spatial statistics to crack a scratch-off game


On Friday, I posted an article about using spatial statistics to detect whether a pattern of points is truly random. That day, one of my colleagues asked me whether there are any practical applications of detecting spatial randomness or non-randomness. "Oh, sure," I replied, and rattled off a list of applications in biology, materials science, manufacturing, and epidemiology.

On Monday, I read in Andrew Gelman's blog about a statistician who, in 2003, figured out how to pick cards in a certain scratch-off game so as to increase the probability of winning. When I followed the link to the original story in Wired magazine, I was astonished to discover that the statistician, Mohan Srivastava, is a geostatistician and that his technique uses spatial statistics that are similar to the ideas that I laid out in my blog post!

The basic idea, which is illustrated below and described halfway through the article, is to look at the distribution of numbers on the ticket and use a frequency analysis to determine which tickets have layouts that are less random than is expected by chance. In the example shown in the article, the ticket has infrequent numbers (numbers with a frequency of 1) in a winning tic-tac-toe configuration. (This is circled in the image below.) Such a configuration is unlikely to happen by chance alone, so you should buy the ticket. Srivastava experimentally showed that the ticket is a winner about 90% of the time.

So, add "picking scratch-off tickets" to the list of applications of spatial statistics.


About Author

Rick Wicklin

Distinguished Researcher in Computational Statistics

Rick Wicklin, PhD, is a distinguished researcher in computational statistics at SAS and is a principal developer of SAS/IML software. His areas of expertise include computational statistics, simulation, statistical graphics, and modern methods in statistical data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.


  1. So this is what people around here know. I've seen people look at the numbers on unscratched lottery tickets and decide whether or not they will buy the ticket. I couldn't understand what method they were using to decide and didn't want to ask. But none of these people are mathematicians or statisticians, so they must have created some sort of ad-hoc shortcut to decide.

  2. Chris Hemedinger on

    My 91-year-old grandmother loves the scratch-offs. She's always telling me about the ones that she wins, so it seems like she wins often. But I suppose there are many more loser tickets that she doesn't brag about; thus, her good fortune is probably just an illusion.

    I'm pretty sure that she doesn't employ spatial statistics.

  3. Well, I guess you could send her the link to my blog...

    On Friday I'll revist this topic. Tell her to stand by.

  4. Pingback: Scratch-off lottery games: How NOT to design them - The DO Loop

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