Tag Archive | "Gambler"


Gambler’s fallacy

The Gambler’s fallacy’, also known as “the Monte Carlo fallacy” or the “fallacy of the maturity of chance”s, is the belief that if deviations from expected behaviour are observed in repeated independent trials of some random process then these deviations are likely to be evened out by opposite deviations in the future. For example, if a fair coin is tossed repeatedly and tails comes up a larger number of times than is expected, a gambler may incorrectly believe that this means that heads is more likely in future tosses. Such an expectation could be mistakenly referred to as being “due”. This is an informal fallacy. It is also known colloquially as the “law of averages”.

The gambler’s fallacy implicitly involves an assertion of negative correlation between trials of the random process and therefore involves a denial of the exchangeability of outcomes of the random process.

The inverse gambler’s fallacy is the belief that an unlikely outcome of a random process (such as rolling double sixes on a pair of dice) implies that the process is likely to have occurred many times before reaching that outcome.

The reversal is also a fallacy, the reverse gambler’s fallacy, in which a gambler may instead decide that tails are more likely out of some mystical preconception that fate has thus far allowed for consistent results of tails; the false conclusion being, why change if odds favor tails? Again, the fallacy is the belief that the “universe” somehow carries a memory of past results which tend to favor or disfavor future outcomes.

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Neglect of probability

The “neglect of probability bias” is the tendency to disregard probabilities when making decisions which involve a degree of uncertainty. It is a simple way in which many people violate the normative rules for making decisions.

This isn’t the only kind of cognitive bias related to probability–others include “the gambler’s fallacy,” “the hindsight bias,” and “the neglect of prior base rates effect”–but this bias differs notably from those ones, as with this bias the person involved completely disregards probability when making his decision, instead of incorrectly applying probability.

An interesting study was done in 1993 which studied this bias. The study asked children the following question:

Susan and Jennifer are arguing about whether they should wear seat belts when they ride in a car. Susan says that you should. Jennifer says you shouldn’t… Jennifer says that she heard of an accident where a car fell into a lake and a woman was kept from getting out in time because of wearing her seat belt, and another accident where a seat belt kept someone from getting out of the car in time when there was a fire. What do you think about this?

One subject responded as below:

A: Well, in that case I don’t think you should wear a seat belt.
Q (interviewer): How do you know when that’s going to happen?
A: Like, just hope it doesn’t!
Q: So, should you or shouldn’t you wear seat belts?
A: Well, tell-you-the-truth we should wear seat belts.
Q: How come?
A: Just in case of an accident. You won’t get hurt as much as you will if you didn’t wear a seat belt.
Q: OK, well what about these kinds of things, when people get trapped?
A: I don’t think you should, in that case.

Here we can see that the subject completely disregards the probability of an accident happening versus the probability of getting hurt by the seat belt in making the decision. In a  normative model for this decision we would use expected-utility theory to decide which option would be most likely to maximize utility. This would involve weighing the changes in utility in each option by the probability that each option will occur, something the subject ignores.

Another subject responded to the same question:

A: If you have a long trip, you wear seat belts half way.
Q: Which is more likely?
A: That you’ll go flyin’ through the windshield.
Q: Doesn’t that mean you should wear them all the time?
A: No, it doesn’t mean that.
Q: How do you know if you’re gonna have one kind of accident or the other?
A: You don’t know. You just hope and pray that you don’t.

Here again you can see the disregard of probability in making the decision by the subject. He treats each possible outcome as equally likely.

It has been suggested that adults can suffer from this bias as well, especially when it comes to decisions like a medical decision under uncertainty. We see that this bias could make actors drastically violate expected-utility theory in their decision making, especially when a decision must be made in which one possible outcome has a much lower or higher utility but a small probability of occurring (e.g. in medical or gambling situations). In this aspect, the neglect of probability bias is similar to the neglect of prior base rates effect.

In another interesting example of near-total neglect of probability, it was discovered that an average person was willing to pay $7 to avoid a 1% chance of a painful electric shock, and $10—to avoid a 99% chance of the same shock. The suggestion is that probability is more likely to be neglected when the potential outcomes arouse strong emotion.

Posted in Decision-making and behavioral biasesComments (1)