1. Cheap Monty Hall The following is a simple simulation of the monty hall problem. It took a totalof 1.5 hours to create. Adding colour and graphics would be simple but the http://www.utstat.toronto.edu/david/MH.html

THE MONTY HALL PROBLEM The following is a simple simulation of the Monty Hall problem. It took a total of 1.5 hours to create. Adding colour and graphics would be simple but the time might better be spent on other examples. The names of links should be changed and the file tripled in size. We haven't spent much time on the words here so read the first few pages carefully. Grab a paper and pencil and remember, looking at the scroll bars is cheating. David Andrews 6:31 p.m. June 5, 1996 START MONTY HALL There are three doors. Behind one is a car, behind the others are goats. For the moment, think that cars are handy and goats are a lot of work. Imagine that you want the car. This, of course, is subject to debate, but this is only a game. The debate comes after. Pick a door. Door 1 Door 2 Door 3 MONTY HALL You picked Door 1. Monty Hall has opened Door 3. It's not a car. But he gives you another chance. You can repick Door 1 or the other door. Should you stick or switch? That is the question. It is interesting to try both strategies. Which one is better?

2. The Infamous Monty Hall Problem Short introduction for beginners. http://www.comedia.com/hot/monty.html

The Infamous Monty Hall Problem 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? The answer lies behind this link Don't look until you've decided upon your answer. Home Broadcatch Technologies CoMedia Consulting Words ... Hot List This page maintained by CoMedia Consulting webmaster@CoMedia.com Last modified: Fri Aug 30 13:51:58 PDT 1996

3. The Monty Hall Problem A probability theory puzzle with solutions. English and German. http://www.remote.org/frederik/projects/ziege/

[remote] [frederik] [projects] [monty hall] The Monty Hall Problem The following problem is taken from a quiz show on TV that really existed (or still exists). It is an interesting topic to discuss in almost any group of people because even the most intelligent often get into trouble, and is (in other languages) referred to as the Goat Problem. New: In compliance with the current domain grabbing hysteria, this page is now also available as http://www.ziegenproblem.de/, which is easier to memorize - at least for speakers of German. The Scenario The quiz show candidate has mastered all the questions. Now it's all or nothing for one last time: He is lead to a room with three doors. Behind one of them there's an expensive sports car; behind the other two there's a goat. (Don't ask me why it's a goat. That's just the way it is.) The candidate chooses one of the doors. But it is not opened; the host (who knows the location of the sports car) opens one of the other doors instead and shows a goat. The rules of the game, which are known to all participants, require the host to do this irrespective of the candidate's initial choice. The candidate is now asked if he wants to stick with the door he chose originally or if he prefers to switch to the other remaining closed door. His goal is the sports car, of course!

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. 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) Go to University of Toronto Mathematics Network Home Page Problems and Puzzles You can select any of the items below: International Mathematical Talent Search Problems Try your hand at these problems, and mail in your answers! 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

6. 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 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. The Monty Hall Problem The monty hall problem http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. The Let's Make A Deal Applet Despite a very clear explanation of this paradox, most students have a difficulty understanding the problem. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Answer To The Monty Hall Problem Answer to the monty hall problem. Hold on to your hats you *double* yourchances by switching. This is, at first look, way counterintuitive, http://www.comedia.com/hot/monty-answer.html

Answer to the Monty Hall Problem Hold on to your hats... you *double* your chances by switching This is, at first look, way counter-intuitive, so here's an attempt at an explanation: Take a look at this matrix of possibilities: Door ~~~~ case A B C ~~~~ 1 bad bad good 2 bad good bad 3 good bad bad Let's assume you choose door A you have a 1/3 chance of a good prize. But (this is key) Monty knows what is behind each door , and shows a bad one. In cases 1 and 2, he eliminates doors B and C respectively (which happen to be the only remaining bad door) so a good door is left: SWITCH! Only in case 3 (you lucked out in your original 1 in 3 chances) does switching hurt you. So, your probability goes up from 1/3 to 2/3 if you switch after being shown a bad door. Caveat: of course, this only works if Monty is guaranteed to show you a bad door every time after you choose a door, something that was not assured in the original game show. Home Broadcatch Technologies CoMedia Consulting Monty ... Hot List This page maintained by CoMedia Consulting webmaster@CoMedia.com

10. 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

11. The Infamous Monty Hall Problem The Infamous monty hall problem http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. The Monty Hall Page Behind one of these doors is a car. Behind the other two is a goat. Click on the door that you think the car is behind. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Andrewgraham.co.uk Simulation of the 3door problem in Flash, along with a brief discussion. http://www.andrewgraham.co.uk/maths.html

I've moved things about. Redirecting you...

14. In Order To Explain Why The Numbers Are Suggesting That It Is In the other 2/3 of the cases, Monty Hall is telling the contestant where the car is! How does this problem change if Monty Hall does not know http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. Monty Hall The monty hall problem. Suppose you re on a game show, and you re given the choiceof three doors Behind one door is the Grand Prize; behind the others, 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.

16. Let's Make A Deal! MetaFilter July 20, 2004. A playable version of the monty hall problem. More information. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. GRAND ILLUSIONS 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 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.

18. Education, Mathematics, Fun, Monty Hall Dilemma Simulation for the Monty Hall Dilemma. Strength in Numbers, John Wiley Sons, 1996. On Internet. The WWW Tackles The monty hall problem Win a car http://www.fortunecity.com/victorian/vangogh/111/9.htm

web hosting domain names photo sharing 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.

19. Marilyn Is Tricked By A Game Show Host Which means, of course, that the only person who can answer this version of the monty hall problem is Monty Hall himself. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

20. 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%) 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

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