Gambler’s fallacy

By Shane Parrish via farnamstreetblog.com   Article

Mental Model: Misconceptions of Chance

“The gambler’s fallacy implies that when we come across a local imbalance, we expect that the future events will smoothen it out. We will act as if every segment of the random sequence must reflect the true proportion and, if the sequence has deviated from the population proportion, we expect the imbalance to soon be corrected.

Kahneman explains that this is unreasonable – coins, unlike people, have no sense of equality and proportion ….

He illustrates this with an example of the roulette wheel and our expectations, when a reasonably long sequence of repetition occurs.

After observing a long run of red on the roulette wheel, most people erroneously believe that black is now due, presumably because the occurrence of black will result in a more representative sequence than the occurrence of an additional red.

In reality, of course, roulette is a random, non-evolving process, in which the chance of getting a red or a black will never depend on the past sequence. …

The gambler’s fallacy need not to be committed inside the casino only. Many of us commit it frequently by thinking that a small, random sample will tend to correct itself.

For example, assume that the average IQ at a specific country is known to be 100. And for the purposes of assessing intelligence at a specific district, we draw a random sample of 50 persons. The first person in our sample happens to have an IQ of 150. What would you expect the mean IQ to be for the whole sample?

The correct answer is (100*49 + 150*1)/50 = 101. Yet without knowing the correct answer it is tempting to say it is still 100 – the same as in the country as a whole.

… It is important to realize that the laws governed by chance are not guided by principles of equilibrium and the number of random outcomes in a sequence do not have a common balance. … In fact, deviations are not ‘corrected’ as a chance process unfolds, they are merely diluted.”

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