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X vs P (for 4xS-61)

Posted By: Nack Ballard
Date: Sunday, 4 April 2010, at 3:00 a.m.

In Response To: RO (David Rockwell)

I’ll start by pointing out, in case it is not obvious to everyone, that Neil asked about the H vs X comparison (to which I responded here). You, David are starting a different discussion which compares P vs X, and you’re expanding the umbrella to include theoretical positions with White’s builder on the 11pt and 9pt (as well as the 10pt and 8pt).

As a general rule, I spend more time on positions that can arise through good play than those that arise through an illegal opening play or blunder, though comparison of such hypothetical positions nonetheless has educational value.


2O ' ' ' '5X '3X1X ' '5O

1X ' ' '1X5O '3O ' ' '4X

44S-61



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

1X ' ' '1X5O '3O ' ' '4X

42S-61



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

1X ' ' '1X5O '3O ' ' '4X

43S-61



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

1X ' ' '1X5O '3O ' ' '4X

54S-61


Here is data for the four positions, isolating P and X. For the first two positions, we have only your short Gnu rollouts, but we’ll make do with that.

44S-61 [P X22] -- Gnu 5k only
42S-61 [P X8] -- Gnu 2k only
43S-61 [X P10]
54S-61 [P X62]

The position for which it is clearest to make the 7pt is 54S-61 (fourth position). Hit-and-split fails to threaten an outfield blot and allows Opp to unstack with 11 21 31 51.

The other positions are closer together because in all three cases splitting attacks a blot. My first thought was the same as yours: the more 4s that are already duplicated, the more efficient P will tend to be (i.e., don't upset the apple cart). All plays duplicate 42 and 31, and it’s not clear how to account for double 4s, so let’s consider only the other 4s (i.e., 64 54 43 41).

44S-61P duplicates 43 41 54 (5pt, 5pt, 4pt).
42S-61P duplicates 64 41 (4pt, 7pt).
43S-61P duplicates 64 (4pt).

I haven’t included duplication of making the 9pt, 10pt or 11pt, the effects of which are relatively small. I only counted “key” points. 4s allow White to make either the 20pt or the key offensive point listed in the parentheses (and the stronger the offensive point the closer in value it is to the 20pt and the more relevant the duplication).

Summarizing, 44S-61P does the best job of duplication (5pt 5pt 4pt), 42S-61P does the second best job (4pt 7pt), and 43S-61P does the worst job (4pt only). And P’s edges over X (by .022, .008 and -.010, respectively) reflect the same ranking.

Given that the 4 duplication factor fits, I don't feel very motivated to look further. (Point-making duplication is much more meaningful than where-to-hit duplication; hitting on the 20pt is so much better than hitting on the 7pt.)

[Nactation key: P = Point (13/7 8/7), X = hit-and-split (24/18 6/5*.]

Nack

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