We consider some well-known families of two-player zero-sum perfect-information stochastic games played on finite directed graphs. Generalizing and unifying results of Liggett and Lippman, Zwick and Paterson, and Chatterjee and Henzinger, we show that the following tasks are polynomial-time (Turing) equivalent. – Solving stochastic parity games, – Solving simple stochastic games, – Solving stoc...