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Re: [Bug-gnubg] Race position theoretical question?

From: Joseph Heled
Subject: Re: [Bug-gnubg] Race position theoretical question?
Date: Wed, 30 Jan 2019 08:46:09 +1300

Don't know if it will work, but have you tried 8 W pieces on point 2,
one black piece on 3 and the rest black pieces at B home. W can win
with two doubles (2 to 6), or lose with a sequence of (2-1, 3-1,...)
throws while B gets a sequence of 6-6. The odds will be low but might
be > 0.


On Wed, 30 Jan 2019 at 08:02, Øystein Schønning-Johansen
<address@hidden> wrote:
> Hi all!
> Here is a theoretical question for all of you:
> Can a race (aka. non-contact) position, be possible to lose backgammon with a 
> good dash of unluck, and still be possible to win (with a good dash of luck). 
> It is assumed that the player is really trying to get of the backgammon, and 
> plays the best move to get off the backgammon. We do not take stupidity into 
> account.
> A bit more mathematically stated:
> Let S be the set of all possible race positions.
> Let A be the subset of S where P(lose backgammon) > 0.
> Let B be the subset of S where P(win) > 0.
> Is the intersection of A and B an empty set?
> I think it is, but I cannot find a simple proof. (It probably is an obvious 
> proof to this, however I'm too narrow minded to see it.)
> If it is not an empty set, can you please post a position in this 
> intersection?
> Thanks,
> -Øystein
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