Monte Carlo Fallacy

The Monte Carlo fallacy — also called the gambler's fallacy — is the belief that past independent outcomes change the probability of future ones. A coin that landed heads five times is not "due" for tails; the next flip is still 50/50. A roulette wheel that hit red ten times does not make black more likely on the next spin. Each trial is independent. The fallacy is named after a 1913 incident at the Monte Carlo casino where black came up 26 times in a row on a roulette wheel; bettors lost heavily believing red was "due." The wheel had no memory. The odds did not shift.

The intuition that "things even out" is strong. We see short runs and expect reversion. In truly random processes, reversion applies to the distribution over many trials, not to the next single trial. The law of large numbers says that as the number of trials grows, the sample proportion converges to the true probability. It does not say that a single outcome compensates for prior outcomes. After 26 blacks, the probability of the next spin being black is still roughly 1/2 (or 18/37 on a European wheel). The run was rare; the next spin is not.

Where the fallacy bites: interpreting streaks as predictive, doubling down after losses because "I'm due," or avoiding a bet because "it just hit." In survival and protection contexts, it appears when people assume a threat that has not materialised recently is "less likely" now, or when they treat past luck as a buffer. In deciding and judging, it distorts allocation (e.g. shifting capital or attention based on recent wins or losses) and evaluation (e.g. firing a strategy after a short bad run that is within normal variance). The corrective: treat each decision under uncertainty as a fresh draw from the same distribution unless you have evidence the process has changed.