  While value iteration (VI) is a standard solution approach to simple
stochastic games (SSGs), it suffered from the lack of a stopping criterion.
Recently, several solutions have appeared, among them also "optimistic" VI
(OVI). However, OVI is applicable only to one-player SSGs with no end
components. We lift these two assumptions, making it available to general SSGs.
Further, we utilize the idea in the context of topological VI, where we provide
an efficient precise solution. In order to compare the new algorithms with the
state of the art, we use not only the standard benchmarks, but we also design a
random generator of SSGs, which can be biased towards various types of models,
aiding in understanding the advantages of different algorithms on SSGs.
