In a conversation on the Internet, a gentleman who plays keno in the California Lottery has developed a strategy for playing the quadrants of the board in such a way that he feels is productive (i.e. profitable).
I’ll take him at his word, but my opinion is that his "system" is working because he’s on a winning streak and not because of any mathematical or statistical reasons.
My correspondent states that five numbers "usually" come up in each quadrant. (He divides the board into four rectangles of 20 numbers each – an upper left and right, and a lower left and right.)
Each quadrant should over time produce an average of five hits per game. But it’s a bit different from the way he states it. Fact is the most likely outcome of a keno draw is a slightly unbalanced one with a 6-5-5-4 distribution in the quadrants, if we ignore order. This happens once every 6½ games.
In contrast, a "perfect" 5-5-5-5 draw occurs only once every 61 games or so! Indeed, even a draw of 8-6-4-2 occurs once every 32 games, almost twice as often as a 5-5-5-5!
He says that often 6, 7 or 8 spots come up in one quadrant (true enough), whereupon he plays numbers exclusively on the next game in the quadrant that is lacking in hits. It is here that he goes seriously mathematically wrong.
Tracking draw histories or ball frequencies is a nice way to spend an afternoon. It may even have some value in disclosing a malfunctioning ball selection device or a poorly programmed random number generator. But suppose we find a draw of 7-7-4-2, which occurs approximately once every 53 games?
By what logic should we assume that the quadrant which produced a 2 on this game, will on the following game produce more than 5 hits, or even be likely to? The answer is that there is no logic which will do so. The exact opposite is true.
If we assume that some sort of mechanical or computational defect produced the unbalanced draw last game, why would it not continue to do so until fixed? Again, the balls have no memory! They cannot appear more or less often in the future merely because of something in the past.
My correspondent concluded that he has used this system for some weeks now, with consistent success. I just think he is in a winning streak and good for him! I hope he will not be dismayed when the system stops working.
Above are the odds against any particular quadrant distributions of keno draws, without regard to order. In other words, a 6/5 is considered the same as 5/6 and a 5/4 like a 4/5.
If you have a keno question, please write me c/o GamingToday or by e-mail at [email protected]. Well, that’s it for now. Good luck! I’ll see you in line!