Black Hole observations - The Bet and BH-PSRs
Further, I bet (with no stakes) that the system will probably be found in a globular cluster (ah, but which one, that I'd like to figure out). Although the field (ie disk of the Milky Way) is a fair bet too.
For a black hole-pulsar system to be found in the galaxy, it has to be formed as a binary, with either a conventional black hole formed first, regular pulsar formed second system; or, a neutron star formed first, with a black hole formed second, after partially respinning-up the neutron star to a millisecond pulsar (probably not a very fast MSP). The latter is lower probability, but is longer lived, so odds of seeing either are probably comparable, and in the one-in-few-thousand range. And we're up to ~ 2000 known pulsars, so any decade now, modulo selection effects. cf this paper.
In a globular cluster, you could make such a system by exchange, and I discuss the processes semi-qualitatively in this paper. That could generally involve a proper MSP, and have some interesting orbital parameters. The goal obviously would be strong field tests of gravity, which would be cleaner, in general in the field, a cluster pulsar is more likely to have contaminated dynamics, but it would still be very interesting.
Anyway, somewhat rash bet, but always helps to provide some incentives to the observers, and if the Nobel prize won't do it then a good bottle of Bonny Doon Red certainly will.