Dear Brian Hayes,
thank you for this helpful review as well as for your highly interesting regular column Comp Sci.
A lot has been written about the Monty Hall affair, however I haven't yet heard of a convincing solution that doesn’t rely on statistical reasoning but logical ones. Here is my attempt:
First it is to be realized that—according to the puzzle's concept—there are restrictions concerning the door(s) Monty Hall is allowed to open:
Neither does he open the door that hides the prize nor the one chosen by the subject.
With this in mind, three situations are to be considered:
1) If the subject initially chooses the door that hides the prize, then of course switching would not be advisable.
2), 3) If the subject initially chooses one of the two other doors, then switching the doors would be advisable. (These are the two situations in which Monty Hall has no choice of which door he opens.)
Consequently, in two of three situations switching is successful.
With best regards
posted by Helmut Gluender
July 2, 2008
Connect With Us:
An early peek at each new issue, with descriptions of feature articles, columns, and more. Issues contain links to everything in the latest issue's table of contents.News of book reviews published in American Scientist and around the web, as well as other noteworthy happenings in the world of science books.
To sign up for automatic emails of the American Scientist Update and Scientists' Nightstand issues, create an online profile, then sign up in the My AmSci area.
Receive notification when new content is posted from the entire website, or choose from the customized feeds available.
JSTOR, the online academic archive, contains complete back issues of American Scientist from 1913 (known then as the Sigma Xi Quarterly) through 2005.
The table of contents for each issue is freely available to all users; those with institutional access can read each complete issue.
View the full collection here.