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21$-65R-43C-21H-11

Posted By: Taper_Mike
Date: Thursday, 22 December 2011, at 9:08 a.m.

In Response To: 21$-65R-43C-21H-11 (Nack Ballard)

In April 2011, Miran posted his rollout of 21$-65R-43C-21H-11.


1O ' ' '1X4X '3X ' '1X4O

1X ' ' '2O4O '2O ' '1O5X

21$-65R-43C-21H-11


Nack gave the Nactations for Miran’s rollout in his follow-up post, also from April 2011.
I have copied Nack’s original Nactations into the table below.

Then, in October 2011, Nack announced a comprehensive retooling of the Nactation system that is described in a post entitled Nactation of Doublets (complete table). Under the updated rules, any play of doublets can be systematically assigned a Nactation. Along the way, twelve of the areal (i.e, area-based) families were split in two, creating regular and underlined versions of each.

Under the new rules, three of the Nactations in Miran’s rollout have changed. The new Nactations are given in the update column below. All other Nactations remain the same.

Traditional Notation Original
Nactation		 Updated Nactation
Bar/23 8/7(2) B
Bar/23 11/9 b
Bar/22 6/5 e E
Bar/24 8/7(2) 6/5 G G
Bar/24 11/9 6/5 g g̲ (lower case, underlined g)
Bar/22 11/10 s
Bar/21 U
Bar/23 Bar/22 V
Bar/23 11/10 6/5 Y
Bar/24 11/10 8/7(2) Z

In the case of the G (Gremlin) family, the moves above are now nactated in the underlined
G (Gremlin) family.

In the case of bar/22 6/5, however, it looks like Nack was trying to use the underlined
E (Each) family, but was off by one rank. He has the play ranked 4th in the family; I’ve got it 5th. This is one of the rare cases where the best play according to the rollout requires breaking out the boldface for its Nactation.

The remainder of this post gives the details of Nactations in three families: E (Each),
G (Gremlin) and S (Split). They are presented in order of difficulty, with the easiest Nactations coming first. At the end is E (Each), where 10 different plays require the use of the color red to rank the lowest two plays!

S (Split) Family

In the S (Split) family checkers are moved in the ratio Far:Down:Jump:Inside = 3:1:0:0. Thus, the fourth best play in Miran’s rollout, bar/24 8/7(2) 6/5, is a member of the family.

In the position 21$-65R-43C-21H-11, these are the possible moves:

  • Far: bar/23 24/23 –or– bar/22
  • Down: 11/10 –or– 8/7

S (Split) Family
Traditional
Notation		 Far
3		 Down
1		 Jump
0		 Inside
0		 Hits on
These Points
(more is better)
(higher is better)		 Owned Points Not Held
by All Members in Family
(more is better)
(closer to 6pt is better)		 Blot and Spare
Destinations
(closer to 6pt is better)
(outer board: farther is better)		 Nactation
bar/23, 24/23, 11/10 bar/24
24/23
24/23		 11/10 8pt* 23pt* 10pt S
bar/22, 11/10 bar/24
24/23
23/22		 11/10 8pt* 10pt 22pt s
bar/23, 24/23, 8/7 bar/24
24/23
24/23		 8/7 23pt* 7pt S
bar/22, 8/7 bar/24
24/23
23/22		 8/7 7pt 22pt s

*This is the deciding criterion. The asterisk marks the reason under Hit/Most/Six that a given row ranks above the row that follows it. Other criteria are either tied or irrelevant.

G (Gremlin) Family

In the underlined G (Gremlin) family checkers are moved in the ratio Far:Down:Jump:Inside = 1:2:0:1. Thus, the fourth best play in Miran’s rollout, bar/24 8/7(2) 6/5, is a member of the family.

In the position 21$-65R-43C-21H-11, these are the possible moves:

  • Far: bar/24
  • Down: 8/7(2) –or– 11/9 –or– 11/10 8/7
  • Inside: 6/5 –or– 5/4

G (Gremlin) Family
Traditional
Notation		 Far
1		 Down
2		 Jump
0		 Inside
1		 Hits on
These Points
(more is better)
(higher is better)		 Owned Points Not Held
by All Members in Family
(more is better)
(closer to 6pt is better)		 Blot and Spare
Destinations
(closer to 6pt is better)
(outer board: farther is better)		 Nactation
bar/24, 8/7(2), 6/5 bar/24 8/7
8/7		 6/5 5pt 7pt* 5pt G
bar/24, 11/9, 6/5 bar/24 11/10
10/9		 6/5 5pt* 8pt* 5pt 9pt g̲
bar/24, 11/10, 8/7, 6/5 bar/24 11/10
8/7		 6/5 5pt* 5pt 7pt 10pt G
bar/24, 8/7(2), 5/4 bar/24 8/7
8/7		 5/4 7pt* 4pt g̲
bar/24, 11/9, 5/4 bar/24 11/10
10/9		 5/4 8pt* 4pt 9pt G
bar/24, 11/10, 8/7, 5/4 bar/24 11/10
8/7		 5/4 4pt 7pt 10pt g̲

*This is the deciding criterion. The asterisk marks the reason under Hit/Most/Six that a given row ranks above the row that follows it. Other criteria are either tied or irrelevant.

E (Each) Family

In the underlined E (Each) family, checkers are moved so that the ratios Far:Down:Jump:Inside equal 1:0:0:3 or 3:0:0:1. In the 21$-65R-43C-21H-11 position diagrammed above, there are a lot of choices. Ranking all of them is an exercise in advanced Nactation.

When Far:Down:Jump:Inside = 1:0:0:3, these are the possible moves:

  • Far: bar/24
  • Inside: 6/3 –or– 6/5 6/4 –or– 6/4 5/4 –or– 6/5(3) –or– 5/2 –or– 5/4 5/3

When Far:Down:Jump:Inside = 3:0:0:1, these are the possible moves:

  • Far: bar/23 24/23 –or– bar/22
  • Inside: 6/5 –or– 5/4

Thus, there are 10 combinations in all, 6 with ratios equal to 1:0:0:3, and 4 more with ratios of 3:0:0:1.

At the top of the family are 4 plays that result in owning 3 points that are not shared by all family members. Below them come 5 others that grab 2 points. At the bottom, is a single play that retains only 1 point that is not held by all other family members.

By the Most-Points Convention, the three plays that make a new point (the 23pt or 24pt), while retaining the 5pt and 6pt, are ranked highest. Next comes a play that trades the 5pt for two new points (the 4pt and 24pt), followed by a play that retains the 5pt and 6pt, but does not add any new points. After that are three plays that trade the 5pt for either 23pt or 24pt, and then one that trades the 6pt for the 24pt. At the bottom, the runt of the litter is a play trades the 5pt for nothing.

E (Each) Family
Traditional
Notation		 Far
1
3		 Down
0
0		 Jump
0
0		 Inside
3
1		 Hits on
These Points
(more is better)
(higher is better)		 Owned Points Not Held
by All Members in Family
(more is better)
(closer to 6pt is better)		 Blot and Spare
Destinations
(closer to 6pt is better)
(outer board: farther is better)		 Nactation
bar/23, 24/23, 6/5 bar/24
24/23
24/23		 6/5 5pt 6pt 23pt* 5pt E
bar/24, 6/5, 6/4 bar/24 6/5
6/5
6/4		 5pt 6pt 24pt 4pt 5pt* e
bar/24, 6/3 bar/24 6/5
5/4
4/3		 5pt* 6pt 24pt 3pt E
bar/24, 6/4, 5/4 bar/24 6/5
5/4
5/4		 4pt* 6pt* 24pt* e
bar/22, 6/5 bar/24
24/23
23/22		 6/5 5pt* 6pt 5pt 22pt E
bar/23, 24/23, 5/4 bar/24
24/23
24/23		 5/4 6pt 23pt* 4pt e
bar/24, 5/4, 5/3 bar/24 5/4
5/4
5/3		 6pt 24pt 3pt 4pt* E
bar/24, 5/2 bar/24 5/4
4/3
3/2		 6pt* 24pt 2pt e
bar/24, 6/5(3) bar/24 6/5
6/5
6/5		 5pt* 24pt* 5pt E
bar/22 5/4 bar/24
24/23
23/22		 5/4 6pt 4pt 22pt e

*This is the deciding criterion. The asterisk marks the reason under Hit/Most/Six that a given row ranks above the row that follows it. Other criteria are either tied or irrelevant.

Mike

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