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Thread: Let's pick a door..

  1. #1
    digitus impudicus
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    Let's pick a door..

    Say that you're on a game show with a chance to win a car.

    There are three doors. Behind one of the doors, is the new car.

    The host asks you to pick a door.

    You do and point to it.

    The host walks up to one of the doors you didn't pick and opens it. Behind that door is a pile of sand.

    He asks if you want to change your choice from the two doors left.

    Should you change your choice to the other door?
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  3. #2
    *****istrator Marcus's Avatar
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    Should you? No. You're odds just went from 33% to 50% that you were right the first time.
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  4. #3
    digitus impudicus
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    Anyone else?
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  5. #4
    3rd Class whoknows's Avatar
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    Change the door There may only be 2 doors now but you still picked while the odds were 1 in 3, now you can pick at 1 in 2
    Last edited by whoknows; 9th January 2017 at 01:39 PM.

  6. #5
    Learning the Ropes
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    First choice. No reason that I can see to changes.

  7. #6
    Slowly improving Brenton's Avatar
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    Take the sand... it does not depreciate like a car... or cost rego and insurance each year... so you actually are saving money.

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  9. #7
    Grand Master Bowman scott p's Avatar
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    https://en.wikipedia.org/wiki/Monty_Hall_problem

    https://betterexplained.com/articles...-hall-problem/


    I honestly don't understand the reasoning behind this one, having read it several times. it doesn't matter that one choice has been shown to be incorrect. it makes no impact on the fact that there are still 2 choices, and thus a 50% chance of being right.

  10. #8
    Slowly improving Brenton's Avatar
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    Andy now I feel ripped off... I'd rather the goat than the sand... at least I would not have to mow the lawn anymore.

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  12. #9
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    Quote Originally Posted by scott p View Post
    https://en.wikipedia.org/wiki/Monty_Hall_problem

    https://betterexplained.com/articles...-hall-problem/


    I honestly don't understand the reasoning behind this one, having read it several times. it doesn't matter that one choice has been shown to be incorrect. it makes no impact on the fact that there are still 2 choices, and thus a 50% chance of being right.
    You read it several times??? I struggled through it once. Even after being bamboozled by the maths I still only feel it's 50/50.

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  14. #10
    digitus impudicus
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    Quote Originally Posted by scott p View Post
    it makes no impact on the fact that there are still 2 choices, and thus a 50% chance of being right.
    This is the bit that I like because you can do heaps of the computer simulations online that prove beyond a doubt that you're better switching.
    You can even do manual simulations that prove that it's better to switch.
    You can even watch myth busters do exactly the same thing and discover that it's best to switch.

    And this is actually one of the better explanations as to why:
    https://betterexplained.com/articles...-hall-problem/


    The issue is sticking to your assumption that the odds don't change and totally ignoring the fact that the host, who knows something has deliberately chosen a wrong door.

    The explanation on that page is on a few others.

    Understanding The Game Filter

    Let’s see why removing doors makes switching attractive. Instead of the regular game, imagine this variant:

    There are 100 doors to pick from in the beginning
    You pick one door
    The host opens 99 others, finds the sand and opens all but 1

    Do you stick with your original door (1/100), or the other door, which was filtered from 99?

    It’s a bit clearer: The host is taking a set of 99 choices and improving them by removing 98 sand piles. When he’s done, he has the top door out of 99 for you to pick.

    Your decision: Do you want a random door out of 100 (initial guess) or the best door out of 99? Said another way, do you want 1 random chance or the best of 99 random chances?
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  15. #11
    digitus impudicus
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  16. #12
    Learning the Ropes
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    Two choices Andrew. 50/50. All the light bending force in the universe won't change that. Blinded by science comes to mind here.

  17. #13
    digitus impudicus
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    It's one of those things that looks like it's 50/50, but all practical demonstrations prove it beyond doubt. If you do this 100 times, changing every time, you'll win the car in 66 percent (or damn close) of times.

    If you keep to the same choice, you'll only win the car 33 percent of the time.

    http://www.grand-illusions.com/simulator/montysim.htm

    (ignore the warning. It should work with all modern browsers)
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  18. #14
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    Will that work with two-up?

  19. #15
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    Or if Occam gave me the choice of a dull and sharp razor.

  20. #16
    *****istrator Marcus's Avatar
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    OK so why?
    Whether you have one false one removed or not should not matter.
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  21. #17
    digitus impudicus
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    It's not straight chance any more when the host removes a dud choice.

    The explanations go through it several ways if you don't want to do the math. And let's face it, I never do until it's pretty simple.

    The 100 doors explanation makes sense to me. Just remember it's not just ONE event. That's called "too small a sample size" and what most people get wrong.

    One coin flip coming up heads doesn't mean the next ten will. And if they did, it doesn't mean that it will happen for the next.

    But changing your initial pick in this case means that two times out of three, you'll win the car.

    Sticking with your initial choice means that only one time out of three you will.

    You're twice as likely to win if you change.

    I like to pose these questions to drive the point home that people totally suck at understanding statistics and how they work. The human brain is wired to get them wrong.

    This is why people can't tell **** from clay when they assess how well things are performing unless they've actually got hard data.

    Archers with hard data don't come along very often.

    What am I not saying?
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  22. #18
    *****istrator Marcus's Avatar
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    But if I KNOW one option is removed that shouldn't impact which of the two remaining comes up over the other.
    Its a matrix glitch I'm sure.
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  23. #19
    Slowly improving Brenton's Avatar
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    The whole thing hinges on whether or not the host actually knows where the prize is or not, and whether they WILL choose to leave the door with a car "in play" IF it is not chosen by the guest.

    In the 3 door scenario.
    If the host knows where the car is and WILL NOT OPEN it if the guest does not choose it... instead, deliberately choosing the sand (goat).
    - Guest has 1/3 change of getting car, this means the host can choose the car 2/3 of the time (and WILL/MUST do so). Once the 3rd door with the sand (goat) is DELIBERATELY eliminated by the host the other door is 2/3 likely to be the car because they can can choose it 2/3 of the time ...so the guest is better off swapping to it as it will be the car more often than not (2/3 of the time)

    If the host does not know where the car is.
    - The guest has 1/3 chance of choosing the car, the host has a 1/3 chance of choosing the car and the unopened door is a 1/3 change of being the car.
    If the door first door the host opens is actually the car (1/3 chance of it being the car)... then the guest does not win a car (this will happen 1/3 of the time) However, if it is not the car then last unchoosen door (which was = 1/3) is still he same chance of being the car as the one originally chosen by the guest which was 1/3.

    1/3 and 1/3 original chances becomes = a 1/2 or 50/50 or 50% of being either of the two remains doors. (guest door and unoppened door)
    So now that there are two remaining choices with equal chance the guest can win a car 50% of the time with EITHER remaining door. The odds have NOW improved BECAUSE they were lucky that the host did not accidentally choose the car.
    Last edited by Brenton; 10th January 2017 at 02:50 AM.

  24. #20
    Grand Master Bowman scott p's Avatar
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    But the host will always pick the door with the goat, so the choice is still 50:50.

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