5 ms·
Understanding this problem means you can differentiate between the two scenarios below: (1) If the host reveals an empty door at random, your odds are 1/3 and
by tedsanders 13y ago
Understanding this problem means you can differentiate between the two scenarios below:
(1) If the host reveals an empty door at random, your odds are 1/3 and you should switch.
(2) If the host reveals a door at random that happens to be empty, your odds are 1/2 and it doesn't matter.
The reason that so many people get confused is that they read the words and their minds automatically jump to scenario 2.
- lstamour 13y agoTo clarify this, (1) means the empty door, as revealed, was not picked from a random set of doors with anything or nothing behind them. Rather, (1) and the link, both refer to a case where the game show host picks a random door only from doors known to be empty, presumably to raise the tension in the show. (Opening the door with something behind it would eliminate the tension, after all.) I also like the answers later in the HN comments where someone mentions the host opening a bunch of empty doors, leaving one closed, then asking if you'd like to switch to the door he or she conveniently left closed.
- teddyh 13y ago“And a very small percentage of readers feel convinced that the furor is resulting from people not realizing that the host is opening a losing door on purpose. (But they haven’t read my mail! The great majority of people understand the conditions perfectly.)“ — Marilyn vos Savant
- ronaldx 13y agoNonetheless, blind swaps are generally suspicious, and there could be a genetically programmed heuristic for humans to undervalue them.
- tedsanders 13y agoInteresting. I guess I'm part of that small percentage! But I really do think that's the case. Even if people say the words ("the host opens a losing door"), they may not be processing what it means ("the host purposefully opens a door that is known to be losing"). I wonder if I'm wrong.