Martingales at the Casino

For more than two centuries, various betting strategies have been called martingales. What makes a betting strategy a martingale? Why have martingales been so popular among gamblers and casinos? The decade after the French revolution marks the beginning of a written record that casts some light on these questions. This record centers on Trente et Quarante, the game that drove the profits of the gaming spas of northwestern Europe and the casinos of Paris before the invention of Roulette in its modern form. Players in Trente et Quarante made successive even-money bets on red or black. Martingaling initially meant doubling one’s bet to recover from a loss. By the beginning of the 19th century, any betting strategy could be called a martingale. A review of this history will help us understand how seductive martingales can be. We still live with the perils of this seduction, inside and outside the casino.