Wolfgang, you've done real life experiments on this? Do you mind if I ask what your profession is?

I'm not sure of this statement of yours:

"If just any cup is opened by chance either you have lost at once (for this cup contains the prize) or you have the choice between the two remaining cups (in the other two third of the cases) then it does not matter at all whether you change your first choice or not."

If the dealer didn't know where the prize was and showed you one cup randomly, then sometimes he would show you the one with the prize so the game would be over for you.

But if he shows you an empty cup, I still think it would be better to switch. Why would the dealer's knowledge or ignorance affect the game from your end of things? It's still true that the prize is more likely to be among the two cups that you didn't pick than in your first choice, and the dealer is still (although unintentionally) showing you which of those two has the prize if either of them does.

Marion