  The best algorithm so far for solving Simple Stochastic Games is Ludwig's
randomized algorithm which works in expected $2^{O(\sqrt{n})}$ time. We first
give a simpler iterative variant of this algorithm, using Bland's rule from the
simplex algorithm, which uses exponentially less random bits than Ludwig's
version. Then, we show how to adapt this method to the algorithm of Gimbert and
Horn whose worst case complexity is $O(k!)$, where $k$ is the number of random
nodes. Our algorithm has an expected running time of $2^{O(k)}$, and works for
general random nodes with arbitrary outdegree and probability distribution on
outgoing arcs.
