Gambler's Fallacy

Definition

Let:

• $E_1,E_2,\dots ,E_n$ : A sequence of independent random events
• $P(E_{n+1})$ : The probability of the next event

Then an argument commits the Gambler’s Fallacy if and only if it asserts:

$$P(E_{n+1}\mid E_1,E_2,\dots ,E_n)\ne P(E_{n+1})$$

Interpretation

Past independent events do not affect future probabilities. Each event is independent.