How good are superstitions?

Jan 4, 2005 2:54 AM

This week we’ll move from the traditional to the supernatural, namely superstitions.

There are many keno systems available on the market that purport to pick good numbers to play. Most of these systems are based on "hot" numbers or "cold" numbers, or a combination of both.

According to these systems, a "hot" number is a number that has come up more than it should have in the past, while a "cold" number is one that has come up less often than predicted. Basic probability suggests that all Keno numbers should come up a quarter of the time, if we assume that the game is fair and all the equipment is functioning perfectly. Thus, over a hundred games, each number should come up about 25 times.

Of course, normal statistical variation will result in some numbers coming up more than others, especially over such a small sample as a 100 games.

Next time you’re playing Keno, ask the supervisor for a "Ball Frequency Report." Most Keno games will be happy to print one out for you. You will see that although the balls come up an average of 25 percent of the time, there is some natural variation in their frequency of occurrence. Over a 100 game period, some may come up 30 or 31 times, while some may occur only 19 or 20 times. (By the way, when you ask for a Ball Frequency Report, you may specify the number of games back in history that you wish to see.)

So the question is, if we see a ball that has come up 30 percent of the time (versus the expected 25 percent) is it fair to call this a "hot number?" Likewise, if we see a ball that has only come up 19 percent or 20 percent of the time is it fair to call this a "cold number?"

Obviously, if we know that a ball will come up 30 percent of the time in the future, this would give us a great advantage in our play. And, just as obvious, if we could avoid playing numbers that will only come up 20 percent of the time, we will easily increase our expectations.

Unfortunately, it is a law of probability that past independent events (and each draw of a Keno game is an independent event) have NO effect on future independent events. Thus, given a fair game as postulated above, our expectation for the future is that each number has a 25 percent chance of occurrence on the next draw.

There are two fallacies inherent in most of these Keno systems. One is that hot numbers must somehow continue to be hot. The other is that cold numbers are "overdue" and thus will come up more often than expected in the future.

Sober reflection upon the laws of chance will tell you that these ideas have no value. More on this next week.