For a general description of feedback systems, I refer to this block diagram, kindly provided by LvW in a previous discussion, a pretty long thread about feedback factor definition:
https://www.edaboard.com/threads/174717/
A1 is the amplifier open loop gain, ß is the feedback factor. The "forward factor" a is often assumed as 1 in text books when discussing feedback systems, but it's ≠ 1 in many real circuits, e.g. yours. I guess, you are referring to a simplified feedback block diagram with a = 1, which causes the confusion about closed loop gain.
I presume, that you can derive a yourself, it's calculated similar to f (or ß), finally you get Acl(ideal) = a/ß = Cs/Cf.