The Goat and the Car: References and Links

Web Sites

Sites that discuss the Three Doors Puzzle, Marilyn Vos Savant, logic puzzles, statistics, and anything else caught up in my tattered old net.
• Behind Monty Hall's Doors: Puzzle, Debate and Answer?, by John Tierney of the New York Times, describes how Monty Hall, who of course was bound to sooner or later hear of this puzzle, tried the experiment at home and his comments on the problem. A real life game show takes advantage of the fact that most people assume their probabilities change - it's called the "Henry James Treatment". In real life, it's a psychology problem more than a math problem.
• Wikipedia article
• This is probably the second best page about the Three Doors Problem. It tells the history of the question and describes "Let's Make A Deal", the actual TV game show the question is based on.
• Jim Loy brilliantly covers the proper reasoning in The Monty Hall Trap.
• This one has nice graphics, too: The Grey Labyrinth. Lots of logic and bizarre object puzzles, geometry teasers, a true story "haunted TV" detective puzzle, etc., most with ray-traced images.
• M. J. Young presents the puzzle, discusses both right and wrong answers, describes some of the assumptions made by both sides of the argument, and his page is generally redundant in concept with my site, and it was up first, too.
• Of course, Marilyn has her own web site There wasn't much there last time I checked. But other people's web pages about her, the questions she answers, and whatever can be found all over the web.
• Kyle Siegrist covers the reasoning in mathematical language.
• Someone wrote an online computer program, an on-line Java applet, to simulate the problem. I'm not sure what it's supposed to do, since I use a simple non-Java browser, but this web page mentions some variations on the puzzle.
• An interesting variation on the problem: In real life, maybe the game show host would offer you the chance to switch only if you initially picked the prize-winning door. If you had initially picked a goat, he'd blah-blah-blah to fill the time, but not offer you the chance to switch - maybe offer you a quick cash choice instead. Of course that changes the math. If the host made this a consistent practice, though, you'd know what was behind your door from whether or not you're offered a chance to switch -- and your chances of winning go up to 100%. Further discussion at Herb Weiner's "Marilyn is Tricked by a Game Show Host" Wakes you up to the difference between pure math questions, and real life. Considers the assumptions made in the original problem, like M. J. Young's site described above. Herb also has several articles on why Marilyn is Wrong.
• Marilyn wrote a column "...where she printed questions that she admitted she couldn't answer ..." according to this site. Good ponderings are to be enjoyed in this list of questions. All kinds of questions, but most aren't logic puzzlers. The very last question is sometimes used at job interviews to weed out the dullards. Teachers may want to study these.
• Many legal conundrums can be, with analysis, reduced to simpler problems resembling brain teasers, though with an added moral dimension. If it weren't goats and cars on TV, but criminal defendants and lawyers, brain-teasers like the Three Doors problem become very serious matters. here's a paper on the use of probability in criminal trials. May be too academic for some people's taste, but very interesting reading. Look in the footnotes. Let me quote one sentence: "Whenever Ms. Vos Savant poses a probability puzzler in her Parade Magazine column, many of her readers insist--with absolute conviction--on the wrong answer." Gee, I'd hate to have many of her readers on the jury if I'm ever on trial for something...

Newsgroups

There are no newsgroups devoted to just this puzzle, but there are newsgroups for logic puzzles, mind teasers, and high-IQ stuff in general.
• rec.mensa - sometimes too full of long-winded threads but always full of well-read and intellegint people who like logic puzzles.
• alt.sci - Holds a lot of wide-ranging scientific topics - and even more non-scientific ones, unfortunately. Probably too general a newsgroup to be useful. "Science" covers a lot of territory these days.
• sci.logic - Covers logic, naturally. The best place to explore logic problems, logic as used in science and society, and probabilites. Tends to be academic and mathematical.
• sci.math - A general newsgroup for all mathematical topics. Students asking about tough homework problems, advanced research questions, how to teach math, and more.

Books and Articles and Other Stuff on Probability, Logic, Games, Philosophy of Mathematics and Related Topics

• The Chance project at Dartmouth: "The goal of Chance is to make students more informed, critical readers of current news stories that use probability and statistics."
• For anyone doubting the usefulness of applying numbers to everything in life, strengthen those doubts with The Future Does Not Compute, by Michail Talbott. The author considers the polar opposites of analysis and meaning. Main point: Why computers can't do everything for us.
• Unless you're already a statistics guru, you should become familiar with the best-selling How to Lie with Statistics by Darrell Huff, ISBN 0-393-31072-8, availabe in inexpensive softcover. Shows you how journalists, advertisers, politicians and others can deliberately, or out of ineptness, distort your thinking with just the facts -- telling lies while telling only the truth! A good book to sharpen your thinking skills.
• How To Solve It, by Polya is another famous popular math book, but applicable to all areas of thinking. General ways to approach a problem, many having nothing to do specifically with math.
• An article asking "Can Jurors Understand Probabilistic Evidence?" does not mention our problem, but makes you wonder about juries...

There are some difficult physics problems involving scattering and quantum mechanics in which one can't just assume all possibilities are equally likely. One must make the right choice of classifying the possibilites (of, for example, the trajectory of an electron) in a way that each is equally likely, or even better, classify the possibilities in ways that are mathematically conventient and assign the correct probabilities to each. To describe this in any detail goes way beyond the scope of this site, but if you are interested, some advanced books to read are:
• ...to be finished "real soon"...
If you have access to a university library, or are searching on the WWW, the best search term is "conditional probabilities". Mastery of conditional probabilities is vital in all analytical sciences. You can't get far in quantum theory without it.

Mensa

Mensa is the international high-IQ society where eggheads of all types gather for fun, discussion and variety. Most of them are not the bespectacled chrome-dome slide-rule types that some people imagine. For example, I don't wear glasses, myself. But I love my trusty old slide rule... never needs batteries... this crosshair slides along so smoothly... ahhh...wooden mathematical perfection... Anyway, Mensans include lawyers, pschologists, postal workers, writers, artists and much more.

They also have a web site, and many of their local chapters have sites, too.

A common misconception is that Mensa is full of intellectual snobs. This is not so. Well, there are a few, of course. But most of us Mensans are just too good to be snobs!

In fact, many of us are quite modest about ourselves. People say I'm very modest. One year, someone talked me into entering a modesty contest. I was surprised - I won Second Prize! Of course, blushing modestly, I turned it down. So they gave me First Prize!

This, and many more kinds of clever humor, available at your local Mensa chapter!

Another high-IQ society is Intertel. I couldn't find a web site, but then I didn't look very hard. Hey, I'm a Mensan.

Otherwise

If, after reading all that, you're STILL confused, you may be wondering Just How Much Do We Really Know?
or perhaps you'd enjoy a visit to the First Church for the Easily Amused.
 Do you know any good references not listed here? email darenw@pipeline.com

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