We show that in perfect-information stochastic parity games with a finite state space both players have optimal pure positional strategies. Contrary to the recent proofs of this fact by K. Chatterejee, M. Jurdziński, T.A. Henzinger [2] and A.K. McIver, C.C. Morgan [14] the proof given in this paper proceeds by a straightforward induction on the number of outgoing transitions available to one of...

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