Thanks to <a_tattletale> for an illuminating response.

I think I see it now.

Essentially the flaw with my counting outcomes approach is that with the Always Switch or Always Stay strategies, what the host does in picking the door to open has no impact on the outcome--hence my two outcomes under case A should really be collapsed into one.

By the way, I don't see how there's 6 possible outcomes. Under the rules as originally stated, the game host will never open the door with the prize. He does have a choice under Case A, where you select the door with the prize, but as I stated above, this choice does not affect the outcome.

Thanks for clearing this up for me.

Don Link