Join us for an accessible deep dive into martingales—the math behind 'fair games' and the random world around us. Trace their origins in gambling, see how a simple coin flip leads to powerful tools, and explore their surprising applications in finance, statistics, budgeting, and ecology. We'll unpack the optional stopping theorem with gut-level intuition and real-world examples, and show why martingale theory helps us understand risk, uncertainty, and the limits of clever stopping rules.
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