Many verification, planning, and control problems can be modeled as games played on state-transition graphs by one or two players whose conflicting goals are to form a path in the graph. The focus here is on simple stochastic parity games, that is, two-player games with turn-based probabilistic transitions and ω-regular objectives formalized as parity (Rabin chain) winning conditions. An efficient translation from simple stochastic parity games to nonstochastic parity games is given. As many algorithms are known for solving the latter, the translation yields efficient algorithms for computing the states of a simple stochastic parity