Wolfgang--
You wrote, "The two more common solutions, one of which is counterintuitive. (1) Monty knows where the prize is, and always (a) opens a door without the big prize and (b) gives you the choice to switch, then you should switch (counterintuitively), for the probability of winning then is 2/3."

This is basically correct, but not complete...Monte will will never reveal your Goat Door under any circumstance, or the game is instantly over. Not an exciting game for a television audience. I don't know if that means Monte is mean or benevolent as he always acts same manner.

You also wrote that the actual game has been retrospectively analyzed, and the results showed that results did not match exactly the expected probabilities, no matter the strategy the contestants followed. This, of course, is to be expected because each game is a new event wherein even the least probable outcome can occur. Since there were hundreds of games played, it would be interesting to know how close outcomes came to expected probability throughout the run of the show.