tag:blogger.com,1999:blog-3475759095200254566.post5341116105517662109..comments2012-05-20T13:43:24.247-07:00Comments on Ugly Hip: A Monty Hall reductio ad absurdumLenoxushttp://www.blogger.com/profile/10809085020841868387noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-3475759095200254566.post-27326760566630641762012-05-20T13:43:24.247-07:002012-05-20T13:43:24.247-07:00Some people come to the viewpoint that even while ...Some people come to the viewpoint that even while staying is a 1/3 shot, switching is "still" just a 1/2 shot (these people usually don't try to explain the missing 1/6). For example, a physics professor to whom I recently introduced the puzzle temporarily made this conclusion. The main argument used above can be tailored to this view.<br /><br />First, John plays a game where he gets to pick any two doors, not just one. Then, one of his two doors is opened to reveal a goat. Immediately afterward, his one remaining door is opened. (He always chooses to "stay", analogous to always switching in the original). He mistakenly expects to win only 1/2 of the time, because there are two doors. Mary plays a simpler version: She picks any two doors, then they are both opened simultaneously; if either contains the car, she wins. She correctly anticipates winning 2/3 of the time.<br /><br />At this point, it should be obvious the two games are the same; the only difference is the order in which the doors are opened. If it's not, I suppose you could have them play together again. After they agree on two doors, John is blindfolded and a single goat door is opened and shut, then the blindfold is removed and both doors are simultaneously opened. A rather silly affair, I suppose.<br /><br />If anyone objects that starting out by picking two doors is different from starting by picking one, remind them they picking one door is exactly the same as choosing "against" two doors. (If your options are soup or salad but not both or neither, then saying "not soup" has exactly the same result as saying "salad".) Ultimately, the probabilities can't be affected by the intangible fact of "owning" one door or two or whatever. (Funnily enough, people who argue the wrong answer have sometimes insisted that this point about ownership being intangible works in their favor, that it demonstrates the absence of a real difference between the two doors. I hope it's been shown why that's not the case.)Lenoxushttp://www.blogger.com/profile/10809085020841868387noreply@blogger.com