One of my correspondents sent me an inquiry regarding a system for playing keno involving so-called "hot numbers." I cannot give you an opinion on this system because I haven’t seen it, and I am not likely to, either, because I would rather spend the $10 on keno tickets rather than on a system of this kind. I can, however, give you an opinion on these kinds of systems in general.
The blurb for this system states that, "In any given period of time, certain numbers frequently repeat while others seldom appear." This statement is obviously true. The advertisement continues, "These REPEATERS are HOT numbers, the occasional repeaters are WARM numbers and the rest are COOL and COLD numbers."
You can, of course, give different numbers any names or labels that you like without altering the facts, so this is a fairly harmless assertion.
The advertisement continues, "When a hot number misses a certain number of times, there is an excellent chance it will soon show again."
This is true, the chance in fact being one chance in four that the number will appear on the next draw.
The next line of the blurb describes where the "system" breaks down. It states, "Conversely, if a number is cold for a period of time, based on the law of averages, the possibility of coming up is strong."
The possibility of a "cold number" coming up on the next draw is, of course, one chance in four, the same as for any other number. Systems like these, and their designers, are always mistaken in their understanding of the "law of averages," which means something entirely different from what most people think it means.
In layman’s terms, the "law of averages" (most mathematicians don’t call it this) states that things will tend to happen at their expected frequency after a number of trials. As the number of trials increases, each event will tend to become RELATIVELY closer to its expected frequency.
We can use an example of two numbers to put all this in terms of keno. Lets take the numbers 1 and 80 for example. In keno we expect each number to come up one-fourth of the time, so after charting 100 games it would not be unusual to see the following results:
|No.||Times Came Up||% Came Up|
After 500 games, we might have charted these results:
|No.||Times Came Up||% Came Up|
Note that after 100 games, number 80 has appeared FOUR more times than number 1, while after 500 games, number 80 has appeared TEN more times than number 1, even though after 500 games both numbers have appeared at a rate that is RELATIVELY closer to their expected appearance (25% for each).
Thus the "cold number," which only came up 23 times in the first 100 draws, and which you would expect to come up more often in the next 400 draws according to the "law of averages" as understood by these system designers, came up only 97 more times.
The so-called "hot number" which came up 27 times in the first 100 draws came up 103 times in the next 400 draws, thus widening the absolute difference between the two numbers.
Both numbers behaved correctly statistically, because both tended towards their relative expectations as the number of draws increased. I think that you can see from this analysis the problem with typical "hot and cold number" systems for playing keno!
That’s it for this week, good luck, I’ll see you in line!