  Gravitational microlensing is a key probe of the nature of dark matter and
its distribution on the smallest scales. For many practical purposes,
confronting theory to observation requires to model the probability that a
light source is highly amplified by many-lens systems. This article reviews
four simple analytic models of the amplification probability distribution,
based on different approximations: (i) the strongest-lens model; (ii) the
multiplicative model, where the total amplification is assumed to be the
product of all the lenses' individual amplifications; (iii) a hybrid version of
the previous two; and (iv) an empirical fitting function. In particular, a new
derivation of the multiplicative amplification distribution is proposed,
thereby correcting errors in the literature. Finally, the accuracy of these
models is tested against ray-shooting simulations. They all produce excellent
results as long as lenses are light and rare (low optical depth); however, for
larger optical depths, none of them succeeds in capturing the relevant features
of the amplification distribution. This conclusion emphasizes the crucial role
of lens-lens coupling at large optical depths.
