  Using a recently introduced algorithm for simulating percolation in
microcanonical (fixed-occupancy) samples, we study the convergence with
increasing system size of a number of estimates for the percolation threshold
for an open system with a square boundary, specifically for site percolation on
a square lattice. We show that the convergence of the so-called
"average-probability" estimate is described by a non-trivial
correction-to-scaling exponent as predicted previously, and measure the value
of this exponent to be 0.90(2). For the "median" and "cell-to-cell" estimates
of the percolation threshold we verify that convergence does not depend on this
exponent, having instead a slightly faster convergence with a trivial analytic
leading exponent.
