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Nactation -- correction/clarification

Posted By: Nack Ballard
Date: Wednesday, 15 February 2012, at 8:17 a.m.

In Response To: Tough and Tricky 65 Nactate This! (Taper_Mike)

Here (alphabetically) are Nactations for a plethora of plays in the position below:

    A = 8/2 6/1
    C = 21/15 8/3*
    c = 24/18 8/3*
    D = 13/8 13/7
    E = 21/15 6/1
    e = 24/18 6/1
    J = 8/3* 8/2
    N = 13/7 6/1
    O = 13/7 8/3*
    o = 13/2
    R = 24/13
    r = 24/18 21/16
    S = 21/10
    s = 21/15 13/8
    S = 24/18 13/8
    Z = 21/16 13/7


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

1O '1X2O '3O '2O ' ' '5X

42P-62S-53X-53R-65


I'll repeat the last four plays:

    S = 21/10 (think of it as 21/15/10)
    s = 21/15 13/8
    S = 24/18 13/8
    Z = 21/16 13/7

In this post, in a rare Nactation mistake, Mike incorrectly ranked the S-family plays. I take responsibility, however, because... In this post, Mike parroted his understanding of the Hit/More/6 rule (then named Hit/Most/6). Under 3.2 (Destination of Blots and Spares), his wording suggests that he believed only final destinations of checkers count. In fact, all destinations count, and I failed to correct him, thereby leaving him with a misunderstanding.

In the position diagrammed above, 21/10 should be thought of as 21/15/10. Although the 15pt is a temporary destination, it is a destination nonetheless. For purposes of ranking plays within a family, intermediate destinations are occasionally relevant (as here).

People familiar with the outer board wrinkle understand why blot/spare destinations farther from the 6pt are ranked higher: they're usually superior plays. Such is the case here. Having played 21/15, continuing the same checker with 15/10 rescues a blot whereas 13/8 does not. A related example is 63R-42P-43 (diagrammed here), where D = 15/11 13/10 and d = 13/10 13/9 (the lower-case play carelessly leaving the 15pt blot behind). Another example can be seen here, where Blue's previous 64S play was 21/15/11 (rather than the terrible 21/15 13/9, which would be nactated with a lower-case s).

[Plays such as Blue's 21/10 in the diagram above, and Blue's 21/11 in this post (as previously linked), and Blue's 22/11 in the first two diagrams of this post, and White's play of 22/11 in this diagram were, once upon a time, in the R family. However, a couple of years ago the definition of R was updated to confine it entirely to the player's far side.]

Finally, I'll paraphrase Mike's (correct) comment for moving a single checker: When the numbers on the dice can be played in either order, the larger number is played first. It seldom matters, but this is a case where it does. 21/10, which is in the S family (i.e., 21/15/10), is not also in the Z family (i.e., not 21/16/10). In the diagram at the top of this post, the only play in the Z family is 21/16 13/7.

Nack

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