The titular characters of Tom Stoppard's film "Rosencrantz and Guildenstern Are Dead" begin the film baffled, confused and finally frightened as each of 157 consecutive flips of a coin comes up heads. Guildenstern's explanations of this phenomenon range from time loops to "a spectacular vindication of the principle that each individual coin, spun individually, is as likely to come down heads as tails ... "
Evolution wired humans to see patterns, and our ability to properly process that urge seems to short-circuit the longer we spend gambling. We can rationally accept that independent events like coin flips keep the same odds no matter how many times you perform them. But we also view those events, less rationally, as streaks, making false mental correlations between randomized events. Viewing the past as prelude, we keep thinking the next flip ought to be tails.
Statisticians call this the gambler's fallacy, aka the Monte Carlo fallacy, after a particularly illustrative example occurring in that famed Monaco resort town. During the summer of 1913, bettors watched in increasing amazement as a casino's roulette wheel landed on black 26 times in a row. Inflamed by the certainty that red was "due," the punters kept plunking down their chips. The casino made a mint [sources: Lehrer; Oppenheimer and Monin; Vogt].