Thats it, SixOfSpades. The reason why its 66 % and not 50 is that you know that that door has been left closed BECAUSE the quiz master didnt want to show the gift. The example of the 1000 doors is so clear. After discarding 998 doors, you have door A (first choice) and door B (the one that the quiz master left closed). Id bet that door B has the prize because the quiz master decided to leave it closed, because he CHOSE that door between 999 doors. You dont have to think that maybe he chose that door randomly because you already had pciked the right one, thinking that wouldnt be clever i think because the chances of you picking the right one the first time are 1/1000, so 999 times out of 1000 the quiz master would have POINTED you the right door.
The odds would be 50/50 if, after the quiz master discarded the doors, a NEW person appeared and had to choose between the 2 doors, without knowing which one is the one that the master decided to keep closed.
I think its clear now, but if you want me to reason it further, just ask
. Im gonna sleep now, see ya