61. Developer Testing: The Monty Hall Problem The monty hall problem comes up every now and again it s currently being Everyone I know has who has thought about the monty hall problem has got it http://www.developertesting.com/archives/month200504/20050411-TheMontyHallProble

document.getElementById('search').value = 'search'; Homepage Individual Weblogs Kevin Lawrence April 11, 2005 - The Monty Hall Problem The Monty Hall problem comes up every now and again - it's currently being discussed on the XP mailing list . It's a great problem. The description of the problem is well discussed on the web , so I won't repeat it here. Everyone I know has who has thought about the Monty Hall problem has got it wrong initially and then, after deeper thought, found the correct answer. The lure of the intuitive answer is so strong for most people (including me), that even after they have read an explanation for the correct answer, they still don't believe it ... everyone has to follow their own road to Damascus ... and everyone finds their own road. I was so insistent that my intuition was correct that I wrote a little Java program to count the probabilities. It was IntelliJ that opened my eyes. Before I even ran the program, I had a code rule violation. open = (guess + 2) % DOOR_COUNT; "The value assigned to 'open' is never used". Code rules are not just about where you put the curly bracket any more.

62. No. 1577: The Monty Hall Problem The monty hall problem and the unexpected value of information. http://www.uh.edu/engines/epi1577.htm

No. 1577: THE MONTY HALL PROBLEM by John H. Lienhard Click here for audio of Episode 1577. Today, we learn not to turn our back on information. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them. I' ve been running into the Monty Hall Problem lately. I suspect that many of you know about it. It came to my attention the other day when I ran into a colleague from the math department. She told me about it and left me scoffing in disbelief. I should've known about the problem, since it goes back to the old TV show, Let's Make a Deal . Host Monty Hall would offer a contestant three doors. One had a prize behind it. If the contestant guessed the correct door, he would win the prize. But, before the door that he chose was opened, Monty Hall (who knew where the prize was) would say, "Of the two remaining doors, I'll open this one, which has no prize behind it." Then Hall would add, "Now, would you like to change your guess?" The contestant could either decide that the first guess was correct or switch to the other unopened door.

63. The Monty Hall Problem An introduction to the monty hall problem. The monty hall problem. An Americangame show left an unexpected legacy many arguments, and more than a few http://www.rdrop.com/~half/Creations/Puzzles/LetsMakeADeal/

MLI Home Creations Puzzles The Monty Hall Problem The Monty Hall Problem An American game show left an unexpected legacy: many arguments, and more than a few Web pages. Some people even learned some probability theory. We'll leave out the theory here to concentrate on different ways to understand the problem's solution. The Problem The game show Let's Make A Deal , hosted by Monty Hall, ended each show the same way. There were three closed doors. Behind one was a prize, while the other two concealed booby prizes. Monty asked the contestant to choose a door. Then Monty opened one of the remaining doors, revealing a booby prize. Monty then offered the contestant the option to stay with the originally chosen door or switch to the other unopened door. The contestant received whatever was behind the chosen door. Now for the big question: is it better to stay , better to switch , or does it make no difference The Importance of Empiricism If you think it doesn't make a difference, stop . Right now, and I mean right now , you're going to play the game. Use this

64. The Monty Hall Problem: Play It Yourself A Java applet demonstrating the monty hall problem. http://www.rdrop.com/~half/Creations/Puzzles/LetsMakeADeal/monty.hall.applet.htm

MLI Home Creations Puzzles The Monty Hall Problem Play it Yourself The Monty Hall Problem: Play it Yourself If you're not convinced that switching is the best strategy for the Monty Hall problem , why not try it yourself? Here's a Java applet that lets you play the game repeatedly. It keeps track of wins and losses for both the stay and switch strategies. It's an honest applet that doesn't try anything underhanded. As a matter of fact, it's so honest that it tells you where the prize is. Try it. You'll see. [You should be seeing an applet now. Turn on Java if you can.] It's easy to use. Just click on one of the question marks. The door you select is marked with a circle. Also, all remaining doors but one are revealed to be a booby prize (denoted by a red X). You can then click on either door that has a question mark. The result is then added to the running win/loss totals. If you want to reset these totals, just click the Reset button. This also has an autoplay feature which lets the machine choose doors randomly. It's a quick way to let numbers add up. It plays 200 games. Scores will reset automatically when 10000 games have been played. Remember that we're dealing with probability. Win/lose ratios won't be exactly 2 to 1 or 1 to 2. It might take a large number of games before the win/lose ratios approach the predicted values. Play more than just a few games. Try a few hundred.

65. Monty Hall Problem The problem is also called the Monty Hall paradox, in the sense that the The monty hall problem is essentially a reasoning problem and involves no http://www.algebra.com/algebra/about/history/Monty-Hall-problem.wikipedia

Monty Hall problem Regular View Dictionary View (all words explained) Algebra Help my dictionary with pronunciation , wikipedia etc You did it! Over US$240,000 was donated in the 21 day fund drive. Thank you for your generosity! You are still welcome to make a donation or purchase Wikimedia merchandise Monty Hall problem In search of a new car, the player picks door 3. The game host then opens door 1 to reveal a goat and offers to let the player pick door 2 instead of door 3. 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 player is shown three closed doors; behind one is a car , and behind each of the other two is a goat . The player is allowed to open one door, and will win whatever is behind the door. However, after the player selects a door but before opening it, the game host (who knows what's behind the doors) must open another door, revealing a goat. The host then must offer the player an option to switch to the other closed door. Does switching improve the player's chance of winning the car? The answer is yes — switching results in the chances of winning the car improving from 1/3 to 2/3.

66. The Monty Hall Problem The monty hall problem. This problem has rapidly become part of the mathematicalfolklore. The American Mathematical Monthly, in its issue of January 1992, http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node32.html

Next: Master Mind Up: Mathematical Games Previous: Mathematical Games The Monty Hall problem This problem has rapidly become part of the mathematical folklore. The American Mathematical Monthly, in its issue of January 1992, explains this problem carefully. The following are excerpted from that article. Problem: A TV host shows you three numbered doors (all three equally likely), one hiding a car and the other two hiding goats. You get to pick a door, winning whatever is behind it. Regardless of the door you choose, the host, who knows where the car is, then opens one of the other two doors to reveal a goat, and invites you to switch your choice if you so wish. Does switching increases your chances of winning the car? If the host always opens one of the two other doors, you should switch. Notice that of the time you choose the right door (i.e. the one with the car) and switching is wrong, while of the time you choose the wrong door and switching gets you the car. Thus the expected return of switching is which improves over your original expected gain of Even if the hosts offers you to switch only part of the time, it pays to switch. Only in the case where we assume a malicious host (i.e. a host who entices you to switch based in the knowledge that you have the right door) would it pay not to switch.

67. Monty Hall Paradox (let S Make A Deal) 2.5. Monty.hall A GameTheoretic Analysis of the monty hall problem, Mathematics Magazine,723 (June 1999) 214-217 - D. Friedman; Monty Hall s three doors construction http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/monty-hall

Monty Hall Paradox (let's make a deal) 2.5. ==> monty.hall <== [decision] http://www.mathematik.uni-bielefeld.de/~sillke/ mailto:Torsten.Sillke@uni-bielefeld.de

68. The Monty Hall Problem - A State-space Explanation The monty hall problem a state-space explanation is better than a 1/3chance, so we tell Monty we ve switched our choice to green. http://www.vendian.org/mncharity/dir2/montyhall/

The Monty Hall Problem - a state-space explanation Here is yet another explanation of the answer. It requires tables and color Some other pages The WWW Tackles The Monty Hall Problem Monty Hall Problem Three Door Puzzle Monty Hall Problem There are 3 doors one of which has a Prize. So the universe is in one of 3 possible states P P P Now, you choose a door Looking inside, we see P in just one of the 3 possible states. P P P If the universe is in state1, we get the P. But if it is in or , we don't. Our chances are 1/3 for "P", and 2/3 for "-" Now "Monty" takes the other two doors P P P and opens one without the prize P P P Now which door do you want, red or green P P P In green , we get two P's! If the universe is in or , we get the P. Only if it is in state1, do we lose. So our chances are 2/3 for "P", and 1/3 for "-" As you know, a 2/3 chance of getting the Prize is better than a 1/3 chance so we tell "Monty" we've switched our choice to green Comments encouraged. Mitchell N Charity mcharity@lcs.mit.edu Notes: A friend called to ask about the Monty Hall Problem. I liked this explanation, but it didn't work over the phone. Not seeing it already online, I wrote this. This presentation is similar to this Answer to the Monty Hall Problem , but sufficiently different that I went ahead with this one anyway. Doables: History: 1998.Oct.15 Created.

69. The Monty Hall Problem (kottke.org) Jason Kottke s Web site, home to some of the world s finest hypertext products. http://www.kottke.org/remainder/04/04/5496.html

The Monty Hall Problem posted April 25, 2004 at 01:56 pm Reader Comments 17 comments gogol13 says: http://everything2.com/?node_id=1532241 http://www.qubit.org/library/intros/gmn/gmn.html by gogol13 on Apr 25, 2004 at 02:10 PM bing says: This guy's methodology is completely flawed. When he "re-spins" the wheel, the spinning should be relegated to the areas where the door Monty opens actually contains the car, that is when the contestant is not correct with his guess. This model splits those "re-spins" between those times and the times when the contestant has actuall guessed correctly. by bing on Apr 25, 2004 at 03:03 PM RotJ says: Are you talking about the first wheel or the second, Bing? Isn't it true that Monty never opens the door that contains the car, so your situation would never occur? by RotJ on Apr 25, 2004 at 05:00 PM bing says: The problem is with the second wheel: (1) The only way Monty Hall can ever pick the door with the car is if the contestant DOESN'T. (the red parts of the wheel) (2) If Monty Hall picks the other door without the car, the contestant switches w/o a problem. (3) If Monty Hall picks the door with the car, he will re-choose. Again, this will only happen if the contestant doesn't have the car.

70. The Monty Hall Problem The monty hall problem. Background. In the late 70s and early 80s there was agame show called The answers to the monty hall problems are not intuitive, http://amath.colorado.edu/outreach/demos/hshi/2004Sum/montyhall.html

The Monty Hall Problem Background In the late 70s and early 80s there was a game show called Let’s Make A Deal hosted by Monty Hall (after whom this type of problem is named). Since the 80s are making a comeback, Fox has decided to launch a new version of Let’s Make A Deal called When Deals Go Bad . You have been chosen to compete on the new show and want to maximize your chances of winning a good prize. The most popular contest is to give you the choice of three doors: Behind one door is 1 million dollars. Behind the other two doors are goats. You pick a door, say No. 1, and Monty, who knows what’s behind the other doors, opens another door, say No. 3, which has a goat behind it. You now have two choices: 1. Stay with your original guess 2. Switch doors. What should you do? Problem With $1 million at stake you don’t want to guess the wrong door, so you want someone from the Mathematics Department to read over your findings. Make sure you explain to them what you are working on. Part 1 The answers to the Monty Hall Problems are not intuitive, so when you are asked for your thoughts, any

71. Blargh Blog: The Monty Hall Problem If you re not familiar with the monty hall problem, go read about it, say, here,because if this post is successful it will spoil the problem without http://blarblog.blogspot.com/2005/01/monty-hall-problem.html

@import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?blogID=8111901"); @import url(http://www.blogger.com/css/navbar/main.css); @import url(http://www.blogger.com/css/navbar/1.css); Notify Blogger about objectionable content. What does this mean? BlogThis! Blargh Blog Wednesday, January 12, 2005 The Monty Hall Problem If you're not familiar with the Monty Hall Problem, go read about it, say, here , because if this post is successful it will spoil the problem without instilling any of the wonder, perplexity, confusion, and amazement that should result from your first exposure to the problem. Okay? Okay. This blog post describes a fictional scene that takes place in one of those TV producers' rooms, with lots of televisions and cool electronic equipment and comfortable chairs. Monty Hall sits in the room with a producer of Let's Make a Deal in front of a television screen. Producer : Look, Monty, you're having this same long exchange with the contestant on every single show, and I have some ideas about how to change it to make it better television. Take a look. The producer starts a clip on the television screen in front of them of a previous episode of Let's Make a Deal. In the clip, Monty Hall is standing, microphone in hand, with a Contestant in front of 3 doors. The clip plays:

72. A Simulation Of The Monty Hall Problem The monty hall problem can be stated as follows A gameshow host displays threeclosed doors. Behind one of the doors is a car. http://www.ram.org/computing/monty_hall/monty_hall.html

73. Empirical Solution Of The Monty Hall Problem (Perl) - Wikisource usr/bin/perl Approximate solution of the monty hall problem Use v to seeeach game. (default off) Use -i to set number of iterations. http://wikisource.org/wiki/Empirical_solution_of_the_Monty_Hall_problem_(Perl)

Empirical solution of the Monty Hall problem (Perl) From Wikisource This page was moved to http://en.wikisource.org/wiki/Empirical_solution_of_the_Monty_Hall_problem_(Perl) Please do not add anymore english pages to this site. Retrieved from " http://wikisource.org/wiki/Empirical_solution_of_the_Monty_Hall_problem_%28Perl%29 Categories Moved to en Views Article Discussion Edit History Personal tools Create an account or log in Navigation Main Page Community portal Scriptorium Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 10:26, 12 September 2005. Content is available under GNU Free Documentation License About Wikisource

74. Empirical Solution Of The Monty Hall Problem (Java) - Wikisource Empirical solution of the monty hall problem (Java). From Wikisource. The followingJava program simulates a million games and compares the success rate of http://wikisource.org/wiki/Empirical_solution_of_the_Monty_Hall_problem_(Java)

Empirical solution of the Monty Hall problem (Java) From Wikisource This page was moved to http://en.wikisource.org/wiki/Empirical_solution_of_the_Monty_Hall_problem_(Java) Please do not add anymore english pages to this site. Retrieved from " http://wikisource.org/wiki/Empirical_solution_of_the_Monty_Hall_problem_%28Java%29 Categories Moved to en Views Article Discussion Edit History Personal tools Create an account or log in Navigation Main Page Community portal Scriptorium Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 10:26, 12 September 2005. Content is available under GNU Free Documentation License About Wikisource

75. Read About Monty Hall Problem At WorldVillage Encyclopedia. Research Monty Hall monty hall problem. Everything you wanted to know about monty hall problem buthad no clue how to find it.. Learn about monty hall problem here! http://encyclopedia.worldvillage.com/s/b/Monty_Hall_problem

Culture Geography History Life ... WorldVillage Monty Hall problem From Wikipedia, the free encyclopedia. In search of a new car, you pick door number 2, Monty then shows you the goat behind door number 1 and asks if you'd like to switch to door number three. 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, say Jane, is shown three closed doors; behind one is a car, and behind each of the other two is a goat. Jane is allowed to open one door, and will win whatever is behind the door she opens; however, after Jane has selected a door but before she actually opens it, the host (who knows what is behind each door) opens another door to show that there is a goat behind it. The host then offers Jane the opportunity to change her mind and switch to the other closed door. The host knows what is behind each door, always opens one of the two remaining doors to reveal a goat, and always offers the chance to switch. Does Jane improve her chance of winning the car by switching or does it make no difference? The question has generated heated debate. The difficulty arises when someone assumes that Monty is choosing elements at random, or making the offer more often (or only) depending on his knowledge of the contestant's original choice. As stated, he

76. Andrewgraham.co.uk: Games - The Monty Hall Problem I ve written a simulation of the monty hall problem in Flash to try out for yourself.Get ready to play Let s Make a Deal! run the simulation Have a go! http://www.andrewgraham.co.uk/monty.html

the monty hall problem It's hard to believe, isn't it? After all, when the host opens one door there's a straight choice between two doors - one hiding a goat, the other the car. The argument that there's a fifty-fifty chance of winning is a very seductive one - but it's wrong. The problem is based on a real-life scenario from the American TV gameshow Let's Make a Deal and gets its name from the show's host. The problem gained notoriety when it became the subject of the syndicated American newspaper column Ask Marilyn . Responding to a correspondent who posed the problem, Marilyn vos Savant provided a detailed explanation of the correct answer, explaining that there is a two in three chance of winning the car by switching doors. The outcome is so different from our intuition that it is very hard to accept. Indeed, after her first explanation Marilyn received a vociferous postbag from a disbelieving public. Many letters came from indignant mathematicians who failed to agree with vos Savant. The true result, however, is quite easy to verify. I've written a simulation of the Monty Hall Problem in Flash to try out for yourself.

77. The Monty Hall Problem The monty hall problem. Standards of rationality are a lot more complicated thana handful As an example, are you familiar with the monty hall problem? http://personal.bgsu.edu/~roberth/monty.html

The Monty Hall Problem Standards of rationality are a lot more complicated than a handful of truisms like “don’t contradict yourself.” There are questions of what counts as evidence, how much and what quality of evidence is needed to establish a claim, or make it reasonable to believe or to overturn a contrary belief, how much weight should be accorded to testimony, how beliefs should be updated on the basis of new evidence and argument, what principles of reasoning should be accepted, and lots more. One area where the problem shows up is in reasoning about probabilities. Most people are pretty bad at it. (There’s a vast literature in psychology about evidence of human irrationality in dealing with probabilities.) And it’s not just that they make mistakes or are careless. If that were the explanation, you’d expect a random distribution around the correct answers. Instead, the answers people give are systematically biased. We come to the same wrong conclusions – which is to say we’re operating with mistaken principles of probabilistic reasoning. People who (eventually) get to be good at probabilistic reasoning generally have to go through a process of beating their intuitions into submission. As an example, are you familiar with the Monty Hall Problem? Imagine you’re a guest on a game show like “Let’s Make a Deal.” The host is about to offer you a choice of three doors behind which prizes may be. Once he hears your answer, but before he opens the door you’ve chosen, he’s going to give you an additional piece of information and ask if you want to change your selection. He will do this regardless of what you choose, and there are no tricks like sliding platforms behind the doors to shift the prizes around.

78. [faisal.com] The Monty Hall Problem The monty hall problem is a classic example of the nonintuitive nature ofprobability. You are playing a game. In the game, there are three doors with http://www.faisal.com/docs/monty.html

The Monty Hall Problem Home Archive Quotes Documents ... Contact Search: Note: for the time being, this page requires a "4.0 browser" in order to display colors properly. I apologize to those of you with older browsers, and also to anyone who has trouble with the page due to red/green color-blindness. The "Monty Hall Problem" is a classic example of the non-intuitive nature of probability: You are playing a game. In the game, there are three doors with prizes hidden behind them. One door hides a new car while the other two doors hide goats. If you pick the door with the car behind it, you win the car. You pick a door. At this point the game host opens another of the doors, revealing a goat. Now the game host offers you the opportunity to change your pick to the other door. Should you switch? Most people believe that there is no advantage to changing their pick: of the two remaining doors, one of them has the car, so they have a 50% chance of winning. In fact, this is incorrect: while 1 of the doors will have the car behind it, 2/3 of the time it will be the other door. It is generally to your advantage to switch.

79. The Monty Hall Problem re The monty hall problem 6/28/2004 651 PM John de Pillis. You might be interestedin a new graphical proof of the monty hall problem. http://www.peterprovost.org/archive/2003/06/10/545.aspx

Home Articles Images Links ... ATOM Feed Calendar Aug September 2005 Oct S M T W T F S Suggested Reading Blog Stats Posts - 1117 Stories - 6 Comments - 1243 Trackbacks - 287 Logos and Stuff The content of this site is my own personal opinion and does not in any way represent my employer, it's subsideries or affiliates. These postings are provided "AS IS" with no warranties, and confer no rights. The Monty Hall Problem Brad Wilson posted a C# demonstration of the classic Monty Hall Problem . I remember getting into a huge argument with some of my co-workers at a previous job and I basically did the same thing. I sat down and busted out a quick program that played the game. I think it was in VB3 though... :) The most interesting thing is to see people in Brad's comments arguing that this isn't real. That it is a hoax or something. It isn't. It worked EVERY TIME. Probabilities don't lie. posted on Tuesday, June 10, 2003 11:55 PM Rating: Feedback re: The Monty Hall Problem 6/28/2004 6:51 PM John de Pillis You might be interested in a new graphical proof of the Monty Hall problem. Please see my website http://math.ucr.edu/~jdp/Monty_Hall/Monty_Hall.html

80. Crooked Timber » » Monty Hall Problem I once spent three weeks arguing the monty hall problem with a friend. He was asmart guy, but he simply refused to accept the math. http://crookedtimber.org/2004/07/20/monty-hall-problem/

Crooked Timber Liberal Islamophobia Main Monty Hall Problem Posted by Brian Via Justin Leiber a playable version of the Monty Hall Problem posted on Tuesday, July 20th, 2004 at 2:01 pm comments Your link makes the decision for us! You should change it to http://math.ucsd.edu/~crypto/Monty/monty.html Posted by Martey July 20th, 2004 at 2:32 pm Posted by Motoko Kusanagi · July 20th, 2004 at 2:54 pm Posted by Brian Weatherson July 20th, 2004 at 3:32 pm Oh, yeah, you would post about the MHP only two months after I took down my nearly ten-year-old MHP site (which was probably the most famous and oft-referenced MHP sure MHP mis understand it. And that last bit is why it fascinates me. The misunderstanding of the MHP is, in my opinion, exemplary of a very common but interesting variety of human miscomprehension. I moved to my own personal domain from my old ISP MHP Posted by Keith M Ellis July 20th, 2004 at 3:38 pm Posted by eudoxis · July 20th, 2004 at 4:03 pm I once spent three weeks arguing the Monty Hall problem with a friend. He was a smart guy, but he simply refused anyone Posted by Morat July 20th, 2004 at 4:08 pm

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