Gambler's Fallacy/Monte Carlo Fallacy

Also known as the Monte Carlo Fallacy, the Gambler's Fallacy occurs when an individual erroneously believes that a certain random event is less likely or more likely, given a previous event or a series of events. This line of thinking is incorrect because past events do not change the probability that certain events will occur in the future.

This line of thinking in a Gambler's Fallacy/Monte Carlo Fallacy represents an inaccurate understanding of probability. This concept can apply to investing. Some investors liquidate a position after it has gone up after a long series of trading sessions. They do so because they erroneously believe that because of the string of successive gains, the position is now much more likely to decline.

For example, consider a series of 10 coin flips that have all landed with the "heads" side up. Under the Gambler's Fallacy, a person might predict that the next coin flip is more likely to land with the "tails" side up.

The likelihood of a fair coin turning up heads is always 50%. Each coin flip is an independent event, which means that any and all previous flips have no bearing on future flips. If before any coins were flipped a gambler were offered a chance to bet that 11 coin flips would result in 11 heads, the wise choice would be to turn it down because the probability of 11 coin flips resulting in 11 heads is extremely low. However, if offered the same bet with 10 flips having already produced 10 heads, the gambler would have a 50% chance of winning because the odds of the next one turning up heads is still 50%. The fallacy comes in believing that with 10 heads having already occurred, the 11th is now less likely.