The paper examines the gambler's fallacy and the hot-hand fallacy, showing how individuals with the gambler's fallacy misinterpret random sequences, leading to incorrect predictions and actions. The model considers an individual observing a sequence of signals that depend on an unobservable state. The gambler's fallacy leads the individual to exaggerate the magnitude of changes in the state but underestimate their duration. When the state is constant (i.i.d. signals), the individual may predict that streaks of similar signals will continue, a hot-hand fallacy. When signals are serially correlated, the individual typically under-reacts to short streaks, over-reacts to longer ones, and under-reacts to very long ones. The paper explores applications, showing that investors may move assets too much in and out of mutual funds and exaggerate the value of financial information and expertise. The model is applied to investor behavior, showing that investors may over-trade and overpay for financial information. The paper also discusses the implications of the model for financial decisions, showing that the hot-hand fallacy can arise in i.i.d. settings if individuals attribute non-zero prior probability that the state is time-varying. The hot-hand fallacy always arises in non-i.i.d. settings, in the form of over-reaction relative to the rational benchmark. The paper concludes that the model provides a framework for understanding the hot-hand fallacy and its implications for financial decisions.The paper examines the gambler's fallacy and the hot-hand fallacy, showing how individuals with the gambler's fallacy misinterpret random sequences, leading to incorrect predictions and actions. The model considers an individual observing a sequence of signals that depend on an unobservable state. The gambler's fallacy leads the individual to exaggerate the magnitude of changes in the state but underestimate their duration. When the state is constant (i.i.d. signals), the individual may predict that streaks of similar signals will continue, a hot-hand fallacy. When signals are serially correlated, the individual typically under-reacts to short streaks, over-reacts to longer ones, and under-reacts to very long ones. The paper explores applications, showing that investors may move assets too much in and out of mutual funds and exaggerate the value of financial information and expertise. The model is applied to investor behavior, showing that investors may over-trade and overpay for financial information. The paper also discusses the implications of the model for financial decisions, showing that the hot-hand fallacy can arise in i.i.d. settings if individuals attribute non-zero prior probability that the state is time-varying. The hot-hand fallacy always arises in non-i.i.d. settings, in the form of over-reaction relative to the rational benchmark. The paper concludes that the model provides a framework for understanding the hot-hand fallacy and its implications for financial decisions.