This is one of my favorite problems because it always baffles me why its so hard to get to "know" the solution. Every time I come across and read it, it's like I'm seeing it for the first time. Holding an intuitive notion of the solution always seems to elude me.
I came across it again today. This time on video explained by
Keith Devlin who is a wonderful explainer.
More about Keith, Monty Hall and why some math needs to be learned "top down" - at least according to Keith - coming soon.