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Simple stochastic games are turn-based 2½-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three known classes of algorithms-value iteration, strategy iteration and quadratic programming-both theoretically and practically. Further, we suggest several improvements for all algorithms, including the first approach based on quadratic programming that avoids transforming the stochastic game to a stopping one. Our extensive experiments show that these improvements can lead to significant speed-ups. We implemented all algorithms in PRISMgames 3.0, thereby providing the first implementation of quadratic programming for solving simple stochastic games. * This research was funded in part by the German Research Foundation (DFG) projects 383882557 Statistical Unbounded Verification (SUV) and 427755713 Group-By Objectives in Probabilistic Verification (GOPro).