Probability of planets in binary star systems? There is much fiction on binary stars with planets, for whatever reason, and this keeps supporting the popular impression that those systems are frequent. Indeed,  the methods for identifying exoplanets and binary stars are somewhat the same. Are there actual observations of a binary star system with at least another planet (habitable or not)?
I know that binary star systems are rather frequent, and I am wondering whether there is any hard-science based statistics on how probable it is that systems of two or more stars have planets? As non-expert, I have the impression that not all configurations of binary star systems seem to be in favor of planets, see e.g. Roche lobe.
There are only about a dozen circumbinary exoplanetary systems known - the first discovered was Kepler 16b.
The statistics of circumbinary planets is a relatively unstudied area. One of the major uncertainties is the inclination distribution of the exoplanets. If they are confined to the orbital plane of the binary system, then transiting circumbinary planets are easier to detect and so their observed frequency translates to a lower actual frequency than if their orbits are scattered around the binary orbital plane. Armstrong et al. (2014) use the Kepler survey results and find that if circumbinary exoplanets are coplanar with the binary, then the frequency of giant exoplanets within 300 day orbits is about 10%, and consistent with the frequency of similar exoplanets around single stars. On the other hand if their orbital inclinations were random with respect to the binary, then the exoplanet frequency could be a factor of 5 higher.
On the other hand we do know that circumbinary planets around very short period binaries (those with periods less than 7 days) are rare Fleming et al. 2018). This probably has something to do with orbital evolution of the binary system in these cases.
Exoplanets that orbit around one of the stars in a binary system are better studied. If the stars are widely separated then they have little influence on each other or on planetary systems that orbit within say 1/10 of the stellar separation. Exoplanets on orbits wider than about 1/5 of the separation are expected to be unstable.