Noisy Monte Carlo revisited

We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. Our algorithm, simplified from that of L. Lin et al. hep-lat/9905033, avoids the computation of almost all non-leading terms. We illustrate its use by simulating SU(2) lattice gauge theory with a 5-loop action, and discuss further applications to full QCD.