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.
-Joseph On Wed, 30 Jan 2019 at 08:02, Øystein Schønning-Johansen <oyste...@gmail.com> 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 > _______________________________________________ > Bug-gnubg mailing list > Bug-gnubg@gnu.org > https://lists.gnu.org/mailman/listinfo/bug-gnubg _______________________________________________ Bug-gnubg mailing list Bug-gnubg@gnu.org https://lists.gnu.org/mailman/listinfo/bug-gnubg
