Gambler's Fallacy
generalThe mistaken belief that past random events affect the probability of future random events.
Key Takeaways
- 1Past random events don't affect future probabilities
- 2Each spin/roll/draw is independent
- 3The gambler's fallacy costs money in every form of gambling
- 4No number, color, or outcome is ever 'due'
What is the Gambler's Fallacy?
The Gambler's Fallacy is the incorrect belief that if something happens more frequently than normal during a given period, it will happen less frequently in the future (or vice versa). It's one of the most common and costly cognitive biases in gambling.
Classic Example
A roulette wheel lands on red 10 times in a row. The gambler's fallacy says "black is due!" But the probability of black on the next spin is still exactly 47.37% (18/38 on a double-zero wheel). The wheel has no memory.
Why It's Wrong
Each spin, roll, or draw is an independent event. The probability is determined by the physical properties of the game, not by what happened before. A coin doesn't "know" it landed heads 5 times in a row.
Where It Costs You Money
- Lottery — "Number 7 hasn't hit in 30 draws, it's due!" (It's not.)
- Roulette — Chasing colors or numbers based on history
- Sports betting — "This team is due for a win" after a losing streak
- Slots — "This machine is due to pay out"
The Math
For independent events:
- P(red on spin 11 | 10 reds in a row) = 47.37%
- P(red on spin 11 | 10 blacks in a row) = 47.37%
- P(red on spin 11 | any previous sequence) = 47.37%
The past is irrelevant. Always.