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Cyprus: Grand Final, containment game

Posted By: Daniel Murphy
Date: Tuesday, 6 December 2011, at 1:48 a.m.

In Response To: Cyprus: Grand Final, containment game (Klaus Evers)

If Blue does not hit, then the best four should be 11/7, because 19/15 is better if White rolls 5-3 or 5-1, but is worse if White rolls 5-2, 5-4 or 5-6.

If Blue plays 11/7, White has few winning rolls, because when White rolls 5-X, Blue hits back about 38% of the time by my count.

If Blue plays 8/4*, White appears to have quite a few good numbers. Any 4 and 3-1 hit in the home board, 3-5 hits in the outfield, and 3-6 runs to the outfield. However, only 4-4 is a near-sure winner, and 5-5 would have been a sure winner after 11/7. On 3-6 Blue gets 23/36 return hits, on 4-5 Blue gets 8/36 return hits. On 4-1 4-2 4-3 4-6 and 1-3, White hits but is stuck on Blue's 4 point. That leaves Blue only a slight favorite to enter immediately, but actually most of Blue's entering numbers can enter and attack, and if Blue doesn't attack again, Blue still has a broken 4-prime that White is only a slight favorite to jump over.

And finally, if Blue play 11/7 and White does not escape, Blue would have a better attack than he has now, but still, only 16/36 of Blue's numbers would point on the 4 point, so Blue would have to play quite a few numbers (6-1 6-5 5-5 5-4 5-3 5-2 5-1 4-1 3-1 2-1 1-1) by hitting loose on the 4 point (I'd hit loose with all those numbers). On the other hand, if Blue plays 8/4* and White does not hit, all 36 of Blue's numbers make the 4 point.

So,, looking only at White's battle to escape immediately and Blue's battle to make prevent that, I give White about 7/36 immediate winning sequences (of White's 11/36 5-X numbers) after 11/7, and about 8/36 immediate winning sequences (of White's 15/36 that hit and/or partially escape) after 8/4* (naturally White will win more games than that "nonimmediately" as Blue continues to try to close White out). On the other hand again, 8/4* followed by a non-hitting number should be more favorable to Blue's GWC than 11/7 after a non-escaping number.

Since we don't have to worry about gammon losses at the score, I'll vote for bar/19 8/4* as Blue's best play here, since it appears to win the most games.

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