User Tag List

Page 3 of 3 FirstFirst 123
Results 41 to 58 of 58

Thread: Let's pick a door..

  1. #41
    Learning the Ropes
    Join Date
    Aug 2013
    Posts
    83
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    500
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    125
    Quote Originally Posted by scott p View Post
    so we now have the original door, and the one remaining door.

    that's a 50/50 chance. all the removal of the known-incorrect doors has done is increase the chances of the initial choice being right.
    The random event is actually the placement of the prize. Imagine the organisers throw a die to decide where to put the prize. Whether or not there is a prize behind the door you chose depends on the die thrown and provided there isn't some shuffling of the prize behind the scenes during the competition, that never changes. How could it? The car, the compartment it is in and the door are all totally unaffected by by opening or closing other doors.

  2. #42
    *****istrator Marcus's Avatar
    Join Date
    Jun 2001
    Location
    Bleeding Green
    Posts
    26,388
    Tournaments Joined
    2
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    0
    Mentioned
    2 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    966590
    I'm going to buy a deck of cards and try this with an unaware subject.
    Last edited by Marcus; 11th January 2017 at 04:57 PM.
    Urban Archery
    Carbon Express
    Beiter
    Truball/Axcel
    Redback Strings

    Before enlightenment: Chop wood, carry water
    After enlightenment: Chop wood, carry water

  3. #43
    Learning the Ropes
    Join Date
    Apr 2015
    Posts
    89
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    500
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    337
    It's pretty simple.
    Do you want 33.3% chance of winning a new car, or 66.7% chance?

  4. #44
    Grand Master Bowman scott p's Avatar
    Join Date
    Jun 2011
    Location
    Keysborough, Melbourne
    Posts
    2,788
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    450
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    74955
    Quote Originally Posted by Matrix Makeover View Post
    I think this is where you are coming unstuck. The host will know if you have picked the right door or not. To keep the suspense going, they will not open the door you first pick - so they have the option of two doors.[/QUOTE

    IF you have picked the right door first, they can open either of the other two doors. So the host has a 50/50 choice.
    IF you have picked the wrong door first, then there is only one door that they can open (the other wrong door) because they again want to keep the suspense going. Thus the host has zero percent choice in which door they open.
    if I pick the right door the first time, of course the host will open a door they know is wrong and perpetuate the suspense. that leaves me with a choice of two doors (50%), and if I change, I lose.

    if I pick a wrong door the first time, the host again opens a door they know full well is wrong. that again leaves me with exactly the same choice, because I *know* they will open a wrong door no matter what, so I face exactly the same choice - 50% win, 50% lose.

    Edit - I think I glued the maths - because you have a 2/3rds chance of picking the wrong door first time, the host has to open the other wrong door 66% of the time?
    no, the host will open the wrong door 100% of the time. you will *always* have a 50% chance of winning, regardless of the accuracy of your initial pick.


    the only way out of that conclusion is if I can be sure that the host *will* tell me if I have picked correctly the first time. if not, the choice is incredibly simple - one out of two.

  5. #45
    Learning the Ropes
    Join Date
    Aug 2013
    Posts
    83
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    500
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    125
    Quote Originally Posted by scott p View Post
    if not, the choice is incredibly simple - one out of two.
    Indeed it is one out of two, but not two equally likely outcomes. You can only work out probabilities by counting the possible outcomes when the outcomes are equally likely and independent.

  6. #46
    digitus impudicus
    Join Date
    May 2007
    Location
    Canberra. Aus.
    Posts
    6,955
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    300
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    13033
    By now, anyone who has actually bothered to do the simulation, or the exercise in real life will have discovered that there are no 50/50 chances involved in the three door puzzle AT ALL.
    It's either a one chance in three if you don't switch or a two chances in three if you do.

    One of these is worse than 50/50. The other is much better.

    If the chances are 50/50, with a reasonable amount of tries, the results will be split down the middle. This absolutely NEVER happens with either option in this scenario.

    You can test it out if you think that I'm lying. scott p is actually arguing against an established fact which is quite consistently provable.

    Most people with common sense would have gone quiet by now. This thread has been more educational than I ever thought possible.
    Status is not defined by the amount of gear in your signature.
    Performance cannot be purchased.

    "The Internet offers everything - except quality control" - K. Anders Ericsson.


  7. #47
    Learning the Ropes
    Join Date
    Aug 2013
    Posts
    83
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    500
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    125
    Quote Originally Posted by Andy! View Post
    Most people with common sense would have gone quiet by now. This thread has been more educational than I ever thought possible.
    Intuition in probability can be very wrong but very strongly held. I once had had a long argument with a fellow engineering student, who should have known better, and was absolutely convinced he could win at two-up by waiting until there had been a run of HH and betting TT.

  8. #48
    Grand Master Bowman scott p's Avatar
    Join Date
    Jun 2011
    Location
    Keysborough, Melbourne
    Posts
    2,788
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    450
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    74955
    Quote Originally Posted by iandall View Post
    Indeed it is one out of two, but not two equally likely outcomes. You can only work out probabilities by counting the possible outcomes when the outcomes are equally likely and independent.
    by all means please tell me how out out of two is not an equal outcome.

    when doing so, make sure you tell me how I don't know the initial choice is not correct, because the entire assumption so far is based on the theorem that the initial choice is not correct.

  9. #49
    *****istrator Marcus's Avatar
    Join Date
    Jun 2001
    Location
    Bleeding Green
    Posts
    26,388
    Tournaments Joined
    2
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    0
    Mentioned
    2 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    966590
    Had it explained to me well, and yep, I've accepted that switching will produce the better result and yes it does make sense.
    Urban Archery
    Carbon Express
    Beiter
    Truball/Axcel
    Redback Strings

    Before enlightenment: Chop wood, carry water
    After enlightenment: Chop wood, carry water

  10. #50
    digitus impudicus
    Join Date
    May 2007
    Location
    Canberra. Aus.
    Posts
    6,955
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    300
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    13033
    Somebody had best explain what the difference is between certainty and probability.
    Status is not defined by the amount of gear in your signature.
    Performance cannot be purchased.

    "The Internet offers everything - except quality control" - K. Anders Ericsson.


  11. #51
    3rd Class
    Join Date
    Jan 2014
    Posts
    242
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    500
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    202
    Quote Originally Posted by Andy! View Post
    Somebody had best explain what the difference is between certainty and probability.
    Are you certain that will work? Probably not.

  12. Thanks Andy!, xracer, Marcus thanked for this post
  13. #52
    Learning the Ropes
    Join Date
    Aug 2013
    Posts
    83
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    500
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    125
    Quote Originally Posted by scott p View Post
    by all means please tell me how out out of two is not an equal outcome.
    Really it is the other way around. Equally likely outcomes are the exception, not the rule, and you really have to justify making that assumption. In games of chance the justification is usually on the basis of symmetry: the die is symmetrical apart from the dots which are presumed not to be significant. In this case we can use symmetry to argue that the initial probabilities are all 1/3. However, once the host opens a door, the game becomes asymmetrical because the host never opens the door the contestant has selected. We would need some other way to argue that the outcomes are equally likely. But they are not so we can't!

    As for showing how they are not equal outcomes, use P(x) as the probability that the prize is behind door x. Then P(A) = P(B) = P(C). Assume ("without loss of generality" as mathematicians say) that the contestant initially chooses A and the host opens C. There are two ways to proceed from here: the easy way and the hard way. In the easy way, lets use P(x') to be the probability that the prize is behind door x after door C has been opened. Now recognize that P(A') = P(A) = 1/3 (i.e. P(A) is unchanged), P(C') = 0 and P(A') + P(B') + P(C') = 1. Then P(B') = 1 - P(A') = 2/3.

    The hard way is to use conditional probability. Use P(x|y) to mean the probability of x given y has occurred. Now Bayes rule states that P(x|y) * P(y) = P(y|x) * P(x). So P(B|Opens(C)) * P(Opens(C)) = P(Opens(C) | B) * P(B). Now P(Opens(C) | B) = 1 according to the rules of the game. Also P(Opens(C)) + P(Opens(B)) = 1 and from symmetry: P(Opens(C)) = P(Opens(B) = 1/2. Solving for P(B|Opens(C)) = (1/3)/(1/2) = 2/3. Also P(A|Opens(C)) = 1 - P(B|Opens(C)) = 1/3. Since P(A|Opens(C) is the same as P(A') in the easy solution and P(B|Opens(C)) is the same as P(B'), the easy method is confirmed.

    Quote Originally Posted by scott p View Post
    when doing so, make sure you tell me how I don't know the initial choice is not correct, because the entire assumption so far is based on the theorem that the initial choice is not correct.
    There is nothing in the above which assumes initial choice is not correct. That would result in P(B) = 1 (certainty) and no one has argued that.

  14. #53
    1st Class Matrix Makeover's Avatar
    Join Date
    Jul 2011
    Location
    Wairarapa
    Posts
    776
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    500
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    14856
    Quote Originally Posted by scott p View Post
    by all means please tell me how out out of two is not an equal outcome.

    when doing so, make sure you tell me how I don't know the initial choice is not correct, because the entire assumption so far is based on the theorem that the initial choice is not correct.
    The entire assumption is 2/3rds of the time the initial choice is not correct.
    In misquoting me, you are correct that the host picks a wrong door every time (my point was that if you had picked one of the wrong doors, then they have no choice but to pick THE OTHER wrong door - but your explanation is simpler).

    Thus at this point in the game, nobody has picked the right door 2/3rds of the time. So 2/3rds of the time it is better to change your mind. Of course 1/3 of the time your original pick will be correct. But let's say you got to play 100 times (with $1000 up for grabs each time). Changing your choice would give you approx $66 000, staying with your original choice = ~$33 000
    "I used to read, but it's faster to make up stuff" - Wally (Dilbert)

  15. #54
    Grand Master Bowman scott p's Avatar
    Join Date
    Jun 2011
    Location
    Keysborough, Melbourne
    Posts
    2,788
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    450
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    74955
    I did not misquote you. I quoted the relevant part to respond to.

    Quote Originally Posted by Matrix Makeover View Post
    Thus at this point in the game, nobody has picked the right door 2/3rds of the time.
    but how do I know that? all I know is that the host is going to open an incorrect door, which they will do every single time. that leaves a choice of 2 doors.

    if I pick the right one the first time, I still have a choice of 2 doors.
    if I pick the wrong one the first time, I still have the identical choice of 2 doors.

    I've read the explanations. every single one of them relies on the concept that because the initial choice is out of three, that's the end result. removing one of the incorrect doors changes that equation.

    I'm over going around in circles on this one.

  16. #55
    Learning the Ropes
    Join Date
    Jul 2011
    Posts
    53
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    500
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    0
    Hey Scott I'll try to explain it a bit differently.

    Rules are the same.

    Contestant gets to pick 1 door.
    Host knows the winning door.
    Host opens up all remaining doors after your pick except yours and one other.
    The winning door must not be opened leaving you with 2 choices.

    Now instead of 3 doors the we have 100

    You pick one...your chance of winning with that door is 1/100,1% and again that never changes(instead of 33%).
    The remaining chances of winning lie in the other 99 doors 99/100, 99% chance of winning(instead of 66%).
    The game show host now opens 98 other doors revealing goats, leaving 1 other door for you to choose from.
    The winning door has not been opened.
    You have 2 doors to choose from, a 50/50 choice!
    Which door do you think will win now?
    I'm telling you right now you have 1% chance with your first pick and a 99% chance with your second pick.(the math don't lie)

    You may still not win by swapping but you would have to be silly not to.

    And with that explanation I am out!

  17. #56
    digitus impudicus
    Join Date
    May 2007
    Location
    Canberra. Aus.
    Posts
    6,955
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    300
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    13033
    This video still gives the nicest explanation when he goes through the three possible choices, clearly demonstrating how it works.

    If you don't understand how at this point and you haven't bothered to watch anything, I don't think it's actually possible to NOT understand it after you have seen this entire walk through.

    This problem has historically caused people issues and here is no different.

    The only amazing thing is that scott is obviously refusing to believe the explanations.

    The explanation of each choice starts at 1:42

    Status is not defined by the amount of gear in your signature.
    Performance cannot be purchased.

    "The Internet offers everything - except quality control" - K. Anders Ericsson.


  18. #57
    Grand Master Bowman scott p's Avatar
    Join Date
    Jun 2011
    Location
    Keysborough, Melbourne
    Posts
    2,788
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    450
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    74955
    Quote Originally Posted by craigr View Post
    Hey Scott I'll try to explain it a bit differently.
    thanks Craig, but I finally found someone to explain it in a way that makes sense to me.

    still doesn't change the outcome though. the host will always open a "wrong" door, regardless of your initial choice. so your choice remains one of two. if people can't see that they can't do basic maths.
    Last edited by scott p; 14th January 2017 at 06:53 PM.

  19. #58
    3rd Class
    Join Date
    Jan 2014
    Posts
    242
    Tournaments Joined
    0
    Tournaments Won
    0
    Post Thanks / Like
    vCash
    500
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Rep Power
    202
    The video for dummies wasn't enough? It even helped me understand it

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •