Gambler’s Fallacy
Past random outcomes do not change future independent ones.
Key idea
Past random outcomes do not change future independent ones.
In depth
Independent events have no memory: after five heads, the next flip is still 50%. Other myths: the hot hand and "law of averages" for short runs, and neglect of base rates.
Worked example
Roulette landing on red 8 times does not make black more likely on the next spin.
Real-world uses
- Explaining why a run of heads does not make tails more likely next time
Common mistake
Believing that randomness must "even out" in the short term.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Gambler’s Fallacy?
Past random outcomes do not change future independent ones. It is a topic at the intermediate level in Probability & Statistics.
Where is Gambler’s Fallacy used in real life?
Real-world examples: Explaining why a run of heads does not make tails more likely next time.
What should I learn before Gambler’s Fallacy?
Make sure you are comfortable with Entropy and Information, the previous topic in Probability & Statistics.
What is a common mistake with Gambler’s Fallacy?
Believing that randomness must "even out" in the short term.
How can I practise Gambler’s Fallacy?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Gambler’s Fallacy?
Move on to Birthday Problem next.
Related intermediate topics in Probability & Statistics
- Collecting Data and Sampling – Surveys, experiments and random sampling.
- Bias in Sampling – Systematic errors that make samples unrepresentative.
- Histograms – Bars showing frequency of numerical intervals.
- Dot Plots and Stem-and-Leaf Plots – Show the shape of small datasets.
- Mean – The arithmetic average.
- Median – The middle value of an ordered list.