Martingale theory is a concept in probability and statistics that describes a fair game where the expected future value of a process is equal to its current value. In simpler terms, it suggests that, in a fair betting scenario, knowing the past outcomes does not help predict future results. This principle is often applied in various fields, including finance and gambling. In finance, martingale theory can be used to model stock prices and other assets, suggesting that price movements are random and unpredictable. This idea is closely related to the random walk theory, which posits that stock prices follow a random path, making it difficult to consistently outperform the market.