[seqfan] Re: MH problem

[Andrew Weimholt]

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