Memoryless Strategies in Stochastic Reachability Games

We study concurrent stochastic reachability games played on finite graphs. Two players, Max and Min, seek respectively to maximize and minimize the probability of reaching a set of target states. We prove that Max has a memoryless strategy that is optimal from all states that have an optimal strategy. Our construction provides an alternative proof of this result by Bordais, Bouyer and Le Roux, and strengthens it, as we allow Max's action sets to be countably infinite.