  We study strong electron tunneling in the single-electron box, a small
metallic island coupled to an electrode by a tunnel junction, by means of
quantum Monte Carlo simulations. We obtain results, at arbitrary tunneling
strength, for the free energy of this system and the average charge on the
island as a function of an external bias voltage. In much of the parameter
range an extrapolation to the ground state is possible. Our results for the
effective charging energy for strong tunneling are compared to earlier -- in
part controversial -- theoretical predictions and Monte Carlo simulations.
