The Duke-of-York gambit (Pullum 1976) involves derivations of the form A->B->A, where underlying /A/ passes through an intermediate stage B before returning to A at the surface. Optimality Theory (Prince and Smolensky 1993) has significant implications for the Duke of York gambit. Furthermore, attested and unattested Duke-of-York cases have implications for the analysis of opacity in Optimality Theory using sympathy (McCarthy 1998, to appear). A key idea pursued in this paper is that derivations must be cumulative, and a measure of cumulativity is incorporated into sympathy theory.