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We present new algorithms for determining optimal strategies for two-player games with probabilistic moves and reachability winning conditions. Such games, known as simple stochastic games, were extensively studied by A.Condon [2, 3] . Many interesting problems, including parity games and hence also mu-calculus model checking, can be reduced to simple stochastic games. It is an open problem, whether simple stochastic games can be solved in polynomial time. Our algorithms determine the optimaldoi:10.1016/j.entcs.2004.07.008 fatcat:tthbkdjtanhbjigtqnrqhdhqoi