In the author’s paper “Coupling and Mixing Times in Markov Chains” (RLIMS, 11, 1-
22, 2007) it was shown that it is very difficult to find explicit expressions for the
expected time to coupling in a general Markov chain. In this paper simple upper and
lower bounds are given for the expected time to coupling in a discrete time finite
Markov chain. Extensions to the bounds under additional restrictive conditions are also
given with detailed comparisons provided for two and three state chains
