This paper presents the results of our computational investigation into algorithms for Simple Stochastic Games (SSGs), motivated by their applications in AI planning, logic synthesis, and theoretical computer science. Our study involves implementing several algorithms for solving SSGs, including variations where stable strategies are determined through both linear programming and a naive approach. We assess these algorithms using random inputs as well as challenging cases identified through experimentation. We are interested in identifying difficult inputs for the Hoffman-Karp algorithm, which performs well in practice. Despite extensive searches of the input space, we have not encountered a case where the Hoffman-Karp algorithm requires more than a linear number of iterations. This observation is noteworthy, as it challenges the general belief that the algorithm performs poorly in practice. In instances where the algorithm’s performance is linear, the otherwise faster algorithms prove inefficient, and the naive algorithms outperform their linear programming counterparts.