  The expected distributions of eclipse-depth versus period for eclipsing
binaries of different luminosities are derived from large-scale population
synthesis experiments. Using the rapid Hurley et al. BSE binary evolution code,
we have evolved several hundred million binaries, starting from various simple
input distributions of masses and orbit-sizes. Eclipse probabilities and
predicted distributions over period and eclipse-depth (P/dm) are given in a
number of main-sequence intervals, from O-stars to brown dwarfs. The comparison
between theory and Hipparcos observations shows that a standard (Duquennoy &
Mayor) input distribution of orbit-sizes (a) gives reasonable numbers and
P/dm-distributions, as long as the mass-ratio distribution is also close to the
observed flat ones. A random pairing model, where the primary and secondary are
drawn independently from the same IMF, gives more than an order of magnitude
too few eclipsing binaries on the upper main sequence. For a set of eclipsing
OB-systems in the LMC, the observed period-distribution is different from the
theoretical one, and the input orbit distributions and/or the evolutionary
environment in LMC has to be different compared with the Galaxy. A natural
application of these methods are estimates of the numbers and properties of
eclipsing binaries observed by large-scale surveys like Gaia.
