[seqfan] Re: MH problem

[Rick Shepherd]

There are many variants of this problem. The English Wikipedia article I
refer to in my comment in A067998 is useful and thought- provoking.  -- Rick
On Oct 28, 2015 3:56 PM, "Frank Adams-Watters" <franktaw at netscape.net>
wrote:

> I think, when you switch away from a door, the next thing that happens is
> that Monte shows you what you just passed up - you can never switch back to
> that door. Under that interpretation, all probabilities for what you might
> switch to are the same, and a "friendly" Monte can't actually help you.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Andrew Weimholt <andrew.weimholt at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Wed, Oct 28, 2015 2:28 pm
> Subject: [seqfan] Re: MH problem
>
>
> On Wed, Oct 28, 2015 at 10:11 AM, Andrew Weimholt <
> andrew.weimholt at gmail.com
> >
> wrote:
>
> > On Tue, Oct 27, 2015 at 7:07 PM, <zbi74583.boat at orange.zero.jp>
> wrote:
> >
> >>     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.
> >>     And I met a Sequence of probability related with n-MH
> problem
> >>
> > [...]
> >
> >>     p(n) : 1,2/3,5/8,11/15,....
> >>
> >
> > p(2) should be
> 1/2. With only two doors, you pick w/ 50/50 probability,
> > and there is no
> opportunity to switch doors. Either you've won, or you
> > didn't.
> >
> > If you
> start the sequence at n=1, then p(1) would be 1
> >
> > If you start the sequence at
> n=0, then p(0) would be 0
> >
> > I've confirmed, by hand, that p(4) is 5/8.
> >
> >
> For
> n=5 and beyond, there are choices for the player to switch doors which
> are not
> symmetric in terms of odds of winning.
> There are multiple ways to handle this,
> which will [most likely] lead to
> multiple sequences.
>
> option 1) player's choice
> of which door to switch to is evenly distributed
> over the remaining closed doors
> (other than the one he's switching away
> from)
> option 2) player's choice of which
> door to switch to is based on the
> probability of the door containing the car. He
> choses the door with the
> highest probability.
> option 3) player's choice of which
> door to switch to is based on the
> probability of the door containing the car. He
> choses the door with the
> lowest probability (anticipating that he'll again
> switch).
>
> Andrew
>
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