A stochastic graph game is played by two players on a game graph with probabilistic transitions. We consider stochastic graph
games with ω-regular winning conditions specified as parity objectives. These games lie in NP ∩ coNP. We present a strategy improvement
algorithm for stochastic parity games; this is the first non-brute-force algorithm for solving these games. From the strategy
improvement algorithm we obtain a randomized subexponential-time algorithm to solve such games.