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Two Goats, One Car!

  • 25-01-2011 12:57PM
    #1
    Closed Accounts Posts: 17,689 ✭✭✭✭OutlawPete


    Nope, not that - although I do have that clip with some fine goats via PM if you want it ;)

    This is from the movie 21, where Kevin Spacey poses the following scenario:




    Many of you may know what the answer to this is and know what the name of this problem is, but would ask that you hold off posting that Wiki page for awhile, so that we can see what people would choose when presented with the problem for the first time. Even certain mathematicians have argued over this, so no shame in not selecting the right answer here and the Poll is private so as to prevent any condescending finger pointing.


    So, to repeat: you are on a Game Show and given the choice of one of three doors, behind two of them stand: Goats .. and the other: a Car!

    The Game Show host knows where the Car is and after you choose, he opens one of the other doors to reveal a Goat!

    He then offers you the chance to change your mind and go for the other remaining door ..

    So, if you were on that Game Show: would you take up the offer and switch doors or would stick with your original choice?

    Is it in your advantage to switch in other words?

    I myself like Goats, and so would be just as happy to lose.

    What would you choose? (Read the OP only before voting) 53 votes

    Stick
    0% 0 votes
    Switch
    37% 20 votes
    How can she slap?
    62% 33 votes


«13

Comments

  • Registered Users, Registered Users 2 Posts: 2,567 ✭✭✭extra-ordinary_


    Atari jaguar?


  • Registered Users, Registered Users 2 Posts: 2,779 ✭✭✭Spunge


    You should always switch, or so i've heard.


  • Registered Users, Registered Users 2 Posts: 3,808 ✭✭✭FatherLen


    i dunno prob stay with the same door.



    am i right?


  • Closed Accounts Posts: 3,783 ✭✭✭Pj!




  • Registered Users, Registered Users 2 Posts: 2,059 ✭✭✭Screaminmidget


    Sounds like a ****e gameshow tbh.
    I think most people would switch, for the simle fat that you odds of winning the car have gone from 3/1 to 2/1??? or am i missing something??


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  • Closed Accounts Posts: 90 ✭✭hypervalve


    Pj! wrote: »

    You just couldn't resist could you?


  • Closed Accounts Posts: 3,783 ✭✭✭Pj!


    No


  • Registered Users, Registered Users 2 Posts: 3,808 ✭✭✭FatherLen


    Pj! wrote: »
    you ruined my day.









    and this thread


  • Posts: 81,308 CMod ✭✭✭✭ Van Dirty Shuffleboard


    This is psychology plus probability isn't it? I never became convinced of it on pure probability :(
    So for the game show I'd switch but in pure theory I'd say you're ok to stick :confused:


  • Closed Accounts Posts: 9,495 ✭✭✭Mr. Presentable


    Pj! wrote: »

    Only took four replies :(


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  • Closed Accounts Posts: 11,148 ✭✭✭✭KnifeWRENCH


    I haven't learned to drive yet. I have no use for a car.

    I'll have the goat, please.


  • Registered Users, Registered Users 2 Posts: 2,481 ✭✭✭Fremen


    Fúck your honda civic. I want a goat.

    Meeeh-eeeeh-eeeeh-eeeeeeh!


  • Moderators, Arts Moderators Posts: 36,496 Mod ✭✭✭✭pickarooney


    I reject all mathematical 'evidence' that it makes a difference either way.


  • Registered Users, Registered Users 2 Posts: 10,758 ✭✭✭✭TeddyTedson


    Well there's 2 doors left so it's a 50/50 chance. Simples!:p



  • Registered Users, Registered Users 2 Posts: 1,106 ✭✭✭flyton5




  • Registered Users, Registered Users 2 Posts: 14,728 ✭✭✭✭Earthhorse


    Every time I see this again I think "This can't be right". But then I read the explanation and it appears it its. It feels wrong though.


  • Moderators, Arts Moderators Posts: 36,496 Mod ✭✭✭✭pickarooney


    I get the explanation but I think it's based on the flawed premise of 'changing' the original 1/3 choice. Essentially, once the goat is revealed you're faced with an entirely new choice between two doors and you pick A or B, 50:50 - what you originally chose is no longer directly relevant.

    In fact, the whole first part - the original choice and the reveal, are completely irrelevant. You can't 'lose' as your choice is not revealed. Whatever you do, the host will simply reveal a goat and leave you with two doors, behind one of which is a car. The idea of a 2/3 probability for two options is false logic.


  • Closed Accounts Posts: 17,689 ✭✭✭✭OutlawPete


    Well, seen as it's now been revealed s 'Monty Hall' now :)

    Here's the full clip:



    Good film by the way and here's an interesting article on the Monty Hall problem from American Scientist:
    Monty Hall Redux
    How do you persuade yourself that a statement is true or an answer is correct? How do you persuade someone else? Various subcultures have evolved strategies and devices for dealing with these issues—scientific experiment, mathematical proof, trial by jury, consulting holy writ or the Guinness Book of Records. The trouble is, these methods are not perfectly reliable. Sometimes they convince people of a falsehood or fail to convince them of a truth.

    In the July-August issue of American Scientist I reviewed Paul J. Nahin's Digital Dice: Computational Solutions to Practical Probability Problems, which advocates computer simulation as an additional way of establishing truth in at least one domain, that of probability calculations. To introduce the theme, I revisited the famous Monty Hall affair of 1990, in which a number of mathematicians and other smart people took opposite sides in a dispute over probabilities in the television game show Let's Make a Deal. (The game-show situation is explained at the end of this essay.)

    When I chose this example, I thought the controversy had faded away years ago, and that I could focus on methodology rather than outcome. Adopting Nahin's approach, I wrote a simple computer simulation and got the results I expected, supporting the view that switching doors in the game yields a two-thirds chance of winning. But the controversy is not over. To my surprise, several readers took issue with my conclusion. (You can read many of their comments in their entirety here.) For example, Bruce Sampsell of Chapel Hill, N.C., wrote:
    The initial statement of the problem as three doors with a prize randomly placed behind them does have a 1/3 probability of being the right choice prior to the opening of a door that doesn't contain a prize. Once a door is opened without the prize, the problem changes to two doors, each of which is equally likely to have the prize behind it. There is no advantage to switching doors.
    It seems we are at an impasse. Neither the mathematical arguments given in my review nor the simulation results I reported there were enough to persuade Sampsell. On the other hand, Sampsell's assertion does not persuade me. How can we settle our differences? I could try further arguments and analysis; so could Sampsell. I could publish my simulation program so that others could run it for themselves; but my program could have an error or might be deliberately rigged to give the result I favor. There's an online version of the game created to accompany a John Tierney article in the New York Times; but in some quarters even the Times is not above suspicion.

    Another correspondent, Ingrid Eisenstadter of New York City, put it this way:
    So, it doesn't really matter that Mr. Hayes has written a program showing that you should switch doors after one has been eliminated, because it is based on the notion that one cannot reselect the original door, leaving arbitrary assumptions, word games and personal opinions. I would be happy to provide a similar computer program showing that the world is flat.
    The mention of assumptions and word games introduces an important caveat. We can't expect to reach the same conclusions unless we all play by the same rules and understand the problem in the same way. A number of commentators—going back to the first wave of controversy in the early 1990s—have pointed out that certain assumptions are crucial to the analysis of the Monty Hall puzzle. In particular, it's important that Monty Hall must always open one door and offer the option of switching, and the door opened can never be the one initially chosen by the contestant, nor can it be the winning door.

    Differences in the interpretation of the problem statement doubtless account for many of the continuing disputes over the Monty Hall puzzle. But there is a residuum of disagreement that is not so easily explained away. In another letter, David Lippmann of Austin, Texas, offers this analysis:
    If Monty Hall always opens a door that does not conceal the prize and that the contestant has not chosen, there are only eight possible outcomes. Suppose that the doors are A, B and C and that the prize is behind C. The possible pairs of guesses are A followed by A, A followed by C, B followed by B, B followed by C, C followed by B, C followed by C, C followed by A, and C followed by C. Four of the second guesses are C, independent of what the first guess was. The probability that the contestant will win the prize is 1/2.
    Lippmann and I apparently share the same assumptions about the game-show rules, and I even agree with his conclusion, in a limited sense: If the player chooses randomly whether to stay or switch, then the probability of winning is indeed 1/2. Nevertheless, I believe that Lippmann's analysis is incorrect, and a player who always switches doors has a two-thirds chance of winning. (The source of the error is that the eight cases do not all have the same probability. Monty Hall sometimes has two choices about which door to open, sometimes only one.)

    The issue that concerns me here is not who is right and who is wrong about the odds of winning on Let's Make a Deal. The issue is how I can persuade anyone that my answer—or any particular answer—is correct. I have been stewing about this for several weeks, frustrated that I am powerless to communicate what I take to be a simple truth. But I've finally decided that what the episode demonstrates is the vigorous good health of the scientific enterprise.

    Making progress in the sciences requires that we reach agreement about answers to questions, and then move on. Endless debate (think of global warming) is fruitless debate. In the Monty Hall case, this social process has actually worked quite well. A consensus has indeed been reached; the mathematical community at large has made up its mind and considers the matter settled. But consensus is not the same as unanimity, and dissenters should not be stifled. The fact is, when it comes to matters like Monty Hall, I'm not sufficiently skeptical. I know what answer I'm supposed to get, and I allow that to bias my thinking. It should be welcome news that a few others are willing to think for themselves and challenge the received doctrine. Even though they're wrong.

    All the same, in the future I think I'll find some other example when I need to illustrate probability calculations.

    The Monty Hall Probability Puzzle
    The puzzle that has entered the lore of mathematics is not exactly the same as the game played on television. The situation in the mathematical puzzle is this: You are shown three doors and told that exactly one of them has a prize behind it. After you choose a door, Monty Hall (who knows where the prize is) opens one of the two unchosen doors, showing that the prize is not there. You are then offered a choice: Stick with your original door or switch to the remaining unopened door.


  • Registered Users, Registered Users 2 Posts: 30,532 ✭✭✭✭Lumen


    Earthhorse wrote: »
    Every time I see this again I think "This can't be right". But then I read the explanation and it appears it its.

    Me too. Then someone posts this...
    Well there's 2 doors left so it's a 50/50 chance. Simples!:p

    ...and I'm back to square one.


  • Closed Accounts Posts: 17,689 ✭✭✭✭OutlawPete


    Lumen wrote: »
    ...and I'm back to square one.

    Aye and as all independent events with 1/2 probability (such as flipping a coin) are always 50:50 chances, it appears that way.

    But because of what has occurred previously (the host was going to show you a Goat no matter what Door you chose) the chances are increased by switching, as if he didn't open the other Door - the chances could be that the reason for that was because it contained the car.


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  • Registered Users, Registered Users 2 Posts: 191 ✭✭dougal-maguire


    Lumen wrote: »
    Me too. Then someone posts this...



    ...and I'm back to square one.

    maybe this is totaly wrong,but the way im lookin at it is chances of picking a goat.you have a 66% chance of picking a goat,if you pick the goat he has to eliminate the other goat,so you switch.if you stick to this you have a 66% chance of picking the car when you switch.

    you have a 33% chance of picking the car from the start,he eliminates a goat,you now have a 50% chance that you picked the car.if you stick you'll win the car 50% of the time if you switch you'll win the car 66% of the time. :cool:


    so would this logic be of any benefit to deal or no deal contestants?


  • Registered Users, Registered Users 2 Posts: 12,556 ✭✭✭✭AckwelFoley


    The odds of winning are good.

    2 goats one car.


    You cant fcuk a car.


    Jackpot


  • Registered Users, Registered Users 2 Posts: 14,728 ✭✭✭✭Earthhorse


    OutlawPete wrote: »
    But because of what has occurred previously (the host was going to show you a Goat no matter what Door you chose) the chances are increased by switching, as if he didn't open the other Door - the chances could be that the reason for that was because it contained the car.

    Yes, and this is where I believe pickarooney is wrong. What goes on before the second choice is actually relevant in determining the probability. I don't know what practical application the problem has though.


  • Posts: 81,308 CMod ✭✭✭✭ Van Dirty Shuffleboard


    I think if it was a, b, c and then one door was *randomly* picked & eliminated, you would then have 50/50 assuming the door *randomly* picked was not the car.

    But because monty knows which door is the car, I think that takes it out of random probability realms, so the explanation probably does make sense for that situation.
    "maybe this is totaly wrong,but the way im lookin at it is chances of picking a goat.you have a 66% chance of picking a goat,if you pick the goat he has to eliminate the other goat,so you switch" yeah, that


  • Registered Users, Registered Users 2 Posts: 1,313 ✭✭✭fabbydabby


    A lot of people know about this problem because of that bestselling book the Curious Incident of the Dog in the night


  • Moderators, Arts Moderators Posts: 36,496 Mod ✭✭✭✭pickarooney


    maybe this is totaly wrong,but the way im lookin at it is chances of picking a goat.you have a 66% chance of picking a goat,if you pick the goat he has to eliminate the other goat,so you switch.if you stick to this you have a 66% chance of picking the car when you switch.

    you have a 33% chance of picking the car from the start,he eliminates a goat,you now have a 50% chance that you picked the car.if you stick you'll win the car 50% of the time if you switch you'll win the car 66% of the time. :cool:


    so would this logic be of any benefit to deal or no deal contestants?

    But imagine a slightly different game where there are three doors. One is open with a goat behind it and two are closed. One has a car. You choose. No game show host, no music, just the doors.

    Obviously, nobody who wants the car is going to pick the open door. That leaves two doors with one goat and one car. 50:50.

    Here's the crux of the difference of opinion and until soemone adequately explains the causality of the initial rigmarole with the guess and the non-random opened door there is no chance that the 50/50 camp will ever be swayed.


  • Registered Users, Registered Users 2 Posts: 14,728 ✭✭✭✭Earthhorse


    But imagine a slightly different game where there are three doors. One is open with a goat behind it and two are closed. One has a car. You choose. No game show host, no music, just the doors.

    Obviously, nobody who wants the car is going to pick the open door. That leaves two doors with one goat and one car. 50:50.

    Here's the crux of the difference of opinion and until soemone adequately explains the causality of the initial rigmarole with the guess and the non-random opened door there is no chance that the 50/50 camp will ever be swayed.
    Not sure anyone can restate the problem, or solution, in such a way that it will sway you. Best way to convince yourself is to set up an experiment if you have enough people to do this with. Have one group follow a strategy of switching and the other of non-switching and see which group wins more. :)


  • Closed Accounts Posts: 17,689 ✭✭✭✭OutlawPete


    Earthhorse wrote: »
    Best way to convince yourself is to set up an experiment if you have enough people to do this with. Have one group follow a strategy of switching and the other of non-switching and see which group wins more. :)

    That's done here, very scripted though:



  • Moderators, Arts Moderators Posts: 36,496 Mod ✭✭✭✭pickarooney


    I first approached the problem with a completely open mind but I'm afraid I've become attached to my reasoning now. The last time I tried to prove something mathematically sound to myself through experimentation (the old shared birthday question) I ended up 'proving' it wrong over and over.

    I'm sure someone has a way of explaining the link between part one and part two. It looks like bluewolf has been successfully won over, bless her little actuarial socks :P


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  • Posts: 81,308 CMod ✭✭✭✭ Van Dirty Shuffleboard


    I first approached the problem with a completely open mind but I'm afraid I've become attached to my reasoning now. The last time I tried to prove something mathematically sound to myself through experimentation (the old shared birthday question) I ended up 'proving' it wrong over and over.

    I'm sure someone has a way of explaining the link between part one and part two. It looks like bluewolf has been successfully won over, bless her little actuarial socks :P

    Only because they're not unbiased random independent events :pac:
    if it was random I'd still stick with 50 50


    edit: interestingly, a friend once decided to experiment to test the hypothesis that it's 66%/switch - she did end up "proving" it in the majority of the runs


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