Playing the quadrants in keno: strategy or luck?

Oct 27, 2009 4:07 PM
by Keno Lil |

This week I engaged in a conversation on the Internet with a keno player who plays in the California Lottery. He has a strategy for playing the quadrants of the board in such a way that he feels is productive (i.e. profitable) for him. I’ll take him at his word, but my opinion is that his "system" is working because he is in a winning streak and not because of any 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 – just like a keno board.)

Well fair enough, each quadrant should over time produce an average of five hits per game. But stating it is a little different. In fact, the most likely outcome of a keno draw is a slightly unbalanced draw, with a 6-5-5-4 distribution in the quadrants, if we ignore order. This happens once every 6.5 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 goes on to state 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 lacking in hits. Here he goes mathematically wrong.

I have nothing against tracking draw histories or ball frequencies. 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 next game produce more than 5 hits, or even be likely to?

There is no logic which will do so. The exact opposite is true. In fact, if we assume that some sort of mechanical or computational defect produced the unbalanced draw, why would it not continue to do so in the same manner until it is fixed? Once again, the balls have no memory! They can’t appear more or less often in the future merely because of what happened in the past.

My correspondent concluded by stating that he has used this system for weeks, with consistent success. My opinion is that he is in a winning streak and I hope he enjoys it, but I also hope he will not be dismayed when the system stops working.

Below 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; 5-4 is the same as a 4-5.


Distribution:         Odds for one:

6-5-5-4                 6.527

7-6-4-3                 8.876

7-5-4-4                 10.442

6-6-5-3                 11.095

8-5-4-3                 13.655

7-5-5-3                 13.869

7-6-5-2                 16.643

6-6-4-4                 16.708

8-6-4-2                 32.773

8-6-3-3                 46.429

8-5-5-2                 51.208

7-7-4-2                 53.256

5-5-5-5                 61.186

Well, that’s it for now. Good luck! I’ll see you in line!

Watch every Tuesday for a brand new Keno Lil article.

Question? Comment? E-mail me at: Keno Lil