Is There Magic in the Numbers in Lotto Games? Some Observations

By John Anderson

Lottery games have been around for centuries. A variant of Bingo was invented in the late 1800s, but the Romans played the numbers long before that. The biggest difference between then and now is the cost to play the game and the size of the payoff for winning. Even the staunchest anti-gambling advocate has to admit to being intrigued by the prizes. By risking a dollar a person might win many millions. Unfortunately, as we all know, not everyone is willing to stop at a dollar. Horror stories, and hopefully mostly just stories, abound about welfare families spending their entire income buying tickets.

Who have been the winners? Was it ever anyone who spent a hundred dollars or more on tickets to cut down the odds? I haven't heard of one, but I do know that a woman won forty million dollars when a clerk refused to change a five dollar bill for her so she could have bus fare. Determined to get her change, she bought a PowerBall ticket. (I hope she went back later and planted a big kiss on top of the curmudgeon's head.) Did any of the winners read a book telling them how to pick the numbers? How many used their own or their spouses' birthdate or the two combined? Or did they use their telephone number, or numbers on a fortune cookie? As far as I know, all but one of the winners let the lottery computer pick the numbers for them. The one great exception was famous. A man in Chicago faithfully bought the same number for the Illinois lottery at the same grocery store for years. One day the number came up. And guess what? He couldn't find his ticket! After learning about his history and considering the fact that no one else claimed the prize, the lottery commission magnaminously awarded the prize to him. It would be the first and last time it would ever happen. Now, you must present the winning ticket to claim your winnings.

The point is, the odds against you are incredible. Imagine, if you will, a hundred yard long sandy beach with exactly one pebble that is different from all the rest. Even if it looks different, what do you think your chances are of finding it?

So who cares, you say. I'll play anyway.

Let's say you like to pick numbers. Which of the two listed below would you say is LESS likely to come up: 1, 2, 3, 4, 5, and 6 or 22, 34, 39, 40, 46, 48 and 55. Niney-nine out of a hundred people would say 1, 2, 3, etc. is less likely because they are the first six numbers in our counting system and we imagine a connection between them. This imagined connection likely will translate into a bias against playing them. But the truth of the matter is, neither is more or less likely to occur than the other. The question is whether there is a practical aspect to this bias. Amazingly enough, there is. But it probably will take a very long time to show up. maybe even several billions of years. Sooner or later, over a infinitely long time span 1, 2, 3, etc. will wind up in the machine's trough. If the bias has continued, no one will have chosen the right numbers. (Never mind that the computer might have selected them for someone.) In fine, over a long enough time span, even the tiniest bias can make an important difference.

For the people who have bought books about picking winning numbers, how many authors claim they have a foolproof way of choosing the numbers? Obviously they don't, or hundreds of people would win every week. What they do say is that they can increase your odds of picking the right numbers. My question is, how do they know this is the case? Are the five non-winning numbers the book helped you find more likely to have been the winners than the millions of other combinations that didn't win either? If so, what is the process that determines these probablilities and how can it be demonstrated?

In conclusion, let's return to the possible practical importance of even the tiniest biases. I have done studies of winning numbers for the PowerBall contest for the last ten years. (I'll let you research this for yourself.) Rather than evenly spread numbers across the complete range, certain ones have appeared significantly more often than others. Mathematicians who study probability theory say that this is a good proof of true randomness. Be that as it may, the question becomes: If a person played these numbers exclusively, would he/she be more likely to win? Probably not. Past performance cannot predict future occurrences. But even so, is there even a slightly greater probability that these numbers COULD actually come up more often in the future than some others?

Possibly. The reason may lie in the mechanics of the way the numbers are chosen. The machine and the pingpong balls that bounce about before they blow out of the chute could contribute their own tiny bias. What if some of these balls were infinitesimally lighter or heavier than the rest? Or is it possible that the laws of randomness select certain numbers more often than others? We can never know. But even an infinitely tiny boost in your ability to predict one or two of the six numbers would cut down the odds against you by several millions. Is that tiny boost worth putting money on the line? That's entirely up to you. In a nutshell, a little research may actually reduce the multi-million odds against you by a tiniest bit. Who knows. It may be enough to help you pick a winner.

Copyright 2005 by John Anderson

John Anderson has been selling stamps and collectibles for more than thirty years. He is now semi-retired and writing his second novel. His first, The Cellini Masterpiece, was written under the pen-name of Raymond John and published by iUniverse. If you have a question for John, or would like to contact him, he can be reached at http://www.cmasterpiece.com

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