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Best of Alan Krigman

Gaming Guru

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Players Aren't the Only Gamblers Who Defeat Themselves

21 May 1996

Maybe you've read or heard about the math whiz who racked-up several big keno scores, after using chaos theory to look for patterns in piles of previous results. The player won a lot of money, legally, before the casino pulled the plug on the game.

It happened. But, little - if anything - in the gaming world is quite as it seems. This tale is no exception.

To understand, you should realize that in keno, a computer picks the winning numbers for each game. The selections are made using a program called a "random number generator." Only, the numbers aren't really random. They're "pseudo-random." This means they appear to be arbitrary, but are actually predictable because they're produced by some sort of mathematical rule.

Pseudo-random number generators are ordinarily satisfactory for gambling purposes. Seas of slot machines, cramming cash into casino coffers the world over, attest to this assertion.


In theory, you can reduce or remove the element of chance from a game driven by a pseudo-random number generator. One approach would be to know or deduce the mathematical rule employed, the current position in the output sequence, and the criterion for proceeding to the next point. With this knowledge, you could reproduce the program and run it in advance. In practice, though, even if inside information were available or the analysis could be done, it wouldn't help because the games routinely include means of imposing additional uncertainty.

Some added uncertainty might involve offset introduced into the stream of numbers when the program is started or reset. This can be done many ways. For instance, the computer could sense how many thousandths of a second the operator takes to do a certain start-up task then use this figure to alter the rule. The time can't be precisely anticipated or repeated, so the modification to the rule - and the numbers generated - will be unpredictable.

Further uncertainty can be injected when choosing which point in the pseudo-random series governs any particular result. The programs normally run continuously, so numbers keep changing. The computer doesn't use each sequential entry in turn; it selects whatever is current at the moment the system calls for a decision, an instant usually determined by human intervention.

So computerized keno should be foolproof. But, as Jack Lord used to say to James MacArthur with eight and a half minutes to go in every episode of Hawaii Five-0, "What if, Danno, what if ..."

What if the system were shut off at night and turned on in the morning? The pseudo-random number generator would be reinitialized daily. What if no offset were provided? Numbers would always follow the same rule. What if the computer - once started - were totally automated? Each new game would began precisely the same interval after the last. Taking these factors together, games would repeat every day. The fifth game Tuesday would duplicate the fifth game Monday, and so forth. Who'd even think to check?

That was the real story. Chaos theory didn't help. There were no patterns to be found. And, the theory wouldn't have found them if there were. Rather, the casino made a mistake to set up and operate the computer this way. And the player found it serendipitously. That is, while searching for patterns in the numbers generated over the course of time, the player unexpectedly discovered something else. The same patternless series of numbers occurred every day. Not unlike Columbus looking for a westward route from Europe to Asia and discovering something else.

So, the anecdote wasn't about a solid citizen smart enough to beat the system. But about a casino dumb enough to beat itself. And a player who exploited it. Just the opposite of the usual scenario. Still, as the immortal muse of pseudo-random meter, Sumner A Ingmark, rhymingly wrote:


Only those of inquiring bent'll,
Make discoveries coincidental.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.