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31P-xxP-31 comparisons
Posted By: Nack Ballard In Response To: 31P-31P-31? (mtuhtan)
Date: Wednesday, 21 April 2010, at 3:09 a.m.
As you can see from the data (and illustrated in the diagrams) below, the "primier" White's newly made point, the better it is for Blue to play E, and the deeper White's point, the better it is for Blue to aim for a priming battle with N.
[Nactation key: E = Each (24/21 6/5), S = Split (24/23 13/10), N = Near (13/10 6/5), U = Up (24/20 when possible, else 24/21 24/23), V = Variant-up (24/21 24/23). Margins are in thousandths of a point, and number of trials is listed (after the brackets, rounded down) in thousands. For example, the first row means E is best, S is -.023, V is -.033, etc., rolled out 5000+ trials.]
31P-61P-31
Snowie .. [E S23 V33 U34 N41] 5k
GnuBG .. [E S21 N26] 5k31P-31P-31
GnuBG .. [E S18 N20 U34] 5k
XG 3-ply [E S14 N20 U33] 20k 10kN 5k31P-53P-31
Snowie .. [N E9 S12] 10k
GnuBG .. [N E7 S12 U31] 10k 5kU31P-64P-31
Snowie .. [N E41] truncFor Backgammon Openings, Paul and I contemplated including (a) either the first or second position, plus (b) either the third or fourth position, to give us a pair that contrast the E and N plays.
The problem was (b). The 53 position is not enough of a contrast: E needs to be at least "barely correct" (i.e., +.010 to +.020 by the Ballard/Weaver error scale) whereas it is only tied. And 64P is too weak a second roll play to qualify for our position selection.
So, from that group we did not have a pair of high enough quality to include in the book. Fortunately, we found plenty of other pairs that did qualify :)
For reference, the four positions are shown in the left-hand column below, with their E/N margins. To the right of each is the position after the best (money) play has been made.
31P-61P-31 [E S22 V33 U34 N34]
Blue played E (better than N by .034)
31P-31P-31 [E S16 N20 U33]
Blue played E (better than N by .020)
31P-53P-31 [N E8 S12 U31]
Blue played N (better than E by .008)
Recap: In the first and second position, where White has a high point, Blue should play E (24/21 6/5). In the third and fourth positions, where White has a low point, Blue should play N (13/10 6/5).
31P-64P-31 [N E41]
Blue played N (better than E by .041)
Nack
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