Using Monte Carlo simulation of the modem scenario of the evolution of
binary systems (the '' Scenario Machine''), we calculated the number
of binary radiopulsars with black holes and some their observational p
roperties. The comparison with observations imposes some restrictions
on the minimal mass of the star-progenitor collapsing to a black hole,
M(cr), and the fraction of the mass that collapses to the black hole,
k(bh) = M(bh)/M, the probable values being M(cr) almost-equal-to 35
M. and k(bh) almost-equal-to 0.3. Our calculations show that binary ra
diopulsars on eccentric orbits around black holes must be discovered i
n the near future.