Author Topic: Gambler's Fallacy  (Read 1834 times)

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Gambler's Fallacy
« on: December 01, 2014, 11:37:12 PM »
Hello Friends. I decided to write on a topic that is important for all of us to keep in mind on our journeys along the way.
The Gambler's Fallacy.  I posted this in another topic, but I want to post it here to make my point.

A fair gambling device has produced a "run"?that is, a series of similar results, such as a series of heads produced by flipping a coin.
Therefore, on the next trial of the device, it is less likely than chance to continue the run.

"On August 18, 1913, at the casino in Monte Carlo, black came up a record twenty-six times in succession [in roulette]. … [There] was a near-panicky rush to bet on red, beginning about the time black had come up a phenomenal fifteen times. In application of the maturity [of chances] doctrine [the gambler's fallacy], players doubled and tripled their stakes, this doctrine leading them to believe after black came up the twentieth time that there was not a chance in a million of another repeat. In the end the unusual run enriched the Casino by some millions of francs."

Source: Darrell Huff & Irving Geis, How to Take a Chance (1959), pp. 28-29.

Many gambling games are based upon randomly-generated, statistically independent sequences, such as the series of numbers generated by a roulette wheel, or by throws of unloaded dice. A fair coin produces a random sequence of "heads" or "tails", that is, each flip of the coin is statistically independent of all the other flips. This is what is meant by saying that the coin is "fair", namely, that it is not biased in such a way as to produce a predictable sequence.

Consider the Example: If the roulette wheel at the Casino was fair, then the probability of the ball landing on black was a little less than one-half on any given turn of the wheel. Also, since the wheel is fair, the colors that come up are statistically independent of one another, thus no matter how many times the ball has fallen on black, the probability is still the same. If it were possible to predict one color from others, then the wheel would not be a good randomizer. Remember that neither a roulette wheel nor the ball has a memory. 

Every gambling "system" is based on this fallacy, or its sibling the "Hot Hand Fallacy". Any gambler who thinks that he can record the results of a roulette wheel, or the throws at a craps table, or lotto numbers, and use this information to predict future outcomes is probably committing some form of the gambler's fallacy.

The Gambler's Fallacy and its sibling, the Hot Hand Fallacy, have two distinctions that can be claimed of no other fallacies:

1.They have built a city in the desert: Las Vegas.

2.They are the economic mainstay of Monaco, an entire?albeit tiny?country, from which we get the alias "Monte Carlo" fallacy.