  Almost a dozen circumbinary planets have been found transiting eclipsing
binaries. For the first time the observational bias of this sample is
calculated with respect to the mass ratio of the host binaries. It is shown
that the mass ratio affects transit detection in multiple, sometimes subtle
ways, through stability and dynamics of orbits, dilution of transit depths and
the geometric transit and eclipse probabilities. Surprisingly though, it is
found that these effects largely cancel out. Consequently, the transit
detections in the Kepler mission are essentially unbiased with respect to mass
ratio, and hence likely representative of the true underlying population. It is
shown the mass ratio distribution of circumbinary hosts may be the same as
field binaries, and hence roughly uniform, but more observations are needed to
deduce any subtle differences. These results are discussed in the context of
close binary formation and evolution, of which the mass ratio is believed to be
a marker, and other surveys for circumbinary planets including TESS and BEBOP.
