[seqfan] MH problem

[zbi74583.boat at orange.zero.jp]

    Hi,Seqfans
    Once I and my friend Kobayashi discussed about n-MH problem.
    Where "n-MH" means n doors Monty Holl
    Kobayashi is a scientist writer.

    http://www.amazon.com/s?ie=UTF8&page=1&rh=n%3A283155%2Cp_27%3AYasumi%20Kobayashi

    I felt that it is interesting
    And again recently my friend Domo posted MH problem to this BBS.

    http://rakuenmetal.blog.jp/archives/42320763.html?1445995925#comment-form

    Essentially it is a music BBS, but the moderator is so lenient that we
discussed about 4-MH problem
    Unexpectedly many music fans responded to the issue

    I feel that  many music fans like scientific theme.
    You may read my posting at 736th and 737th.

    And I met a Sequence of probability related with n-MH problem

    p(n) : 1,2/3,5/8,11/15,....

    This is the probability that the player gets a car changing the doors every
time.
    Could anyone confirm  it and compute more terms?

    By the way I think that it is  ambiguous  when Monty is a friend of the player.
    In 5-MH problem the case of G-G-G-C
    Where "G" means goat, "C" means car


    o PL selects G  probability=4/5
    o MH opens G
    o PL changes to G  probability=2/3
    o MH opens G
    o PL changes to G  probability=1/2
    o MH opens G
    o PL changes to C probability=1


    So, Probability of this case =4/5*2/3*1/2*1=4/15
    But if MH is a friend of PL then at the second time he must open G which is
different from the G which PL selected at first, so PL changes to the first
G
    It means that the probability becomes 8/15

    The other two cases
        Probability of the case of C-G-G-C =1/5*1*1*1=1/5
        Probability of the case of G-C-G-C =4/5*1/3*1*1=4/15

    Kobayashi said that in 4-MH problem it is ambiguous too.
    But I don't understand



    Yasutoshi