gamblers fallacy

The gambler’s fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that if something happens more frequently than normal during some period, then it will happen less frequently in the future; likewise, if something happens less frequently than normal during some period, then it will happen more frequently in the future (presumably as a means of balancing nature). In situations where what is being observed is truly random (i.e. independent trials of a random process), this belief, though appealing to the human mind, is false. This fallacy can arise in many practical situations although it is most strongly associated with gambling where such mistakes are common among players.


Gambler’s fallacy is the false belief that a random process becomes less random, and more predictable, as it is repeated. This is most commonly seen in gambling, hence the name of the fallacy. For example, a person playing craps may feel that the dice are “due” for a certain number, based on their failure to win after multiple rolls. This is a false belief as the odds of rolling a certain number are the same for each roll, independent of previous or future rolls.


The Gambler’s Fallacy is committed when a person assumes that a departure from what occurs on average or in the long term will be corrected in the short term. The form of the fallacy is as follows:
X has happened.
X departs from what is expected to occur on average or over the long term.
Therefore, X will come to an end soon.
A person is assuming that some result must be “due” simply because what has previously happened departs from what would be expected on average or over the long term.
For example, one toss of a fair (two sides, non-loaded) coin does not affect the next toss of the coin. So, each time the coin is tossed there is (ideally) a 50% chance of it landing heads and a 50% chance of it landing tails. Suppose that a person tosses a coin 6 times and gets a head each time. If he concludes that the next toss will be tails because tails “is due”, then he will have committed the Gambler’s Fallacy. This is because the results of previous tosses have no bearing on the outcome of the 7th toss. It has a 50% chance of being heads and a 50% chance of being tails, just like any other toss.

Gamblers fallacy originated in the roulette of Monte Carlo

The most famous example this phenomenon occurred in the game of roulette at the Monte Carlo Casino on August 18, 1913,[5] when the ball fell in black 26 times in a row. This was an extremely uncommon occurrence, although no more nor less common than any of the other 67,108,863 sequences of 26 red or black. Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an “imbalance” in the randomness of the wheel, and that it had to be followed by a long streak of red.


Gambler’s fallacy, has its roots in gambler’s psychology. Arises out of a belief in a “law of small numbers”, or the erroneous belief that small samples must be representative of the larger population. According to the fallacy, “streaks” must eventually even out in order to be representative.


bias wheel


Counterargument by R.D. Ellison: The BIG LIE.

The prevailing wisdom among gaming experts and mathematicians is that every table decision (at games like roulette or craps) is an independent event. The opposing view (that a number can be “due”) is derided as being a foolish viewpoint and is referred to as the premise of the Gambler’s Fallacy.

As it turns out, this so-called fallacy is in itself false. The following are the in congruencies of this ‘independent events’ issue that the experts have not addressed:

At American Roulette, for example:
Experts agree that every number has a 1 in 38 chance of appearing on the next spin.
This 1 in 38 chance is also known as that number’s statistical expectation.
If an entity has or takes on any kind of expectation, it ceases to be independent.

If these numerical events did not have an inherent predictability, there would be no way to assign a statistical expectation to them. And anything that has a predictable quality to it cannot be “independent.”

As Frank Barstow said in his book, Beat the Casino, “Dice and the wheel are inanimate, but if their behavior were not subject to some governing force or principle, sequences of 30 or more repeats might be commonplace, and there could be no games like craps or roulette, because there would be no way of figuring probabilities and odds.” This, of course, goes against the thinking and teachings of all other gaming authors, but that, in itself, does not prove that statement to be wrong.

This truth becomes more clear when one considers that the ‘independent events’ premise gaming experts embrace actually contradicts itself. Table results at roulette are in an ongoing state of conforming to their probabilities, but anything that is truly ‘independent’ does not conform. Many gaming authors contradict themselves as well, by advising their readers to hold out for a specific table condition (like the “five-count” at craps).

But if all table results were as independent as they claim, it would not make the slightest difference when a player placed his bets. Anything that occurred in the past would have no relevance whatsoever.

Gaming authors, statisticians and math experts all agree that the numbers will conform to the probabilities given a large enough sampling. What they’re saying is that numbers conform in large groups but not in small groups. Another contradiction.

An accumulation of small groups will form a large group; therefore, anything that applies to a large group will also apply to a small group, in a smaller way. So, the statistical pressure for numbers to conform to their probabilities will be felt in all numbers that form any small group, just as they do for a large group.

For lack of a better expression, each number is a tiny part of a greater conspiracy that will ultimately reveal itself as the trials accumulate.

It comes down to this: in a controlled environment that invokes a statistical certainty, there has to be a cause, and an effect. The effect is that the numbers conform to their statistical expectation. The ‘other guys’ will tell you that there is no cause; that the effect is the result of willy-nilly random chance that conforms through unabated coincidence! And the entire world has been buying this illogical horsepuckey for a hundred years!

Truth is, these numbers are influenced by the equivalent of a countdown that adjusts itself with every spin, which is programmed into the device itself. The more precise the manufacturing technique of that device, the more accurate (unbiased) the table decisions will be.

How did so many experts arrive at such an erroneous conclusion? Their viewpoint rested largely on the seemingly incontrovertible argument that “the wheel has no memory.” Hard to argue with that, because it does sound like the rantings of a madman to claim that the wheel can remember what has happened, then compensate accordingly.

That implies that the wheel possesses some form of intelligence! Ah, but what they overlook is the fact that man does possess the technology to create a balanced device that distributes the numbers evenly. And that is all the wheel is doing when it performs this artificial “thinking” task that they all say is impossible!
So, the roulette wheel does not actually ‘think’, but it IS constructed to perform the equivalent task, insofar as the fair distribution of numbers is concerned. It was designed, through precision crafting, to produce numbers that match the probabilities.

The illusion of memory is an inherent part of the construction. So, in effect, it does have a memory. In effect, it ‘knows’ when number 5 is underperforming, and, given enough time, it will compensate for that. It is self-correcting.

This logic applies to anything that has been formally assigned a statistical expectation. At craps, the dice are precision ground to within 1/10,000th of an inch. The dice don’t need to have a memory to act as if they did; they are just doing what they were constructed to do.

The numbers that are generated will automatically pursue a state of balance among themselves. What this means is that a craps or roulette number can be technically “due,” after all. Its appearance may be sidetracked by an opposing trend, but that is just a temporary delay of the inevitable.

Well then, if these events are not independent, shouldn’t gaming systems work? Not necessarily. There are two forces at play: statistical propensity (the law of averages), and trends. At times, these two work in concert with each other; at other times they clash. But in any such contest, trends have the strategic advantage.

Think of statistical propensity as the underlying constant, which will frequently be disrupted by trends, which don’t take orders from anyone!

All those experts, all these years, have been wrong. And it took the 3qA, which defies explanation by those same experts, to bring this new reality to light. This is the true reality. This is the one explanation that would not cause the scientific community to stutter and grope for meaning when trying to explain why the numbers do what they do.