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Nactation: division of labor for B, S, Z

Posted By: Nack Ballard
Date: Tuesday, 1 February 2011, at 10:40 p.m.

In Response To: Nactation (Stick)

So B as a non doublet does not have the same meaning as B as a doublet. I didn't register that before and even though I could have used S or Z, B is the first that jumped into my mind from all the early game doublets playing into those quadrants I've nactated over the years.

That's right. The non-doublet B meaning is not in the current tutorial; that information is only sprinkled about in various Nactation posts. A quick example for your consideration is 43D-42P-21 or 43D-42P-61 (shown below): for B, the ace is played 10/9 and the other part of the roll (2 or 6) splits.

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

2X ' ' ' '5O '3O1O1O '5X

Roll of 21 or 61... B = 24/22 10/9 or 24/18 10/9

To help the distinction between non-doublet B, S and Z sink in, I'll provide a glimpse of the example slated for the tutorial update. Below, for a roll of 42, can you guess what B, S and Z each mean? (Answers appear below the diagram.)

 ' ' ' ' '5X1X3X ' ' '4O

2X ' ' ' '5O '3O1O '1O4X


In the diagram above, B = Bar/21 11/9, S = Bar/21 13/11, and Z = Bar/23 13/9.

Doublet S and doublet Z also have different meanings from non-doublet S and Z, though they are closely related and thus easy to remember. For doublets:

    B = 2:2
    S = 3:1
    Z = 1:3

...where the first number tells you how many move portions are played on the far side of the board, and the second number tells you how many move portions are played to or within the outer board. (This time, the "to or within" phrase applies to all three, and of course there is no larger or smaller number because all four portions of a doublets move are the same size.)

You can think of it this way: Non-doublet S splits with the larger number, while doublet S "splits" with THREE portions of the (four-portion) roll. Non-doublet Z splits with the smaller number, while doublet Z "splits" with ONE portion of the (four-portion) roll. [And doublet B is between the other two: it "splits" with two portions.]

For example, with a (theoretical) opening roll of double 3s, B = 24/21(2) 13/10(2), S = 24/21(3) 13/10, and Z = 24/21 13/10(3), as illustrated in the three diagrams below.

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

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

Blue played 33B

1O ' ' ' '5X '3X '1O '4O

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

Blue played 33S

[IF the opening position started with three checkers on the 24pt, 33S would be 24/21(3) 13/10, and 24/15 13/10 (the play diagrammed above) would be 33s.]

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

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

Blue played 33Z

You have now learned how to use two complex doublet letters: S and Z. The term "complex doublet" sounds scarier than it actually is; it mainly means that doublets are not played in simple pairs. The final three letters (G, Y, and M) are evoked, and new uses for non-doublet letters you already know are logically expanded, allowing you to unambiguously (i.e., without assumption) nail down any doublets move played on a backgammon board.

By the way, the B/S/Z division of labor, both for non-doublets and for doublets, turns out to be very efficient.


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