Solving Stochastic B\"uchi Games on Infinite Arenas with a Finite Attractor

We consider games played on an infinite probabilistic arena where the first player aims at satisfying generalized B"uchi objectives almost surely, i.e., with probability one. We provide a fixpoint characterization of the winning sets and associated winning strategies in the case where the arena satisfies the finite-attractor property. From this we directly deduce the decidability of these games on probabilistic lossy channel systems.