On the Mabinogion urn model

In this paper we discuss the Mabinogion urn model introduced by Williams (1991). Therein he describes an optimal control problem where the objective is to maximize the expected final number of objects of one kind in the Mabinogion urn model. Our main contribution is formulae for the expected time to absorption and its asymptotic behaviour in the optimally controlled process. We also present results for the noncontrolled Mabinogion urn process and briefly analyze other strategies that become superior if a certain discount factor is included.