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21S-42P-65@-65, and variant

Posted By: Nack Ballard
Date: Thursday, 26 August 2010, at 12:06 p.m.

In Response To: 62S-42P-51@-65? (Timothy Chow)

I altered the first and third rolls/plays of the sequence in case someone later searches for this fourth roll position under a more likely move order. (62S-42P is a weak reply.)


2O ' ' ' '5X '3X ' '1X5O

 ' ' '2O '4O2X2O ' ' '4X

21S-42P-65@-65



2O ' ' ' '5X '3X ' '1X5O

 ' ' '2O '3O2X3O ' ' '4X

43Z-21X-F-61H-51>-65H-54@-65R-54H-21P-62@-65


White's builder is not on the 10pt. Is splitting still better than running?

Yes, even so; I agree with Neil and Paul. I have some clarifying comments to add about distribution.

On the left is the position Tim posted. On the right is a variant position, also reached by strong play, though the sequence is necessarily longer. In essence, Blue's third 6pt spare is moved two pips back, restoring the 8pt spare that he has normally lost after having made an inside point.

From each diagram, visualize and compare the positions after playing R (Run, 24/13) and S (Split, 24/18 13/8). In both cases, there is a three-checker swing in the resulting 13pt/8pt distributions (six-three vs four-four on the left, and six-two vs four-three on the right). It is not the distributional difference that is relevant -- that's a three-checker constant in the S/R decision. Rather, it is that the value of Blue's first 8pt spare is greater than the value of his second 8pt spare. I'm confident that R (if not better outright) loses to S by a smaller margin in the right-hand position than in the left-hand position.

Other factors (in addition to Blue's lack of 8pt spare) that enhance the value of S relative to R are (a) placing White's builder on her 10pt, (b) White's advanced anchor and (c) relative board strength. In the diagrammed positions, moving White's builder from her 11pt to her 8pt or midpoint, or pushing back White's anchor (even if you pip-reimburse her with a spare adjustment on the other side) or weakening Blue's board or strengthening White's board will enhance R relative to S.

Nack

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