Errata for: A subexponential lower bound for the Random Facet algorithm for Parity Games

In Friedmann, Hansen, and Zwick (2011) we claimed that the expected number of pivoting steps performed by the Random-Facet algorithm of Kalai and of Matoušek, Sharir, and Welzl is equal to the expected number of pivoting steps performed by Random-Facet∗, a variant of Random-Facet that bases its random decisions on one random permutation. We then obtained a lower bound on the expected number of pivoting steps performed by Random-Facet∗ and claimed that the same lower bound holds also for Random-Facet. Unfortunately, the claim that the expected numbers of steps performed by Random-Facet and Random-Facet∗ are the same is false. We provide here simple examples that show that the expected numbers of steps performed by the two algorithms are not the same.