A simple example that highlights the strength of this method: a 137Cs point source is at the origin. A detector consisting of a right cylinder at arbitrary distance and orientation is nearby. What is the solid angle?
There may exist an analytical solution for this, but I wouldn't trust myself to derive it correctly. It would certainly be a huge mess.
If we add that the source is also a right cylinder instead of point source, and we want to add first order attenuation of emitted gammas by the source itself, the spreadsheet becomes only a bit more complex, but there will not be a pen and paper equation solution.
In this example every row of the spreadsheet would represent a hypothetical ray. One could randomly choose a location in the source, a random trajectory, and check if the photon intersects the detector. An alternative approach would be randomly choosing points in both target and detector, then doing additional math.
The results are recovered by making histograms and computing stats on the outputs of all the rows. You probably need a few thousand for most things at least. Remember roughly speaking 10k hits gets you ~1% statistics.