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Monty Hall Problem:     more detail
1. The Monty Hall Problem: Beyond Closed Doors by Rob, Deaves, 2007-01-16
2. The Monty Hall Problem and Other Puzzles (Mastermind) by Ivan Moscovich, 2005-02-11
3. The Monty Hall Problem & Other Puzzles (Mastermind Collection) by Ivan Moscovich, 2004-11-01
4. Monty Hall Problem and Other Puzzles by Ivan Moscovich , 2005-02-11

1. The Infamous Monty Hall Problem
Short introduction for beginners.
http://www.comedia.com/hot/monty.html
##### The Setup
• you are presented with 3 doors (A, B, C) only one of which has something valuable to you behind it (the others are bogus)
• you do not know what is behind any of the doors
##### You choose a door
Monty then counters by
• showing you what is behind one of the other doors (which is a bogus prize), and
• asks you if you would like to stick with the door you have, or
• switch to the other unknown door
##### The question is
should you switch?
##### Another question is
Does it matter?

2. Monty Hall Problem Web Sites
The WWW Tackles The monty hall problem. Discourse on the monty hall problem Simulationsof the monty hall problem Three Door Puzzle A great site!
http://math.rice.edu/~ddonovan/montyurl.html
##### Discourse on the Monty Hall Problem:

3. The Monty Hall Problem
The monty hall problem. The Statement. Game show setting. There are 3 doors, behind one of which is a prize. Monty Hall, the host, asks you to pick a door, any door.
http://astro.uchicago.edu/rranch/vkashyap/Misc/mh.html
##### The Statement
Game show setting. There are 3 doors, behind one of which is a prize. Monty Hall, the host, asks you to pick a door, any door. You pick door A (say). Monty opens door B (say) and shows voila there is nothing behind door B. Gives you the choice of either sticking with your original choice of door A, or switching to door C. Should you switch?
##### The Solution
Yes. In other words, the probability that the prize is behind door C is higher when Monty opens door B, and you SHOULD switch! kashyap@ockham.uchicago.edu

4. A New Approach To The Monty Hall Problem
Introduces the problem and tries to look at the problem in a new light.
http://www.reenigne.org/maths/montyhall.html
##### A new approach to the Monty Hall problem
Reams and reams have been written about the Monty Hall problem, but no-one seems to have mentioned a simple fact which, once realised, makes the whole thing seem intuitive. The Monty Hall show is a (possibly fictional, I'm not sure) TV gameshow. One couple have beaten all the others to the final round with their incredible skill at answering questions on general knowledge and popular culture, and now have a chance to win a Brand New Car. There are three doors. The host explains that earlier, before the couple arrived, a producer on the show rolled a dice. If a 1 or a 4 was rolled, the car was placed behind the red door. If a 2 or a 5 was rolled, it was placed behind the blue door and if a 3 or a 6 was rolled, it was placed behind the yellow door. The host invites the couple to pick which door they think the car is behind. He then opens one of the other two doors and there's no car behind the door! (He knows where the car is, so he can always arrange for this to happen). Then the host asks the couple if they want to change their mind about which door they think the car is behind. Should they change? Does it make a difference. Most people's first reaction is that it can't matter. How can it? The car has a one in three chance of being behind each of the doors.

5. Monty Hall Problem
THE monty hall problem. Throughout the many years of Let's Make A Deal's popularity, mathematicians and a mathematical urban legend has developed surrounding "The monty hall problem
##### THE MONTY HALL PROBLEM
Throughout the many years of Let's Make A Deal 's popularity, mathematicians have been fascinated with the possibilities presented by the "Three Doors" ... and a mathematical urban legend has developed surrounding "The Monty Hall Problem." A heated debate began when Marilyn Savant published a puzzle in her Parade Magazine column. One of her readers posed the following question: ÂSuppose youÂre on a game show, and youÂre given a 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 whatÂs behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, ÂDo you want to pick door No. 2?Â Is it to your advantage to take the switch?Â Ms. Savant, whoÂs listed in the Guinness Book of World Records Hall of Fame for ÂHighest IQÂ (228), answered ÂYes.Â Because of the estimated 10,000 letters she received in response, she published a second article on the subject. Due to the fervor created by Ms. SavantÂs two columns, the New York Times published a large front page article in a 1991 Sunday issue which declared:

6. Andrewgraham.co.uk.games
Simulation of the 3door problem in Flash, along with a brief discussion.
http://www.andrewgraham.co.uk/maths.html
 Picture the scene. You've made it through to the final round of a game show. There are three doors in front of you. Behind one of the doors is the star prize - a brand new car. There is a goat behind each of the other two doors. You make your choice, hoping to select the star prize. The game show host (who knows where the car is hidden) opens a different door to reveal a goat. The choice is now down to two doors. He asks whether you'd like to stick with your original choice or whether you'd like to switch doors... do you switch? yes no it doesn't matter I don't care, take me to the index ... e-mail

7. U Of T Mathematics Network -- Problems And Puzzles
Includes interactive games, problems and puzzles including the monty hall problem and the Tower of Hanoi and questions pages with answers and discussion.
http://www.math.toronto.edu/mathnet/probpuzz.html
Navigation Panel: Go backward to Interactive Activities and Games
Go forward to Questions and Discussion
Switch to text-only version (no graphics)
##### Problems and Puzzles
You can select any of the items below:
##### Interesting Mathematical Games
If your interest is in recreational mathematics, try playing these games, then figuring out the mathematics behind them. The following sites are not part of the University of Toronto Mathematics Network, but since there are already many good traditional-style problems available on the Internet, we decided we'd just point you to them, while we spend more time developing the interactive projects and activities unique to this site.
##### The Math Forum
A good, comprehensive source of many mathematical materials.
##### MAT 007 I News
Not a problem collection, but a newsletter chock full of puzzles, trivia, humour, and even some real mathematics. Published by undergraduate mathematicians at the University of Toronto. This page last updated: September 27, 1999

 8. The Monty Hall Problem The monty hall problem. The monty hall problem gets its name from the TV game show, "Let's Make If the monty hall problem ended with the selection of the firsthttp://www.io.com/~kmellis/monty.html

9. Marilyn Vos Savant's Monty Hall Problem
Simulator. Uses buttons as labels and controls. Counts tries and provides percentages. Can be Reset without page refresh.
http://www.mindspring.com/~tluthman/vossavant.htm
 Tom Luthman's webpage has moved! The new webpage is: PlanetTom.home.mindspring.com

10. Education, Mathematics, Fun, Monty Hall Dilemma
Monty Hall Dilemma. The Monty Hall Dilemma was discussed in the popular "Ask Marylin" questionand-answer column of the The WWW Tackles The monty hall problem. Win a car
http://www.cut-the-knot.com/hall.html
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##### Monty Hall Dilemma
The Monty Hall Dilemma was discussed in the popular "Ask Marylin" question-and-answer column of the Parade magazine. Details can also be found in the "Power of Logical Thinking" by Marylin vos Savant, St. Martin's Press, 1996. Marylin received the following question: 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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors?
Craig. F. Whitaker
Columbia, MD Marylin's response caused an avalanche of correspondence, mostly from people who would not accept her solution. Several iterations of correspondence ensued. Eventually, she issued a call to Math teachers among her readers to organize experiments and send her the charts. Some readers with access to computers ran computer simulations. At long last, the truth was established and accepted. Below is one simulation you may try on your computer. For simplicity, I do not hide goats behind the doors. There is only one 'abstract' prize. You may either hit on the right door or miss it. You make your selection by pressing small round buttons below input controls that substitute for the doors. Down below other controls update experiment statistics even as you progress.

11. Interactive Mathematics Miscellany And Puzzles, Probability
1 2 3. If this computer simulation of random selection seems sufficiently credible,you may want to continue and tackle the monty hall problem. Remark.
http://www.cut-the-knot.org/probability.shtml
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##### Probability
In a world as crazy as this one, it ought to be easy to find something that happens solely by chance. It isn't. Kevin McKeen
The Orderly Pursuit of Pure Disorder.
Discover, January, 1981
American Heritage Dictionary defines the Probability Theory as the branch of Mathematics that studies the likelihood of occurrence of random events in order to predict the behavior of defined systems. Starting with this definition, it would (probably :-) be right to conclude that the Probability Theory, being a branch of Mathematics, is an exact, deductive science that studies uncertain quantities related to random events. This might seem to be a strange marriage of mathematical certainty and uncertainty of randomness. On a second thought, though, most people will agree that a newly conceived baby has a 50-50 chance (exact but, likely, inaccurate estimate) to be, for example, a girl or a boy, for that matter. Interestingly, a recent book by Marilyn vos Savant dealing with people's perception of probability and statistics is titled "The Power of Logical Thinking". My first problems will be drawn from this book.

12. Answer To The Monty Hall Problem
Answer to the monty hall problem. Hold on to your hats you *double*your chances by switching. This is, at first look, way counter
##### you *double* your chances by switching

13. Monty Hall
The monty hall problem. (This is similar to the routine on the TV game showLet s Make a Deal, hosted by Monty Hall, hence the name of the problem.)
http://www.hofstra.edu/~matsrc/MontyHall/MontyHall.html
##### The Monty Hall Problem
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is the Grand Prize; behind the others, Booby Prizes. You pick a door, say Door A, and the host, who knows what is behind each door, opens another door, say Door B, revealing a Booby Prize. The host then offers you the opportunity to change your selection to Door C. Should you stick with your original choice or switch? Does it make any difference? (This is similar to the routine on the TV game show Let's Make a Deal , hosted by Monty Hall, hence the name of the problem.) Assuming that the host always chooses to open a door with a Booby Prize, and would never reveal the Grand Prize, the possibly surprising answer is that you should switch to the third door, which is now twice as likely as your original choice to be hiding the Grand Prize. This problem can be analyzed using Bayes' theorem or trees (see "You're the Expert" at the end of Chapter 7 of Finite Mathematics , Second Edition ), but here is an intuitive argument. When you chose Door A, the probability that you chose the Grand Prize was 1/3 and the probability that it was behind one of the other doors was 2/3. By showing you which of Doors B and C does not hide the Grand Prize (Door B, say), the host is giving you quite a bit of information about those two doors. The probability is still 2/3 that one of them hides the Grand Prize, but now you know which of the two it would be: Door C. So, the probability is still only 1/3 that the Grand Prize is behind Door A, but 2/3 that it is behind Door C.

 14. The Monty Hall Problem The monty hall problem Let's Make a Deal If you're shown a goat behind the second of three doors, should you stay with your first choice or switch? Math Forum, a Classic Problem from the Ask Dr.http://rdre1.inktomi.com/click?u=http://mathforum.org/dr.math/faq/faq.monty.hall

15. GRAND ILLUSIONS
THE monty hall problem. This story is true, and comes from an Americantv game show. Here is the situation. Finalists in a tv game
http://www.grand-illusions.com/monty.htm
##### THE MONTY HALL PROBLEM
This story is true, and comes from an American tv game show. Here is the situation. Finalists in a tv game show are invited up onto the stage, where there are three closed doors. The host explains that behind one of the doors is the star prize - a car. Behind each of the other two doors is just a goat. Obviously the contestant wants to win the car, but does not know which door conceals the car. The host invites the contestant to choose one of the three doors. Let us suppose that our contestant chooses door number 3. Now, the host does not initially open the door chosen by the contestant. Instead he opens one of the other doors - let us say it is door number 1. The door that the host opens will always reveal a goat. Remember the host knows what is behind every door! The contestant is now asked if they want to stick with their original choice, or if they want to change their mind, and choose the other remaining door that has not yet been opened. In this case number 2. The studio audience shout suggestions. What is the best strategy for the contestant? Does it make any difference whether they change their mind or stick with the original choice? The answer to this question is not intuitive. Basically, the theory says that if the contestant changes their mind, the odds of them winning the car double. And over many episodes of the tv show, the facts supported the theory - those people that changed their mind had double the chance of winning the car.

16. The Monty Hall Problem
Sorry, this program require Javascript, it will not work for you. ? ? ? Loading,Please wait Keep choice 0 times Wins 0, cars, (0%). Losses 0, goats, (0%).
http://www.grand-illusions.com/simulator/montysim.htm
##### Sorry, this program require Javascript, it will not work for you
Loading, Please wait... Keep choice: times Wins: cars Losses: goats Change choice: times Wins: cars Losses: goats Run times and keep change the choice: Cheat

17. Math Forum: Ask Dr. Math FAQ: The Monty Hall Problem
The monty hall problem. Let s Make a Deal Francois Bergeron The monty hall problem- Keith M. Ellis Marilyn is tricked by a game show host - Herb Weiner.
http://mathforum.org/dr.math/faq/faq.monty.hall.html
The Monty Hall Problem
Dr. Math FAQ
Classic Problems Formulas Search Dr. Math ... Dr. Math Home
For a review of basic concepts, see Introduction to Probability and Permutations and Combinations. Let's Make a Deal! Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does. The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors. After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch?
One way to think about this problem is to consider the sample space, which Monty alters by opening one of the doors that has a goat behind it. In doing so, he effectively removes one of the two losing doors from the sample space. We will assume that there is a winning door and that the two remaining doors, A and B, both have goats behind them. There are

18. Monty Hall Problem - Wikipedia, The Free Encyclopedia
http://en.wikipedia.org/wiki/Monty_Hall_problem
##### Monty Hall problem
This article has been nominated on Wikipedia:Featured article candidates . Please refer to that page if you wish to second or contest the nomination.
The Monty Hall problem The Monty Hall problem is a puzzle in probability that is loosely based on the American game show Let's Make a Deal ; the name comes from the show's host Monty Hall . In this puzzle a contestant is shown three closed doors; behind one is a car, and behind each of the others is a goat. The contestant chooses one door and will be allowed to keep what is behind it. Before the door is opened, however, the host opens one of the other doors and shows that there is a goat behind it. Should the contestant stick with the original choice or change to the remaining door; or does it make no difference? The question has generated heated debate. As the standard answer appears to contradict elementary ideas of probability, it may be regarded as a paradox . As the answer relies on assumptions that are not in the statement of the puzzle and are not obvious, it may also be considered a trick question. Table of contents 1 Problem and solution 1.1 The problem

19. The Monty Hall Problem
The monty hall problem. This problem goes back a number of years and is used todemonstrate how angry people can get when they donÂt agree with an answer.
http://www.coastaltech.com/monty.htm