Normal Distribution and the Lottery
Date: 20 Jun 1995 11:45:29 -0400 From: Mike Kelly Subject: Random Raving Dr. Math, For a friend, I wrote a Visual Basic program to generate "Pick 6" lottery numbers, producing six random numbers from 1 to 46. Curious, I re-wrote the routine to generate sequences until it hit a pre-determined sequence, say 1, 6, 12, 29, 39, 44, or a stop limit of 100,000 iterations. When five of the six were matched, I kept track of which digit was not matched and found that the non-matches occurred on 12 or 29 more often than on 6 or 39 and much more often than on 1 or 44, the result being a somewhat normal distribution, with the no-match count being, on one particular run, 6, 9, 15, 12, 9, 5, for the six pre-defined numbers respectively. This pattern was born out over numerous runs. I have read something about random number generation being related to a normal distribution but can't understand why this is the case given the random nature of the routine. I'm not looking to win the lottery, but I'd appreciate your explanation of this phenomenon. Mike Kelly
Date: 21 Jun 1995 15:14:30 -0400 From: Dr. Ken Subject: Re: Random Raving Hello there! Well, I'm inclined to say that the short answer is "your numbers aren't really random." I don't know about the particular algorithm your program uses (and I don't know all that much about _any_ random number algorithm), but I do know that if the numbers are truly random, they have the property that one number is roughly as likely to be chosen as any other number. In your case, if your program is truly picking six independent random numbers (that is, if the numbers that have already been chosen have no effect on the choice of the remaining numbers) then your intuition is good; there's no reason why you should get a normal distribution. Think of it this way: in your program, there's no significance to the concept of the order of numbers. Instead of the order 1, 2, 3, 4, ..., the numbers might as well be ordered 6, 39, 14, 1, 20, ... and there should be no difference in the Lottery. The Lottery doesn't care that 1 is lower than 2, which is lower than 3, and so on, it just cares that there are 40 (or whatever it is) little symbols, and you can't have more than 1 of the same symbol whenever you pick 6. Thinking this way, there can be no legitimate way to get a consistent imbalance of any kind. So the problem must lie in your random number generator, and I'm not sure what would be going on there. Thanks for the question! -K
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