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A Note on Optimal Stopping for Success Runs
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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The following model is considered by Starr 1972 At most n tosses of a coin, having a constant probability p of coming up heads, are made. After each toss one has the option of either stopping and receiving an amount equal to the length of the terminal run of heads that is, if one was on a streak of k heads in the last k tosses, then one could stop and receive k, or of paying an amount c and tossing the coin again. When n tosses have already been made, one must stop. The purpose of this note is to point out that with a simple modification the above problem fits the framework in which a one-stage look ahead policy is optimal.
APPROVED FOR PUBLIC RELEASE