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## [Bug-gnubg] Race position theoretical question?

 From: Øystein Schønning-Johansen Subject: [Bug-gnubg] Race position theoretical question? Date: Tue, 29 Jan 2019 20:00:49 +0100

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