| 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. This is the last of my four-part series on craps and deals with some mathematical issues related to the subject of rhythmic rolling. This is a term that refers to controlled shooting, specifically, setting and delivering the dice in a manner that increases the frequency of a seven occurring on the comeout roll and reduces the frequency of a seven occurring the rest of the time. Many people are skeptics and doubt that this can be done and others flatly state that it is a bunch of hooey. In particular I have been asked how, as a mathematician, I can buy into such a notion. Let me address this. Originally, I was one of the skeptics. Then back in September of 2002, while attending the G2E convention in Las Vegas, I was having dinner at the Hilton with Frank Scoblete and John Grochowski when Frank suggested that we shoot some craps after dessert. John had other obligations so Frank and I headed for the craps tables. While we were playing Frank suddenly said "Sharpshooter is at the next table. Let's go." I had heard of this guy, Sharpshooter, but had never met him. The whole story is related in my review of Sharpshooter's book which appeared earlier on this site. Suffice it to say that the guy was impressive. Still, I left unconvinced that an average Joe like me could develop a shot controlled enough to make any money playing craps. |
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