  I present a generalization of the Newman-Ziff algorithm, a standard technique
in numerical percolation, to the random cluster model. The new method is
straightfoward to implement, works for real $q>0$, and is completely free of
the critical slowdown problem. By using the method to sample the critical
polynomial, accurate estimates of Potts critical points can be found using
relatively small lattice sizes. Furthermore, results for all values of $q$ can
be found at once within a single simulation. I demonstrate its utility here by
computing critical points for non-integer values of $q$ on the square lattice
to compare with the exact solution, and on the non-planar square matching
lattice.
