Re: observation selection effects

From: John M <jamikes.domain.name.hidden>
Date: Sun, 10 Oct 2004 14:57:16 -0400

Dear Kory,
your argument pushed me off balance. I checked your table and found
it absolutely true. Then it occurred to me that you made the same
assumption as in my post shortly prior to yours:
a priviledge of "ME" to switch, barring the others.
I continued your table to situations when the #2 player is switching and
then when #3 is doing it - all the way to all 3 of us did switch and found
that such extension of the case returns the so called 'probability' to the
uncalculable (especially if there are more than 3 players) like a many -
many body problem.
Cheers
John

----- Original Message -----
From: "Kory Heath" <kory.heath.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Sent: Saturday, October 09, 2004 6:17 PM
Subject: re: observation selection effects

> At 10:35 AM 10/9/2004, Stathis Papaioannou wrote:
> > From the point of view of typical player, it would seem that there is
> > not: the Winning Flip is as likely to be heads as tails, and if he played
> > the game repeatedly over time, he should expect to break even, whether he
> > switches in the final step or not.
>
> That's not correct. While it's true that the Winning Flip is as likely to
> be heads as tails, it's not true that I'm as likely to be in the winning
> group as the loosing group. Look at the case when there are only three
> players. There are eight possible outcomes:
>
> Me: H Player 1: H Player 2: H - WF: T
> Me: H Player 1: H Player 2: T - WF: T
> Me: H Player 1: T Player 2: H - WF: T
> Me: H Player 1: T Player 2: T - WF: H
> Me: T Player 1: H Player 2: H - WF: T
> Me: T Player 1: H Player 2: T - WF: H
> Me: T Player 1: T Player 2: H - WF: H
> Me: T Player 1: T Player 2: T - WF: H
>
> I am in the winning group in only two out of these eight cases. So my
> chances of winning if I don't switch are 1/4, and my chances of winning if
> I do switch are 3/4. There's no paradox here.
>
> -- Kory
>
>
Received on Sun Oct 10 2004 - 15:18:30 PDT

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