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?
I believe Srivastava’s argument about is correct rather than Mazur’s argument which may highly be improbable.
It is merely because I believe Pick 6 drawings are independent events, where one draw does not have any impact over future drawings down the line. People bank on certain numbers not appearing three drawings in a row or such, and invest in wheeling system (where you select a subset of the 47 numbers and buy all combinations of the numbers so that if at least 3 of the numbers are within the subset, the player wins); all that does not increase a chance of someone winning. A good amount of winners win by the quick pick purchase.
As for the scratchers (a California lottery term I am very used to) or scratch off tickets games, it is based on conditional probability. There is a set amount of tickets printed by GTECH/Scientific Games (I do not know what other major manufacturers). If people purchase losing tickets, the higher the chance at getting the bigger prizes. And vice versa, if people were to win the bigger prizes, there would be less remaining. It would mean you would have to be at the right place at the right time. I did find it amazing Dr. Ginther pulled it off because the state of Texas is huge, same with California. For the Pick 6 drawings, Dr. Ginther could go to a liquor store, convenience store, or a gas station near by to play and have location not play a role into winning.
The Texas (and California) lottery on their website provides the stats of the tickets, the odds, the prizes available and the number claimed. I think by lottery laws, if all the top prizes are claimed, the game has to be pulled from all outlets.
http://www.txlottery.org/export/sites/lottery/Games/Scratch_Offs/details.html_252727535.html
I might also want to add that I do not believe universities are ranked by their curriculum to teach students concepts. It is more based on the quality of research performed by the professors and the students. It stands to reason Stanford is prestigious and will only admit the brightest students who have great potential towards the research and giving back time to the community. One thing I never found out is, what Dr, Ginther’s thesis and dissertation was to earn the Ph. D degree at Stanford University.
I’d look at it from a different perspective. Ginther’s knowledge and qualifications make it very hard to believe that she was simply playing the game without having at least a PERCEIVED edge–especially since PhDs tend to be well paid and she probably didn’t need to fantasize about hitting the big one. Therefore, she likely thought she had an edge of some sort–so the real question to ask is how likely was it that her perceived edge was real. You could attribute her four wins to dumb luck or to that edge, and the likelihood of her having actually had that edge is what skews the probabilities toward her having been lucky or skillful.
Someone who at least perceives an edge is likely going to be playing a lot more than typical players. Someone who plays video poker all day every day is more likely to hit 2 royals within a 30 minute window, than a recreational player who plays an hour here and there.
If the lottery player actually has an edge and has determined a way to increase the probability of purchasing a winning ticket (by looking at some printed code), but he also decreases the other players’ chances of hitting that big winner, because he takes those tickets for himself. Sort of like a card counter who wongs into a positive shoe, he eats some of the good cards (thus fewer rounds) for the ploppies who were already playing, thereby decreasing their chances of hitting, say, a blackjack. Although, if we’re talking about pick 6’s, this wouldn’t have an effect on other players’ chances of hitting a 6/6, only for scratchers.
For a more complete look at the Joan Ginther story google Joan Ginther and read the Harper’s article from 2011. Ginther lived in Vegas at Turnburry.
Okay, let me weigh in on this, as the author of Fluke. True, Joan Ginther was at one (very short) time a mathematician at Stanford. Her first win was not a scratch off. So I’m quite skeptical of the notion that somehow her math expertise had something to do with that first win. But that first win gave her a tremendous edge from her win of 5.9 million dollars. Ah, what does a winner do with house money the size of 5.9 million? It doesn’t take a mathematician to bet again with an even better edge than one can get from figuring out the distribution of scratch offs from the printed numbers. With 5.9 million to spend over the next 15 years (her first win was in 1993) to get her next win, she has plenty of time and cash to buy lots of non-winning tickets before she hits her next win.
But that’s only one point. Another to consider is that Joan is just one of many people who win four times. There are others who are NOT mathematicians in any sense of the word. So her background connection to Stanford leads only to a bit of circumstantial suspicion that math had something to do with it.
Nice discussion, folks. Hope you read and enjoy reading Fluke.
You can get it on Amazon:
https://www.amazon.com/Fluke-The-Math-Myth-Coincidence/dp/0465060951/ref=zg_bs_13942_2
You can also get it as an audio CD.
Professor Mazur, thank you for joining our discussion.
I am not arguing that her first win, a Pick 6 ticket possibly purchased by her father, had any skill element to it.
My focus in life is that there are many casino games where skillful players can obtain an advantage. I am such a player and know hundreds of others who have been successful over an extended period of time. While lotteries are not casino games, the possibility of skillful play rings more true to me than just the luck factor. As a successful professional gambler, my perspective is different from that of most of your readers.
Joan Ginther hasn’t done interviews. We’d surely like to talk to her on our radio show. The length of time between the first “all luck” win and her second one (which I believe had a skill element) could as easily been explained by she didn’t have the bright idea on how to attack this problem and didn’t even try for several years. Is my speculation more accurate than your suggestion that she was trying all the time and just hadn’t been successful? I don’t know. I’d sure like to ask her some questions.
Smart gamblers know there is no such thing as “house money.” Whether Joan Ginther is a smart gambler or not, I don’t know. Her Ph.D. in math from Stanford suggests she’s smart enough to be an intelligent gambler, but it takes more than just brains. For example, you, Professor Mazur, have your own Ph.D, may be as smart or smarter than Ginther, and are comfortable using a concept smart gamblers don’t use. It could be you considered yourself writing for a lay audience, and I consider myself an expert.
I did enjoy your book and just my writing about it will inspire a certain number of others to read it. It may come down to us agreeing to disagree. Thanks again for posting here.
Dr, Mazur’s participation does uncover a revelation. With that said, my opinion is not completely valid anymore. Both arguments from Mazur and Srivastava are reasonable.
Scratchers have a high variance with the top prize being once in a lifetime odds and the lottery only gives back around 60% of the ticket purchases back as prizes. A player would need massive bankroll to absorb the cost of the losing tickets before finding a winning
With that kind of win and bankroll, Dr. Ginther certainly knows what to do with it. Though travelling around the state of Texas to pull it off is a big feat.
As I remember it Ginther bought all her scratch offs at only 1 store. A very specific store that later encountered legal trouble of some sort and I believe was closed down. Additionally, how many6 Phds of ANY sort play the scratch off tickets in any quantity. Ginther’s background and the scratch offs suggest some sort of edge.Probably real and not imagined. Google the Massachusetts lottery. The MIT kiddies and a married couple seperately figured out a distribution flaw with a meaningful edge. Ginther will likely not ever appear on Bob’s show. His questions would be too specific. He would know exactly what to ask.
Sy Fuchs wrote: “Ginther will likely not ever appear on Bob’s show. His questions would be too specific. He would know exactly what to ask.”
I suspect you’re right about her avoiding our show, but I hope you’re wrong.
Certainly accommodations could be made.
We use a script — generally — and our guests have the right to pre-screen and eliminate any questions should they so choose. That option is always offered and rarely exercised. Our show is for educational and entertainment purposes — and not full of “gotcha” moments.
Should a guest refuse to talk about anything of substance then we would not have him/her on. But if Richard and I judge that there is value for our audience even not discussing certain topics too closely, we’d certainly consider it.
In Ginther’s case specifically, unless there was some significant illegal stuff going on, there would be plenty of room to work out questions that were acceptable to both her and us. And it would be a show worth listening to!
Thanks for the clarification. I am speculating that the store must have requested specific ticket number ranges from the distributor, but I will never know. I will share that there was and maybe still is a positive opportunity for the California Lottery, going through garbage dumpsters for losing tickets and enter codes for the 2nd chance drawing. Rumor has it that people won as much as $100,000 that way without having to buy expensive tickets.
Continuing the lottery theme allow me to more fully post about the MIT kids who plundered the MA WinFall offering. From TIME magazine “a group of MIT students realized that, for a few days every three months or so, the most reliably lucrative lottery game in the country was Massachusetts’ Cash WinFall, because of a quirk in the way a jackpot was broken down into smaller prizes if there was no big winner. The math whizzes quickly discovered that buying about $100,000 in Cash WinFall tickets on those days would virtually guarantee success. Buying $600,000 worth of tickets would bring a 15%–20% return on investment, according to the New York Daily News.” Advantage play worth talking about. Further read about the Australians who won the Virginia lottery.
As a statistics teacher and a gambler, I find it extreamly hard to believe that anyone with a PhD in mathematics would continue to pure money into scratch offs unless they had an edge. Around here they pay about 50 cents on the dollar. That is just too high of a house edge for me to believe any true mathematically gifted person would engage in this outside of the occasional fun lark.
I have read and listened to the podcasts about those who have discovered patterns in the bingo and crossword type cards that give a lot of information before being scratched to see what is underneath. I can certainly believe that Dr. Ginther discovered a similar flaw that let her play with a positive expectation such that she was collecting enough small wins to continue through to the big wins.
If scratch tickets had a much smaller house edge and she was not mathematically enclined, then I could go with the math that shows it should almost certainly happen to someone, so why can’t she be that someone.
Look up Peter Mucha, He’s written several articles about this. I’d appreciate it if BD would read them and comment on the points raised by Mucha.
What are the odds of a recreational video poker player hitting a natural royal flush (that is, being dealt the royal flush, and having the machine hold all 5 cards for you, and post the words, “Jackpot – Call Attendant”) ? I am a recreational player. My first such experience was at the Westward Ho Casino, which no longer exists. It was on a nickel machine, where they had two progressives, building simultaneously. This one was for a bet of 5 nickels, playing Jacks or Better, with the progressive built up to $435.00. As I recall, the machine started doing some crazy things, like hitting several 4 of a kinds, flushes, and full houses, very close together. Then everything turned red and the cards were all held by the machine for a hearts royal flush. Of course, I was ecstatic. My next two such experiences were on my home computer, which don’t really count for anything, except hands played in practice. One was on a game from an old floppy disk, with a screwed up version of Jacks or Better in which the straight paid more than the flush. The other was on “Bob Dancer Presents WinPoker” on the Jacks or Better game. Then, my most recent one was on a 5 nickel bet on a Deuces Wild game, just a few months ago, here in Mississippi, at the Treasure Bay Casino. Apparently, this can occur once in 650,000 hands. I’m just not sure how much time I have spent playing the hands I have played, but I don’t think I could reasonably expect to get another one in my lifetime. I’m currently playing only once or twice per week (recreational). I put more time into Pickle Ball, actually.