# The Gambler's Fallacy: Key Examples and Impact

## What Is the Gambler's Fallacy?

Often called the Monte Carlo fallacy, the gambler's fallacy is the incorrect belief that past outcomes affect future ones, despite each event being independent. This misunderstanding is prevalent in gambling and investing, where individuals wrongly predict outcomes based on previous results.

### Key Takeaways

*   The gambler's fallacy incorrectly assumes future random events are influenced by past events.
*   Each event is independent, making past outcomes irrelevant to future probabilities.
*   Traders and investors often fall for this fallacy by predicting market trends based on recent outcomes.
*   A notable historic instance of the fallacy was observed in 1913 at the Casino de Monte-Carlo.
*   Avoiding the gambler's fallacy involves using independent research and not relying on past events to predict future ones.

## How the Gambler’s Fallacy Distorts Probability Perception

When events are independent and random, the outcome of one cannot predict or influence the next. The gambler's fallacy involves mistakenly believing that the next event's outcome will oppose previous events, ignoring their randomness and independence.

### Coin Flip Example of the Gambler's Fallacy

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 falling prey to the gambler's fallacy with their predictions.

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](https://www.investopedia.com/terms/o/objective-probability.asp) 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 is believing that with 10 heads having already occurred, an 11th heads up is now less likely.

> **Fast Fact**
>
> Traders aware of the gambler's fallacy can try to avoid it by strictly following a trading system of their own design that has specific buy and sell signals and is based on independent research. They can track their own behavior before and after trades for review and analysis later.

## Examples of the Gambler's Fallacy

People bet heavily on red, believing it was due next. However, red appeared only after 26 turns, resulting in huge losses.

The gambler's fallacy reflects a flawed grasp of probability and can also relate to investing. Some investors sell after a series of gains, wrongly thinking that the previous rise means a decline is coming.

## How Far Back Does the Gambler's Fallacy Go?

Pierre-Simon Laplace, a French mathematician who lived over 200 years ago, wrote about the behavior in his "Philosophical Essay on Probabilities."

## What Is the Cause of the Gambler's Fallacy?

The gambler's fallacy is a behavioral issue primarily derived from the belief in small numbers. People erroneously believe that small sample sets are always representative of larger populations or outcomes.

## How Do You Avoid the Gambler's Fallacy?

In the area of trading and investing, individuals can avoid the gambler's fallacy by letting go of the belief that previous occurrences are representative of future occurrences. To do this, traders and investors need to use independent research, be up to date on all facts, figures, and strategies, track trades and outcomes, and ask for feedback.

## The Bottom Line

The gambler's fallacy, also known as the Monte Carlo fallacy, is the erroneous belief that the likelihood of a random event is influenced by previous outcomes. This misconception can lead individuals, including traders and investors, to make poor decisions based on perceived patterns that do not exist.

Understanding that each event is independent and that past occurrences do not impact future probabilities is crucial. By employing independent research and adhering to well-designed trading strategies, individuals can avoid this common pitfall and make more informed financial decisions.

> **Article Sources**
>
> 1.  University of Wisconsin. "[The Gambler's Fallacy: On the Danger of Misunderstanding Simple Probabilities](https://online210.psych.wisc.edu/wp-content/uploads/PSY-210_Unit_Materials/PSY-210_Unit06_Materials/Effectivology_GamblersFallacy_NoDate.pdf)."
>     
> 2.  University of Wisconsin. "[The Gambler's Fallacy: On the Danger of Misunderstanding Simple Probabilities](https://online210.psych.wisc.edu/wp-content/uploads/PSY-210_Unit_Materials/PSY-210_Unit06_Materials/Effectivology_GamblersFallacy_NoDate.pdf)," Page 3.
>     
> 3.  American Statistical Association, Chance. "[The Mathematical Anatomy of the Gambler's Fallacy](https://chance.amstat.org/2022/02/gamblers-fallacy/)."