How abundant is the population of binary radio pulsars with black holes?

Using a 'scenario machine' we have carried out a population synthesis of radio pulsars with black hole binaries (BH+Psr) in the context of the most widespread assumptions concerning star mass loss during evolution, the mass ratio distribution of binary stars, the kick velocity and the envelope mass loss during collapse. Our purpose is to show that under any plausible parameters for the evolution scenario, the BH+Psr population should be abundant in the Galaxy. It is shown that in all models (including those evolved by Heger et al. and Woosley, Heger & Weaver), the expected number of black holes paired with radio pulsars is sufficient for such systems to be discovered within the next few years.