I recently read the book Fluke by Joseph Mazur. This book looks at some improbably real “coincidences” and helps us understand the math behind what happened.
Like somebody who writes that she hit a royal flush on the first hand she played two days in a row and wants to know, “What are the odds on that?” Mazur correctly points out that there’s a huge difference between looking at how often that happens to someone anywhere and how likely it was to happen to Mary Smith on December 12 and 13 in 2015? Hugely different problems and Mazur does well to explain that.
If you’ve ever been amazed by that day in 2004 when you ran into somebody you hadn’t seen in 30 years — and you and he both just happened to be in a small café in Turkey at the same time — then this book will help you understand that it wasn’t as flukish as you thought.
One case Mazur covers, however, is Joan Ginther, who won the Texas lottery at least four times over 18 years. Although I accept that Mazur’s mathematical talents in this area are far beyond mine, this is a situation that, in my opinion, Mazur misanalyzes.
Mazur goes through the probability of anybody picking a winning lottery number — and he focuses on the type where you pick six numbers. He goes through the math of winning several times, the number of people playing, the number of lotteries there are in the United States, and concludes that it’s not that unrealistic to expect someone winning four or more times.
He also duly notes that the actual winner, Joan Ginther, has a Ph.D. in mathematics from Stanford University and possibly figured out some way to boost the odds in her favor. He mentions this and then ignores it.
I think Ginther’s background and intelligence are the crux of the matter.
Without precisely ranking Stanford among the elite universities of the world, I’m going to posit without proof that it’s on that list somewhere and that Ph.D.s in mathematics from that university typically have genius-level intelligence with a great facility at numbers.
Further, according to reports in several publications, Ginther’s wins weren’t on lottery tickets where you pick six numbers. Ginther’s wins were on scratchers, which is totally different animal. On a scratcher, some numbers on a grid are already exposed when you buy the ticket. It’s very possible that Ginther used this pre-printed information to decide which lottery tickets to buy. If so, the odds against her were significantly different than what they would be for someone who picked the cards blindly.
This type of advantage was discussed by Mohan Srivastava in https://www.wired.com/2011/01/ff_lottery/. When Srivastava was a guest on our Gambling with an Edge radio show, he said he didn’t know the details of Ginther’s wins, but based on the analysis by a journalist named Peter Mucha, Srivastava speculated that Ginther used methods related to ticket distribution to win. (Listen here) If you like that podcast, Srivastava was on our show earlier (found here) where he went more into the basics of beating the lottery, but only mentioned the Joan Ginther case in passing.
Mathematicians (and video poker players, for that matter) tend to be better than average at “pattern recognition.” I can’t quantify this, but it does seem to lend more credence to the possibility that perhaps Ginther noticed and exploited certain patterns. Srivastava’s personal success was certainly based on this.
So, who’s right? Ginther isn’t talking, although she is said to live in Las Vegas and we’d love to have her on the show. Let’s look at some assumptions and do a sort of Occam’s Razor analysis:
Mazur: Pick 6 lotteries are played in a lot of places and have been for a long time. Getting four big wins could happen once by chance to anyone, and it just happened to be Joan Ginther.
Srivastava: The lotteries Ginther won were not Pick 6, but had other characteristics. It’s possible to analyze those characteristics to gain an edge — if you’re smart enough and dedicated enough. A Ph.D. in mathematics from Stanford University is likely smart enough and dedicated enough to succeed. Although Ginther’s success had a luck element to it, assuming she was a skilled gambler makes a lot more sense than assuming she just got lucky.
In my opinion, Srivastava’s argument makes more sense. What do you believe?
