(n.) the misguided belief that because something has happened less frequently than might be expected, it is now more likely to occur

Imagine a coin is tossed 10 times in a row, and every single time, bar none, it lands on heads. To some, that curious run of heads might make it appear that the coin landing on tails is now somehow ‘overdue’, and therefore somehow more likely to appear on the next flip—or, at least, sooner rather than later. That is the Monte Carlo fallacy.

Every toss of a coin of course yields a 50/50 chance of either heads of tails, of course, so with each flip taken in isolation, a run of ten heads doesn’t seem all that unusual, and certainly wouldn’t do anything to alter the odds of tails coming up next. But despite being so clearly misguided, the presumption behind the Monte Carlo fallacy is a common trait: humans are hard-wired to look for and appreciate patterns in streams of data, and to find any perceived imbalances worthy of note. And it’s that that led to this curious phenomenon—also known as the gambler’s fallacy, or the maturity of chances—earning itself a nickname that name-checks the gambling capital of Europe.

In August 1913, a game of roulette at a casino in Monte Carlo attracted the attention of a crowd of gamblers when the ball landed on black numbers 26 times in a row. The longer this streak of black numbers continued, the longer the game seemed to play up to the fallacy: surely, the gamblers started to feel, a red number was now overdue?

The fact that each spin of the roulette wheel, like each flip of a coin, has a roughly equal change of landing on red or black did not matter. The bets were placed, and as the run of black numbers went on, the bets grew larger and larger. Millions of francs were placed and lost as more and more players bought into the misguided feeling that this uncommon—but by no means impossible—run of black numbers had to be balanced out by a red number.

Eventually, a red number did appear and the run was broken. But by then, presumably the players had learned a very valuable and very expensive lesson.