The gambler’s fallacy is the belief that random independent events “even out” over time. In Monaco in August 1913, this belief cost casino gamblers millions because of an extraordinary streak at a roulette table.
When an event – like the roll of the dice – is truly random, the outcomes in the past do not affect those in the future. But that doesn’t stop people believing that they will. Especially gamblers.
Here’s an example: you have three daughters, and your partner is pregnant. What’s the chance that your fourth child will be a son? The answer is 50% – the fact that you’ve had three daughters already doesn’t have any impact on the chances here.
The beginning of the brilliant play (and film) Rosencrantz and Guildenstern are Dead has the titular characters betting on the flip of a coin. It comes up heads ninety-two times in a row. Improbable, but completely consistent with how probability works.
August 18, 1913. Monte Carlo Casino in Monaco. The roulette wheel. Black has come up ten times in a row. Surely, the gamblers think, red will come up soon, so they bet heavily on red. Black comes up an eleventh time. Lots of money is lost. But it cannot come up twelve times, can it? Another round of betting… and black comes up again. And again. And again. In total, black came up 26 times and the poor gamblers lost millions of French francs.