Gambler's Fallacy

The Gambler’s Fallacy: people expect that deviations from the expected occur, they will be evened out in the future.

On August 18th, 1913, at the casino in Monte Carlo, black came up a record twenty-six times in succession [in roulette]. … [There] was a near panicky-rush to bet on red, beggining about the time black had come up a phenomenal fifteen times.” — Huff and Geis, How to take a chance

Probability of 26-consecutive blacks: $1/2^{26}=1/67,108,865$

Probability of 26-consecutive blacks when the previous 25 rolls where black: $1/2$, because the events are independent.