After 3 days, this is my 3rd posting, and the most humble. We have to distinguish between the probability of winning at all, which is 50%, and the way in which the winning outcomes are split between sticking and switching doors.

Anyone who wants to convince themselves of the correct answer should draw a decision tree, like Peter Stikker (www.cut-the-knot.com/peter.shtml). But once it's drawn, create a table of the probability for winning and losing against sticking or switching doors. I found it convinced my head - though not my heart. It still FEELS wrong, but now I know although that it really is twice as likely that you'll win if you switch.

Stick & win: (1/36)*6 = 1/6
Stick & lose: (1/18)*6 = 1/3
Switch & win: (1/18)*6 = 1/3
Switch & lose: (1/36)*6 = 1/6

Thank you to all the contributors to this forum, whose postings have finally led me to the truth.

:7