The gambler's fallacy
Believing that 'runs' occur to statistically independent phenomena such as roulette wheel spins.
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. So whilst there may be a very small chance that heads will come up 20 times in a row if you flip a coin, the chances of heads coming up on each individual flip remain 50/50, and aren't influenced by what happened before.
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 up. Suffering an economic form of natural selection with this thinking, he soon lost all of his savings.