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21$-xxx-66

Posted By: Nack Ballard
Date: Friday, 29 April 2011, at 10:15 p.m.

In Response To: 21$-MISS-66 (Mochy)


2O ' ' ' '5X '3X ' ' '4O

2X ' ' '1O4O '3O ' '1O5X

21$-xxx-66



1O ' ' ' '5X1O3X ' ' '3O

2X ' ' '2O4O1O3O ' ' '5X

Blue has one 6 to play


After Blue plays 21$ as shown in the left-hand diagram above (masking White's reply), the proper Nactation for 66 played 24/18 13/7(2) 11/5 is G (Gremlin split), and for 24/18(2) 13/7 11/5 it is Y (Yoga split).

However, for purposes of this post, I'll assume that three 6s are played 24/18 13/7 11/5, as shown in the right-hand diagram. If the fourth 6 is used to cover the 7pt, I'll call that P for Point; if it is used to cover the 18pt, I'll call that @ for anchor.


1O ' ' '1X4X1O3X ' '1X3O

2X ' ' '2O4O1O3O ' ' '4X

21$-21$-66, with one 6 left to play



1O ' '1X '4X1O3X '1X '3O

2X ' ' '2O4O1O3O ' ' '4X

21$-32$-66, with one 6 left to play


Your first position, 21$-21$-66, is shown in the left-hand diagram (with Blue having one 6 to play). As you say, P would leave White an intolerable number of rolls that hit on her 7pt and cover her 5pt.

If we artifically move only White's 11pt builder to her 10pt, 9pt or 8pt (not diagrammed), Blue's choice becomes closer, because there are fewer offensive hit-and-covers.

If we move White's blots one space to the right, as shown in the right-hand diagram, Blue's choice becomes much, much closer because the offensive hit-and-cover numbers are less devastating even though the 6 duplication is still there.

If we artificially move White's blots again to the right (to the 9pt and 3pt, not diagrammed), Blue should definitely switch from @ to P because the offensive hit-and-covers are a relatively weak threat.


1O ' ' ' '5X1O3X ' '1X3O

1X ' '1X2O4O1O3O ' ' '4X

Diagram 21$-32S-66, with one 6 left to play



1O ' ' ' '5X1O3X '1X1X3O

2X ' ' '2O4O1O3O ' ' '3X

21$-32D-66, with one 6 left to play


Here are your two "confusing" positions. You essentially asked: "Why is @ a relatively better play than P on the left than it is on the right?"

One important factor is that the more outfield blots White has, the more (not less) incentive Blue has to come out to the 18pt. This is a pitfall that almost everyone seems to fall into: They're less willing to play 24/18 when White has a checker on her 11pt, 10pt and/or 9pt, when (usually) they should be more willing.

24/18 is a deflection ploy that frustrates White's aim of using her new builder(s) to make her 5pt or 4pt (hopefully unstacking her 6pt in the process). She can't use any of her three 6pt spares to point on the 7pt; rather she might have to reduce, strip or break her midpoint to do so. Moreover, it is harder for White to clean up her blot(s) if she chooses not to hit you.

For more on this topic, click here: 1, 2, 3, 4, 5, 6

Another important factor is that White's 3s are duplicated in the left-hand diagram (repeated below for scrolling convenience). Try changing White's play from 32S to 32Z (i.e., 24/22 13/10, not diagrammed), and now Blue's @ play (leaving the 7pt blot exposed) goes from being slightly better/tied to being almost a double-whopper!

Admittedly, some of the impact of the 32S to 32Z change is that priming a 22pt checker is more effective than priming a 21pt checker, and an 18pt blot fares better vs a 10pt builder than an 11pt builder. However, even if the only change you make to the left-hand diagram is to nudge White's 24pt checker up to her 23pt, @ becomes whopperish.

If (as I just said) priming a 22pt checker is more effective than priming a 21pt checker, then the difference in priming a 24pt checker (vs a 21pt checker) is even greater; hence the elevated value of P on the right.

If Blue plays P on the left, White is happy to anchor with her 3 (thereby rendering Blue's four-prime less powerful) and either hit Blue's unanchored 18pt blot this roll or threaten to do so next roll; or if she doesn't roll a 3 she might anchor next roll with a 3 (or with a 4 from the roof). By contrast, if Blue plays @ (still referring to the left-hand diagram), I believe White will hit rather than anchor with a 3 on this roll, but duplication is still doing its job.

Specific rolls (in rough order of ranking) that most greatly demonstrate @'s superiority over P on the left and/or P's superiority over @ on the right are: 66, 61, 54, 55, 62, 41 and 52. Contrary rolls (though less impactful overall) are 44, 43, 53, 51, 31, 42 and 65.


1O ' ' ' '5X1O3X ' '1X3O

1X ' '1X2O4O1O3O ' ' '4X

Diagram 21$-32S-66, with one 6 left to play



1O ' ' ' '5X1O3X '1X1X3O

2X ' ' '2O4O1O3O ' ' '3X

21$-32D-66, with one 6 left to play


Nack

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