An article by Junpei Sekino begins thus:
On one Sunday of September 1990, the following question appeared in the Ask Marilyn column in Parade, a Sunday supplement of local newspapers.
Suppose you're on a game show, and you're given the choice of three doors; Behind one door is a car; behind the others, goats. You pick a door, say No.1 and the host, who knows what's behind the doors, opens another door, say No.3, which has a goat. He then says to you, "Do you want to pick door No.2?" Is it to your advantage to switch your choice? -Craig F. Whitaker, Columbia, Md.
Now, having read the original version of the Monty Hall puzzle, try to find an answer. Then read various excellent accounts of this puzzle in the article by Junpei Sekino, as well as here, and here. I found all these links in a comment by Enrico Scalas to a post by Tommaso Dorigo over at the Quantum Diaries website, through which you can "follow physicists from around the world as they live the World Year of Physics 2005"
Finally, let me quote Tommaso Dorigo: "...several Professors of Physics got it [the puzzle] wrong when I tried it with them, and one well-known theoretical physicist actually had to run a Monte Carlo simulation in order to become convinced of the solution".
2 comments:
I think the MH puzzle is almost trivial once you look at it this way: increase the doors to 100; first select one; then MH shows you that 98 of the remaining 99 doors don't have the prize; that leaves only two unopened doors -- one you selected and on that you can select if you switch; now if you switch, you lose only if you selected the correct door the firs time (probability 1/100) and you win if you originally selected the wrong door (probability 99/100); so it is a no brainer that you should switch in this case; same logic holds for the case of 3 doors.
Atanu
www.deeshaa.org
The difficulty is that the problem is ill-stated as vos Savant published it, and that caused some (but probably not all) of the controversy. If you read Sekino's article, his wife raises a correct objection: you don't know, in the problem as stated, if Monte acts capriciously. Maybe he ONLY offers you the chance to switch when you've guessed RIGHT! That would change the probability, wouldn't it? Rather dramatically, it would make the right strategy to stay put, for one thing! There is it least one techical paper out there that goes into problem more deeply and explains all the things needed for the problem to be what we THINK Marilyn intended. I'm no fan of hers: she's bit of a fraud, on my view, and she really screwed up with this problem and caused unnecessary confusion through her sloppiness. She never did admit that she messed up. And if you think about it, she did. I've mentioned just one loophole, and there are others.
Post a Comment