Optimal Stopping for the Urn Problem Based on Success Runs
Abdullah-AI-Kafi Majumdar, Minoru Sakaguchi · Journal of Information and Optimization Sciences · 1983
In this paper we deal with an optimal stopping problem for success runs where random drawings are made without replacement from an urn containing predetermined numbers of “plus” and “cancel” balls. Our results extend the works in Boyce [2], [3], on the need to incorporate success runs in the analysis of optimal stopping problems. Here the fundamental inequalities which are intuitively plausible are theoretically proved and an optimal stopping strategy is derived. The table of the values of the urn containing plus and cancel balls both up to 100 is given. For the urn with 87 plus and 13 cancel balls, the optimal play would give an expected score of 164. Also the extension to the random-urn case is considered and an algorithm to obtain an optimal stopping strategy is given.