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# Gaming Guru

### Lottery Nonsense

3 January 2004

As some of you may be aware, my book The Lottery Book: The Truth Behind the Numbers has finally been released and is now available from the publisher, Bonus Books, as well as from Huntington Press, Barnes and Noble, Amazon, Wal-Mart, and other booksellers. I want to take this opportunity to publicly thank Frank Scoblete for writing a very entertaining foreword to the book and for helping me throughout the writing. One of the things I advise lottery players in the book is to not buy so-called winning schemes for playing lotteries - there are none. The fact is, however, that as far back as there is recorded history there have always been snake oil salesmen or their equivalent and the same is true today. One of my readers, Maxine Nelson from Tampa Florida (who is acknowledged in my book for her inquiry about anonymity of winners), recently wrote to tell me about a scheme for playing called The Bell Curve. Here is the story.

Let's consider a lottery game such as Powerball wherein one picks five white balls from a population of 53 balls numbered 1 through 53. Every set of five white balls is equally likely, the chance of each being 1 in 2,869,685. This number ignores the one red powerball which is chosen from among 42 red balls. Any set of five white balls and the red powerball is as likely as the next and is 1 chance in 120,526,770. If you're interested to see how one arrives at this number, the calculation is explained on page 70 of my book. That should be the end of the story. The Bell Curve purveyors, however, claim to have a scheme to increase your chances of selecting the winning five white balls.

Among the many things at which I'm not very good, one is trying to give a sensible explanation of nonsense. So, if you want to get it "straight from horse's mouth" so to speak, go to the web sites: www.gailhoward.com/balanced.htm or www.mindtech.com.vu/Anomalies.html.

Otherwise, here's my explanation. If you pick any five white balls and add up the numbers on the balls, you'll get a total of 15 through 255. 15 is 1 + 2 + 3 + 4 + 5 and 255 is 49 + 50 + 51 + 52 + 53. If you look at how frequently each total occurs, 15 and 255 can only occur one way but totals in the middle, such as 135, occur many, many ways. In fact, if you plot the frequency of each sum versus the sum, the resulting curve is bell shaped. This is no surprise and is an illustration of a theorem in Statistics called the Central Limit theorem.

Now here is the (phony) pitch. Since numbers near the middle occur more frequently than numbers near the ends of the [15, 255] interval, one should play numbers whose totals are near the center of the frequency distribution. I hope you can see how silly this is. To be sure, if one were wagering on what the total of the five numbers would be, then this advice would make sense. But that isn't the bet! When you play the lottery you are wagering on what the five individual balls will be, not what their total will be, and the numbers 1, 2, 3, 4, 5 are just as likely to occur as the numbers 25, 26, 27, 28, 29.

The scam is that the purveyors of this advice will sell you software or tables that will tell you the frequency information for the totals of any lottery you wish. Well, I'll go them one better. You tell me what lottery you have in mind and I will send you the most likely total for that lottery and I'll provide this information absolutely free of charge. Of course, I will be providing you with absolutely useless information, so I think my price is about right!

See you next month with, hopefully, useful information.

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Best of Donald Catlin
Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers
Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers