We evaluate moments of the completion time in the classical duration of play problem, equivalent to a symmetric random walk with absorbing endpoints on {-n, ,n} starting from x. We show that the rth cumulant of the absorption time has the form P r (n 2 ) - P r (x 2 ), where P r is a degree r polynomial, and evaluate P r for r = 1, ,6. Measured in arithmetic operations, our algorithm to compute P r has amortized cost comparable to the inversion of an r r matrix. We obtain similar results for unequal initial stakes, and under conditioning on a win by one player. The conditional results settle some open questions due to Beyer.