Abstract

In its simplest form, the Robin Hood game is described by the following urn scheme: every day the Sheriff of Nottingham puts s balls in an urn. Then Robin chooses r (r s) balls to remove from the urn. Robin's goal is to remove balls in such a way that none of them are left in the urn indefinitely. Let T-n be the random time that is required for Robin to take out all s . n balls put in the urn during the first n days. Our main result is a limit theorem for Tn if Robin selects the balls uniformly at random. Namely, we show that the random variable T-n . n(-s/r) converges in law to a Frechet distribution as n goes to infinity. (C) 2019 Elsevier B.V. All rights reserved.