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| XGID=-b----E-D---cDa--c-ccA--A-:0:0:1:13:0:0:3:0:10 | |||||
54S-21H-61U-21P-21U-51N-31 | |||||
[David]: It is funny that you are posting this position because recently I re-read your book and one sentence that keeps nagging me refers to this position indirectly. The discussion is in the context of 32S-31P-31 (A155) and I quote: "If White's offense in A155 were strengthened by playing a 5 from her midpoint to her 8pt (giving her nine checkers in the zone), Black's anchoring as in A157 would be barely correct."
[Nack]: Refer to the three diagrams below, and my analysis.
As much as this book is profound and accurate, I am not sure that I agree with this specific principle. 9 checkers in the opponent's zone will not stop me from making the 5. Make it 10 in the zone and I will consider the alternatives as in this case.
Thanks for the compliment. I should clarify, though, that the authors of the book (Paul and I) did not intend to imply that the presence of an opponent's ninth checker in the zone automatically favors anchoring on the opponent's 4pt over making one's own 5pt. However, we DO believe it is a notable factor. Based on a comparison of the first and second positions diagrammed below, it makes a difference of .045 to the P/@ margin (which happens to swing the P/@ decision in that case).
According to our definition of the "zone" (see the book's glossary), the 11pt checker is no longer in the zone once the 5pt is made. (I realize that there are still people who do not make that distinction.) Hence, we count nine (rather than ten) checkers in the zone for White in the above position, though it would be reasonable to count the 11pt checker as some fraction. [Even checkers within the zone can vary substantially in value and are sensitive to changing circumstance and purpose, but one could write a whole book just about that.]
As for this specific case, I see it in the following way: with 4 checkers on my 8 point the thematic play should be to make the 5. However, because of the 10 in the zone problem and extremely well diversified checkers for the opponent (moving a spare from the 6 to the 5 makes a huge difference in terms of equity) this could be an exception in which anchoring is right. I have no idea which play is right but my decision OTB would be to make the 5 (when in doubt...). If the opponent's blot was moved one pip forward (from his 11 to his 10), I would be more inclined to anchor.
Now, that is a tenth checker in the zone. :)
You are right to place a high value on Blue's unstacking of his fourth 8pt checker. That turns out to be bigger than the combined effects of 6/5, 13/8 and 13/11 on White's side -- but only very slightly bigger, which makes the above a useful reference position (as is 41$-32S-31A-31 below).
The first position diagrammed below is 32S-31P-31 (i.e., A155 in Backgammon openings). White has eight checkers in the zone, and Blue's P (Point, 8/5 6/5) is clearly correct -- 5k rollout result is [P B40 E85].
The second position below (reachable by 41$-32S-31A-31, and can be viewed as the right-hand position if you widen your window) is the nine-in-the-zone variant Paul and I referred to in our text. According to our Snowie rollout of the time, anchoring edges out making the 5pt by .011. According to XGR++ evaluation, the margin is .005. For purposes of this post, let's use the latter.
Many pages in Backgammon Openings are accompanied by an extra position diagrammed in the lower left corner. On the same page that 32S-31P-31 (i.e., A155) is featured, we considered using the third position diagrammed below (52S-31P-31) as the A158 accompaniment; however, We judged it to be more obvious and less instructive (than the 32Z-31P-31 we actually used); it's too easy to see that the fourth checker on Blue's 8pt (which is aching to be unstacked) causes P to be beat @ by an even larger margin than the already-significant one of .040.
However, for reasons of accounting in this post, it has become useful to see just how much moving the 8pt checker from the 11pt/10pt to the 8pt does increase that .040 margin. To this end, I rolled out 52S-31P-31 (5k), which generates a whopping result of [P @114].
Compare to the main position above, where the rollout result is [P @7]. We can loosely conclude that the combined effect of the ninth checker in the zone (13/8) plus the spreading of White's builder from 6/5 (plus whatever difference 13/11 might make) is hefty, but it still adds up to only .107, which is not quite enough to overturn the .114 (P-motivating) effect of Blue's second 8pt spare. We might further conclude (based on a comparison of the rollouts of the first and second positions below) that White's 13/8 part accounts for .040 + .005 = .045, and that her 6/5 + 13/11 therefore accounts for .062 (i.e., the remainder of the .107 that nearly offsets the .114 difference).
Nack
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32S-31P-31 | |||||
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| XGID=-b----E-C--AdD---c-dbA--A-:0:0:1:13:0:0:3:0:10 | |||||
41$-32S-31A-31 | |||||
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| XGID=-b----E-D---eD---b-db-A-A-:0:0:1:31:0:0:3:0:10 | |||||
52S-31P-31 | |||||