Analysis of 3 Stage CS Ring Oscillator

I am new to the world of oscillators, so take it easy on me.

I have been attempting to analyze the following common source ring oscillator:

However, I am having some trouble here. So based on my understanding: Each stage of the FETs provides 270 degrees of phase shift total. 180 from the inverting common source, and 90 from a pole due to the capacitor. In order to oscillate we need 360 degrees total. With only two stages of the CS FETs, the necessary phase shift for oscillation is there but would be stable at either rail. Can someone explain this? Why would it still be stable?

Now, at 3 stages, the circuit oscillates provided the gain of each stage is greater than or equal to 2. Can someone explain this as well? I do not understand why it is 2 instead of one, nor can I seem to understand the math behind this.

Thank you for your time and help.

According to the Barkhausen criterion we need in total -360 deg (identical to zero deg) for a certain frequency. For this purpose, we have three 1st order lowpass stages - each with a cut-off frequency at app. $$\wc=1/R_DC_L\$$.