Over the weekend, I came across a X validated question asking for clarification about our 2012 Vanilla Rao-Blackwellisation paper with Randal. Question written in a somewhat formal style that made our work difficult to recognise… At least for yours truly.
Interestingly this led another (major) contributor to X validation to work out an uncompleted illustration as attached, when the target distribution is (1-x)². It seems strange to me that the basics of the method proves such a difficulty to fathom, given that it is a simple integration of the (actual and virtual) uniforms…. The point of the OP that the improvement brought by Rao-Blackwellisation is only conditional on the accepted values is correct, though.