The Gambler's Fallacy
The Fallacy
Believing that 'runs' occur to statistically independent phenomena such as roulette wheel spins.
Why it's wrong
This commonly believed fallacy can be said to have helped create an entire city in the desert of Nevada USA. Though the overall odds of a 'big run' happening may be low, each spin of the wheel is itself entirely independent from the last.
Example
Red had come up six times in a row on the roulette wheel, so Greg knew that it was close to certain that black would be next. Suffering an economic form of natural selection with this thinking, he soon lost all of his savings.