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51$-62$-61 and 51$-63$-61

Posted By: Daniel Murphy
Date: Sunday, 15 April 2012, at 8:48 p.m.

In Response To: 51$-62$-61 and 51$-63$-61 (pontiac)

Seems to me that whatever admittedly good argument that can be made for 6/5 24/18 after 51$-62$-61 is much weaker if the position is instead 51$-63$-61. In the first position 24/18 gives 6s and 1s to hit and 3s and 1 to cover. With 1s duplicated 31 won't hit (6/5 24/21) is better (41 and 51 won't hit after either play). In the second position 24/18 gives 3s and 1s to hit and 4s and 2s to cover -- no duplication.

I rely on the Gnubg 2-ply temperature map for the following table:

51$-62$-6151$-63$-61
MoveHitsCoversHits or CoversHits and CoversHitsCoversHits or CoversHits and Covers
6/5 24/1821 24301127 263117
6/5 13/7 14 21 30 514 21 31 4
8/7 13/712 23 30 51415254

From that, I would expect 6/5 13/7 to be clearly best for 51$-63$-61 -- fewer numbers that hit, fewer that cover, and fewer that both hit and cover. 6/6 13/7 has similar advantages for 51$-62$-61 but the differences are smaller, and the bald numbers of hits and covers aren't all that matter.

(Note: I've counted hits on ace point, but I've ignored probably important differences in numbers that make a point other than the 5 or 4 point, and duplication of numbers other than those that either hit on the 7 point or make the 5 or 4 point.)

Despite any apparent advantage for 13/7 8/7 in either position, that play should be third best in both positions. The 5 point blot is practically begging to be covered with ace from the 6 point stack, but 6/5 should be right with smaller stacks too. More importantly the made 5 point will be permanently strong whether or not Blue profits from the next exchange of rolls. That includes how the 2 point board will make Blue's return hits stronger if White hits. The bar point just isn't nearly as strong as the second home board point.

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