Gambler's Fallacy: Overview and Examples

What Is the Gambler's Fallacy?

The gambler's fallacy, also known as the Monte Carlo fallacy, occurs when an individual erroneously believes that a certain random event is less likely or more likely to happen based on the outcome of a previous event or series of events. This line of thinking is incorrect, since past events do not change the probability that certain events will occur in the future.

Understanding the Gambler's Fallacy

If a series of events are random and independent from one another, then by definition the outcome of one or more events cannot influence or predict the outcome of the next event. The gambler's fallacy consists of misjudging whether a series of events are truly random and independent, and wrongly concluding that the outcome of the next event will be the opposite of the outcomes of the preceding series of events.

For example, consider a series of 10 coin flips that have all landed with the "heads" side up. A person might predict that the next coin flip is more likely to land with the "tails" side up. However, if the person knows that this is a fair coin with a 50/50 chance of landing on either side and that the coin flips are not systematically related to one another by some mechanism then they are committing the gambler's fallacy.

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.

Examples of the Gambler's Fallacy

The most famous example of gambler's fallacy occurred at the Monte Carlo casino in Las Vegas in 1913. The roulette wheel's ball had fallen on black several times in a row. This led people to believe that it would fall on red soon and they started pushing their chips, betting that the ball would fall in a red square on the next roulette wheel turn. The ball fell on the red square after 27 turns. Accounts state that millions of dollars had been lost by then.

Gambler's fallacy or Monte Carlo fallacy represents an inaccurate understanding of probability and can equally be applied 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.