parameters: the cost of a single search, the probability of finding the object by a single search if the object is there, and the probability that the object is there. A searcher looks for the object. They know the a priori probabilities at the beginning and update them by Bayes’ law after each (unsuccessful) attempt. The problem of finding the object in minimal expected cost is a classical problem solved by David Blackwell. Surprisingly, the optimal policy is easy to describe: at each stage look into the location which maximizes . This is actually a special case of the Gittins index. See also References Stone, Lawrence D., The Theory of Optimal Search, published by the Operations Research Society of America, 1975 Stone, Lawrence D., In Search of Air France Flight 447. Institute of Operations Research and the Management Sciences, 2011. https://www.informs.org/ORMS-Today/Public-Articles/August-Volume-38-Number-4/In-Search-of-Air-France-Flight-447 Iida, Koji., Studies on the Optimal Search Plan, Vol. 70, Lecture Notes in Statistics, Springer-Verlag, 1992. De Groot, Morris H., Optimal Statistical Decisions, Wiley Classics Library, 2004. Richardson, Henry R; and Stone, Lawrence D. Operations Analysis during the underwater search for Scorpion. Naval Research Logistics Quarterly, June 1971, Vol. 18, Number 2. Office of Naval Research. Stone, Lawrence D. Search for the SS Central America: Mathematical Treasure Hunting. Technical Report, Metron Inc. Reston, Virginia. Koopman, B.O. Search and Screening, Operations Research Evaluation Group Report 56, Center for Naval Analyses, Alexandria, Virginia. 1946. Richardson, Henry R; and Discenza, J.H. The United States Coast Guard computer-assisted search planning system (CASP). Naval Research Logistics Quarterly. Vol. 27 number 4. pp. 659–680. 1980. Ross, Sheldon M., An Introduction to Stochastic Dynamic Programming, Academic Press. 1983. Search theory Search algorithms Operations research Search procedures