This paper considers two-player zero-sum simultaneous stochastic games (CSGs) with reachability and safety objectives on graphs. While degenerate classes such as Markov decision processes and turn-based stochastic games can be solved using linear or quadratic programming, in practice, Value Iteration (VI) outperforms other approaches and is the most commonly implemented method. This practical performance makes VIs an attractive alternative to standard theoretical solutions using existential real number theory for CSGs. Existing VIs start with an approximation of the target value for each state and iteratively update it, traditionally terminating when two successive approximations approach ε-approximation. However, these termination criteria lack guarantees regarding the accuracy of the approximation. In this paper, we present a bounded (interval) VI for CSGs that compensates for over-approximation sequences that converge to the standard VI and terminates when both over- and under-approximation approaches ε-approximation.
