May 14, 2002 2:47 AM

Suppose for a moment that you are out for an evening of keno, one of your favorite casino pastimes. Being an astute player, the first thing that you do when you get to the game is you request a ball frequency printout from the Keno supervisor for the last 25 games. As you scan the printout, your interest is piqued by the fact that No. 49 has not appeared once in the last 25 games. What inferences should you make from this data?

Because you are interested in the game, you have visited the Gambler’s Book Club and browsed the collection of books written on keno; several of them suggest the idea that there are "hot" numbers and "cold" numbers and that one should play the "cold" numbers on the theory that the "law of averages" will even everything out in the long run and these "cold numbers" will come up more often in the future. Unfortunately this theory sinks like a stone in the cold pool of liquid reality.

Consider: What could cause a ball NOT to come up at least once in 25 games? One reason ”” simple probability. The odds against any one number not coming up once in 25 games is about 1,400 to one, similar to the odds against a solid five. The odds against this event are a little long but clearly not impossibly long. And, since there are 80 numbers, we can say with confidence that all 80 numbers will come up at least once every 17 games or so, on the average. So a run of 25 games without one number coming up at least once is unremarkable, even though it is interesting. Since each keno draw is independent, and the balls have no memory, we will gain no advantage by playing the "cold numbers."

Another reason: If we apply Occam’s Razor to this problem, we might postulate that a ball that does not come up once in 25 games is simply not there. Perhaps the last time the keno crew changed the set of balls, an error of omission occurred. The ball was simply left out of the bowl. Should we then play this number, assuming it will come up more often in the future? Yes, this can and does happen.

Or another scenario: A ball has split, though not entirely into two pieces. Somehow, due to air pressure or kinetic energy, it has wrapped itself totally around our No. 49. Although No. 49 does come up in this case, it is cloaked by another number, unbeknownst to Keno employee and player alike. I ask again: Should we play No. 49 in this case, expecting this "cold number" to come up with higher frequency in the future? This can and does happen occasionally as well.

And another, possible, but less likely: A ball has completely split in two, wrapping halfway around two other balls. This occurrence will skew the ball frequency as well, though it is likely to be soon discovered. Within a few games, to the consternation of the Keno supervisor and perhaps to attentive players, the split ball will appear twice in a single draw, and the defect will be embarrassingly apparent.

And there are other permutations and combinations of this theme, though none of them suggest that you SHOULD play a "cold number." Stick to the "hot" ones, if you stick on any numbers at all.