An urn contains a known number of balls, an unknown number $R$ of which are red. Sequential sampling with replacement is possible and cost is proportional to sample size. The objective is to estimate $R$ with 0-1 loss, given that a priori $R$ has a discrete uniform distribution. It is shown that optimal stopping regions may be disconnected and composed of islands and peninsulas.
"Optimal Stopping Regions with Islands and Peninsulas." Ann. Statist. 10 (2) 634 - 636, June, 1982. https://doi.org/10.1214/aos/1176345806