The Gambler's Fallacy

The Gambler's Fallacy

The Gambler's Fallacy is a powerful and deceptive false belief — if this fallacy were to suddenly disappear, many gambling casinos would go out of business.

Here's how it works — let's say we flip a fair coin, one that has an equal chance of coming up heads or tails. By definition, the probability for heads on the first flip is 0.5 or ½. Now think about these questions:

* If you have just gotten one heads result, what is the probability for heads on the next flip?
* If you have just gotten one tails result, what is the probability for heads on the next flip?
* If you have just gotten eight heads results in a row, what is the probability for heads on the next flip?

Contrary to a widely held belief, the answer to all the above questions is ... 0.5 or ½. Regardless of what has happened before, the probability for heads in the next coin flip is exactly the same.

This fallacy has its roots in confusion between the probability of a sequence of events and the probability of an event separate from the sequence in which it appears:

* The probability of tossing eight heads in a row is 2-8, or 1/256.
* But during the eight coin tosses, the probability of each new heads result considered separately is ½.

Casinos make vast sums of money from people who think, "I've lost repeatedly at this (roulette wheel / slot machine / card game), therefore my probability of winning must be increasing, so no only should I keep playing, but I should increase my bets." But in fact, a past winning or losing streak cannot change one's future odds of winning.

I've often wondered whether an education in math might cure the Gambler's Fallacy.

The Gambler's Fallacy