Gambler's Fallacy

Description:

The argument assigns a probability to a random event based on the notion that the past history of that type of event has some influence on its probability for future occurrences.

Comments:

Bad gamblers frequently make the mistake of thinking that they can detect non-random patterns in a random (causally independent) sequence of events. Thus, the fallacy of thinking that causally independent events are somehow causally related has come to be known as the Gambler's Fallacy, even though the fallacy is not restricted to that setting. An alternative version of the fallacy (sometimes called the Lottery Fallacy) is to say that a past event must have been highly probable (or even inevitable) merely because it did in fact occur.

Examples:

"This slot machine hasn't hit the jackpot in the last hour. It should pay off big any minute now."

"Our community suffered a devastating hundred-year flood just last year. So now we should be safe from further flooding for at least a hundred years."

"Given all the logically possible combinations of which DNA molecules are capable, the odds against human life evolving would appear to be staggering. Why didn't something else evolve instead? The fact that we are here at all proves that evolution was guided and that humans were meant to evolve."

Discussion:

It is a matter for metaphysical speculation whether all events are caused or whether some events are truly uncaused. Whatever the outcome of that debate, it is certainly true that some events are not caused by (or are causally independent of) other specific events or conditions. For example, a coin toss must come up either heads or tails. The specific result is caused by the force with which the coin is flipped, the precise angle at which the coin was held, etc. However, the result was not caused by the result of the previous toss, as common sense should tell us if we keep in mind the normal ways in which cause and effect function. These events are said to be causally independent of each other. However, humans are notoriously bad at reasoning about probabilities and notoriously good at recognizing patterns (even where they do not exist). This makes us prone to mistake the Gambler's Fallacy for good reasoning.

This fallacy takes numerous forms--virtually every logically possible combination. All the forms are essentially related, however, since they all involve thinking that there is a causal connection between events when common sense should tell us that there is none. Here are some possibilities:

(1) supposing that a random event is more likely to occur because it has not happened for a long time;

(2) supposing that a random event is less likely to occur because it happened recently;

(3) supposing that a random event is less likely to occur because it has not happened for a long time;

(4) supposing that a random event is more likely to occur because it happened recently.

Source:  Pierre Simon LaPlace, Philosophical Essay on Probabilities, 1819.

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