The Law of Disproportionate Occurrences
The Law of Disproportionate Occurrences
We can all agree, in our rational moments, that the dice, the roulette wheel, and the cards have neither brains nor a memory. We can also probably agree that sometimes it appears that they do have, at least, some kind of “conscience” This so-called ‘conscience’ is really known as the “Probability Model.”
As most may already know, a different probability model exists for all casino games. The probability model is what is used to determine the “odds” on the various bets that make up the games.
The various probability models are generally concerned with “Infinity” or the “Long-Run.” These models provide that there will be, in general, 50 “heads” for every 50 “tails” and 50 “Pass-Line” winners for every 50 “Pass-Line” losers in craps. Also in roulette, there will be 50 “red” numbers for every 50 “black” numbers, etc., etc. Each game has its own individual probability model.
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The Long-Run Vs. the Short-Run
Few people will contest the mathematicians and statisticians’ reliance on infinity, “the long-run.” Casinos are getting wealthy because of infinity. After all, they have it on their side! Few of us have the resources to out-wait, or out-gamble, the casino’s bankroll.
People have been trying to beat the casinos for years. Most authors have designed their so-called “winning gambling systems” by using the various probability models.
Unfortunately, most of the “beat-the-casino” type books and literature presently on the market are based on misconceptions. The misconceptions come from equating short-term results with long-term results.
What about Computer simulation?
Recent advances in the computer industry have been remarkable. The developments in this industry have led many authors into the trap of “computer simulation.”
Students of gaming and many authors have eagerly taken advantage of the computer’s speed in the handling of numbers. The computer can run vast amounts of data in a very short time.
The idea was to simulate a large number of “decisions” in a short time-span. “Decision” is the term used to signify the outcome on a roll of the dice, a card hand, or the number on the wheel that the roulette ball finally “decides” to select.
Prior to the availability of high-speed computers, gaming students and authors relied heavily on various books of “decisions” when evaluating their newly designed “winning systems.” These books of decisions have been laboriously compiled by someone carefully observing and documenting long periods of consecutive rolls of the dice, many-many card hands or 300 hours of roulette spins, etc.
In retrospect that was probably a much better way to evaluate new systems instead of trying to emulate real-life results with computer decisions.
The computer provides “random decisions.” Computer simulation has now been used for 20 years or more in an attempt to gather, or simulate, a large number of so-called “gaming decisions” in an unrealistically short period. Unfortunately, many people who had used the computer to simulate “games of chance” have now discovered that the results are not reliable. Because the computer makes decisions on a purely random basis, its decisions do not duplicate “real life.”
We have all seen “runs” of numbers on the craps table and even the roulette wheel. We have also remarked when repetitive card values appear in the card table-games. This repetitive-number phenomenon is seldom if ever, emulated by any computer simulation. What is happening here?
Many experienced roulette players use the affordable software Roulette Xtreme to test roulette strategies. Roulette Xtreme is not a system: it was designed to develop and test roulette systems using large amounts of spins.
The Model Governing the Short-Run
Reality unquestionably tells us that there must be a SECOND MODEL in addition to the infinity model that is governing the short-run. We have all witnessed this “Second Model” phenomenon when we say: “Things don’t happen like they are supposed to!”
If the model governing the long-run (Infinity) was truly duplicated in the short-run, then the casino table games would have been extinct a long time ago. There would be “no challenge” because we would already know, for example, that for every 100 spins of the roulette wheel there would be exactly 50 “red” numbers for every 50 “black” numbers occurring within those specific 100 spins.
Well, it doesn’t work quite that way, does it?
We can all state from our own experiences that real life doesn’t work that way. We can also accurately state that the Law Of The Long-Run does not work in the short-run.
Through actual observation of the short-run, we can observe that the long-run is not duplicated in the short-run. This also describes the “challenge of the games.” We now recognize this unique paradox: “The short-run is always inequitable to the long-run.” The whole is still equal to the sum of its parts. However, the parts themselves are simply not abbreviated versions of the whole.
This now brings us to the explanation for previously “inexplicable” results. This new explanation is the “missing link” that has apparently eluded us for a long time. This “missing link” is known as the “Law of Disproportionate Occurrences.” We now have an explanation for the occasional “clumps” of high or low cards and for the so-called “unusual runs” of repetitive numbers in craps, etc.
We instinctively want to rely on our existing knowledge and understanding to explain reality. Our former confusion has been created by the existence of the Law of Disproportionate Occurrences. Now that we recognize its contribution to real-life results, we can finally understand why events don’t happen in their presumed and preconceived manner.
Real Life Doesn't Work as the Long-Run
If we had to come up with a very short definition for the “Law of Disproportionate Occurrences,” it would be something like:
“The Law that governs the results of a random series of short-run consecutive events as compared to the results of the same, or similar, series of consecutive events over infinity.”
OR
“When the results of any defined relationship are viewed over a short-to-moderate number of occurrences, those results will not conform truly and exactly to the results found in the infinite probability model.”
The Law of Disproportionate Occurrences doesn’t need to be academically justified or philosophically rationalized. We have simply made our best attempt to put its abstract identity into words and illustrations and into our game of roulette. Just like the law of gravity, the Law of Disproportionate Occurrences simply commands acknowledgment. In addition, just like the law of gravity, there is nothing we can do to fight or eliminate it. Why should we try anyway? As you will discover here, we should learn to exploit it instead of challenge it. The results will be greatly to our advantage!
Furthermore, this is the same exact law that the online casinos now worship! The casino actually operates on an 11% commission on our wagers. This is most apparent in the Sportsbook, the poker rooms and in online baccarat.
However, because of the “short-run” phenomenon, they actually enjoy a “net profit” of 15 to 20 percent! If the “normal 11% commission” were the only way for casinos to make money from our wagers, they would only net, approximately, a minuscule plus-minus 2 percent.
We must recognize that the casino is really nothing more than the Host for “The Games.” We can now also accept that the “Law of Disproportionate Occurrences” is absolutely “THE PHENOMENON” that will allow us to take the casino’s money home with us. Moreover, they are left void of a defense.
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