martingales

A martingale is a mathematical model of a fair game, where future outcomes are unpredictable based on past results. In essence, the expected value of the next outcome equals the current value, meaning there’s no guaranteed profit or loss over time. For example, in betting, if you have a fair coin toss game, your expected winnings after any number of rounds remain the same as your current amount, regardless of previous results. Martingales are used in probability theory to study situations with no inherent advantage, emphasizing the idea that future changes cannot be predicted from past data alone.