Will Chaos Theory Beat Keno?
(From Casino Player, August 1994)
By Arnold Snyder
© 1994 Arnold Snyder
Question: According to a recent New York Times article, a computer whiz keno player in the new Montreal (Quebec) Casino used “chaos theory” to win $600,000 at keno one night in April. According to the article, the player picked 19 out of 20 keno numbers three times in a row! Then, the casino manager shut down the keno game.
Chaos theory, as I’m sure you are aware, is a relatively new branch of mathematics that attempts to find patterns in seemingly random results. If it’s true that a mathematician has now cracked this problem to the extent that what was believed to be random is now highly predictable, how will the casinos survive? Won’t new types of systems be developed, not only for keno, but also for games like roulette and craps and many others?
In fact, since blackjack is one of the few table games, along with baccarat, which — as card games — are dependent on less than perfectly random human shuffling, will we find that the truly random games, those which typically have a fixed house percentage, will become the new games of choice for professional players?
I’m not a mathematician, but I don’t understand how a game with a fixed house edge can be beaten in the long run. Isn’t this contrary to the generally accepted logic of mathematics? Please give us laymen the whole scoop on this new chaos theory, which must be the gambling system of the century, and may spell doom for the casinos as we know them.
How a Canadian College Student Beat Keno
Answer: When this story broke, it was, as you might have guessed, of enormous interest to mathematicians. It seemed inconceivable that this Canadian college student, Daniel Corriveau, could have employed chaos theory — as he reportedly claimed he had done — to essentially predict the future in a game like keno. In fact, had Corriveau done what the newspapers reported he had done, his mathematical discovery would have such far reaching impact on virtually every branch of mathematics and science that the changes to the casino industry would pale in comparison to the advances you would see in electronics, chemistry, aviation, communications, etc., etc.
Unfortunately, when the whole story came out, it turned out that there wasn't any great discovery with regards to applied chaos theory. There was simply an inadequate electronic number generating system in use at the Montreal Casino. Unlike the swirling ping pong ball systems used in many Nevada casinos, the Montreal Casino was using a state of the art computer random number generator to pick keno numbers. Corriveau simply discovered that the random number generator (RNG) was anything but random, and the only chaos theory he proved was that if you pick 19 out of 20 keno numbers three times in succession, casino management is thrown into chaos.
As RNGs are used these days in virtually all electronic slot machines, and are also frequently used by casino game analysts in simulating betting systems and player/house expectations, etc., allow me to explain what an RNG is, what it does, what it doesn’t do, how it works, and what went wrong in Montreal.
First of all, an RNG is not a piece of hardware, as you might normally assume from the term “generator.” It is a computer program, or more specifically, a mathematical formula, or a series of formulas, utilized to derive a “random” series of numbers. Can any mathematical formula actually produce a series of totally random numbers? No. And no RNG is truly random.
As an example, one RNG with which I am familiar is that used by Dr. John Gwynn in testing blackjack systems. His RNG has a cycle length of 2.7 billion. This means that his RNG will produce a string of 2.7 billion numbers which exhibit no discernible or predictable pattern, random for all intents and purposes, but that the cycle will begin repeating itself after 2.7 billion numbers.
All such RNGs require a “seed” number, which must be fed into the formula in order to start the series. With the RNG utilized by Dr. Gwynn, starting with a different “seed” does not change the 2.7 billion number cycle, but it will start the cycle at a different point. The same 2.7 billion number series, however, will be repeated.
In order to assure the most “random” results, many RNGs pick a seed number by utilizing whatever nanosecond the computer’s internal clock has at the moment the operator starts the program.
Such a random number generator works well for testing blackjack systems if what you want is “randomly” ordered cards, and your tests are going to be in the millions of hands, or even hundreds of millions of hands. If, however, Dr. Gwynn were attempting to pinpoint some expectation to umpteen decimal places, requiring a test of ten billion randomly dealt hands, his RNG would be inadequate because every 2.7 billion hands he would be recycling through the exact same series of cards.
How to Beat Keno: Find a Casino Without a Clock Chip
The problem in Montreal was that they did not purchase the clock chip for picking different seed numbers. As many Nevada casinos also use this same electronic keno number generator, and use it without the clock chip that generates seed numbers, Montreal management may have been under the impression that the seed generator was not a necessary component of the system, or that it was automatically included.
The major difference between Nevada casinos and the Montreal Casino, however, is that the Nevada casinos operate 24 hours per day, never turning off their keno games, while the Montreal Casino shuts down each night and reopens again in the morning. Without the clock chip to generate different seeds, each day the Montreal Casino was cycling through the same numbers, beginning at the same starting point! This is what Daniel Corriveau discovered. And this discovery paid him $600,000 in keno winnings.
So, unfortunately for mathematicians, there is no great breakthrough in chaos theory. Casinos can breathe a little easier, knowing that computer nerds will not start walking away with fortunes from games like keno and craps.
I will assume, of course, that those Nevada casinos which have not been using the clock chip on their electronic keno games, by now have purchased the chip, as this whole scenario has provided scam experts with one of the easiest, potentially most lucrative, and hitherto unknown “inside jobs” that could be imagined. In order to take a fortune from any casino in Nevada which uses this electronic keno random number generator, and which fails to utilize the clock chip for seed number generating, all a casino employee would have to do is turn the game’s power off for a moment at the end of each day, and the same number sequences would start repeating, just as they did in Montreal.
Incidentally, Daniel Corriveau was paid his $600,000 after investigators determined that he did not work in collusion with any casino employees. He took advantage of the game exactly as he found it. Hats off to Mr. Corriveau for teaching the Montreal Casino a lesson in mathematics. If there is a way to beat a game, someone will find it. ♠
For more information on how professional gamblers have beaten a wide variety of casino games, including lotteries, slots, roulette, and every other casino game, see the Blackjack Forum Professional Gambling Library, plus The Big Book of Blackjack
by Arnold Snyder and Gambling Wizards: Conversations with the World's Greatest Gamblers, by Richard W. Munchkin.
If you are already an experienced card counter and wish to move up to the next level of professional gambling, see Advanced Tactics in Casino Advantage Play, by Abram Alexander. All pros should own Beyond Counting 2, by James Grosjean.
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