  Computer simulations of photon transport through an absorbing and/or
scattering medium form an important research tool in astrophysics. Nearly all
software codes performing such simulations for three-dimensional geometries
employ the Monte Carlo radiative transfer method, including various forms of
biasing to accelerate the calculations. Because of the probabilistic nature of
the Monte Carlo technique, the outputs are inherently noisy, but it is often
assumed that the average values provide the physically correct result. We show
that this assumption is not always justified. Specifically, we study the
intensity of radiation penetrating an infinite, uniform slab of material that
absorbs and scatters the radiation with equal probability. The basic Monte
Carlo radiative transfer method, without any biasing mechanisms, starts to
break down for transverse optical depths above ~20 because so few of the
simulated photon packets reach the other side of the slab. When including
biasing techniques such as absorption/scattering splitting and path length
stretching, the simulated photon packets do reach the other side of the slab
but the biased weights do not necessarily add up to the correct solution. While
the noise levels seem to be acceptable, the average values sometimes severely
underestimate the correct solution. Detecting these anomalies requires the
judicious application of statistical tests, similar to those used in the field
of nuclear particle transport, possibly in combination with convergence tests
employing consecutively larger numbers of photon packets. In any case, for
transverse optical depths above ~75 the Monte Carlo methods used in our study
fail to solve the one-dimensional slab problem, implying the need for
approximations such as a modified random walk.
