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Abstract:   In the realm of statistics and economics, there are several important problems that can be described as stopping problems; a kind of decision problem where an actor must observe some sequence of random variables, and based on observations of those variables implement a stopping rule (often gaining some reward based on observations). The gold standard for "solving" these stopping problems is providing a stopping rule for maximizing expected gains or minimizing expected losses, but such a stopping rule need not be the "best" rule depending on context. In this talk we will introduce stopping problems by way of a classical example of coin flipping, and explore the role of experimental mathematics in the construction of a family of stopping rules for the problem of Shepp's Urn.