Some random thoughts: No love here for cluster strategy

March 20, 2012 2:00 AM

I have seen lots of ink spilled regarding keno machines and whether or not numbers "cluster" on these machines, and whether or not playing "clusters" of numbers is a good strategy.

I just don’t buy the "cluster" strategy. The only mathematical rationale behind the clustering theory would be the theory that the random number generators built into these machines is faulty to the extent it will produce visible clusters of numbers on the board.

Is this impossible? No it isn’t impossible due to the fact random number generators are software written by humans. However it is highly unlikely.

Random numbers are useful things to mathematicians and statisticians and – before computers – were usually produced by some mechanical process.

I remember in the 1960’s there was even a famous book published by the Rand Corp that simply consisted of random digits, It was called "One Million Random Digits" or something like that, and it was produced by rolling dice or something more arcane like clocking the physical decay times of a radioactive isotope.

When computers came on the scene the possibility of producing random numbers by machine became possible. A mathematician/computer scientist named Donald Knuth published a book call "The Art of Computation" in which he outlined the theory of random number generation.

The "random" numbers that are produced by the computer chips in the Keno machine are actually "pseudo-random numbers." In plain English, they are not really random, but they fit a statistical profile that is random enough to suit the purpose of "randomicity" in nature.

Philosophically we are on a bit of a slippery slope because it is not terribly clear how random nature is of course. But the numbers produced by random number generators (RNGs) do satisfy simple statistical tests anyway, such as reasonable distributions, etc.

All algorithms will eventually produce a loop. The trick for the software developer is to push the loop out to billions of cycles before it repeats. Can things go wrong with RNGs? Yes. And they have.

But think about this. Keno machines have been around for something like 25 years or so. If any of them had a defective RNG in them, they would have been noticed by now. A win of $10,000 more than expected would produce a 1% deviation from expected win in a million dollar coin-in.

If this happened once in a while no big deal, but if it happened consistently a casino would pull the machine and send it back to the manufacturer. I guarantee it.

You have to ask yourself, even if the software is faulty and is producing groups of numbers, why would these groups appear as visible clusters? And on the other hand, even a well designed RNG will produce visible clusters from time to time. As a matter of fact, it would be highly suspicious if they didn’t!

So, are the people who claim success with a clustering strategy telling lies? Not necessarily. They might just be people who play clusters and have had a string of good luck, and sincerely believe their system is responsible.

One good hit at keno can give you a couple of good years. On the other hand, they might just be wanting to sell you a book.

Well, that’s it for this week, good luck! E-mail me at