  In this paper we discuss the Mabinogion urn model introduced by D. Williams
in Probability with Martingales (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 formulas for
the expected time to absorption and its asymptotic behavior in the optimally
controlled process. We also present results for the non-controlled Mabinogion
urn process and briefly analyze other strategies that become superior if a
certain discount factor is included.
