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Nactation question (41S-66B-22)

Posted By: Taper_Mike
Date: Thursday, 26 January 2012, at 6:10 a.m.

In Response To: Nactation question (41S-66B-22) (Nack Ballard)

Nactation Quiz

In all these positions, the N (Near) family for doublets makes two moves down and two moves inside.

Position 1


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

1X ' ' ' '5O '3O1O '1X5X

43Z-64R-22


In Position 1, there are 3 ways to make two moves down:

  • 13/11*(2)
  • 13/11*/9
  • 13/11*, 9/7

In the same position, there are 2 ways to make two moves inside:

  • 6/4(2)
  • 6/2

By forming all the possible combinations, we generate the 6 members of the N (Near) family. In no particular order, they are:

  • 13/11*(2), 6/4(2)
  • 13/11*(2), 6/2
  • 13/11*/9, 6/4(2)
  • 13/11*/9, 6/2
  • 13/11*, 9/7, 6/4(2)
  • 13/11*, 9/7, 6/2

In order to rank these 6 plays, first remember the home-board exception in the Hit Convention. More owned points in the inner board beats any hit (inside or out). Thus, the three plays that make the 4pt outrank the plays that do not, and we can make the following cut immediately:

Top 3 members:

  • 13/11*(2), 6/4(2)
  • 13/11*/9, 6/4(2)
  • 13/11*, 9/7, 6/4(2)

Bottom 3 members:

  • 13/11*(2), 6/2
  • 13/11*/9, 6/2
  • 13/11*, 9/7, 6/2

Subsequent ranking is straightforward. All plays hit on the 11pt, so the next tie-breaker is the More Points Convention. Whichever play makes or retains the most points, ranks highest. In case of a tie, the 6pt Convention gives preference to the position in which an owned point is closest to the 6pt. By these measures, owning the 9pt beats owning the 11pt, and owning the 11pt beats owning nothing.

The following table gives a breakdown of the top 4 members of the family.

Traditional
Notation
Far
0
Down
2
Jump
0
Inside
2
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
13/11*/9, 6/4(2) 13/11*
11/9
6/4
6/4
11pt 4pt 9pt* N
13/11*(2), 6/4(2) 13/11*
13/11
6/4
6/4
11pt 4pt 11pt* n
13/11*, 9/7, 6/4(2) 13/11*
9/7
6/4
6/4
11pt 4pt* 7pt 11pt N
13/11*/9, 6/2 13/11*
11/9
6/4
4/2
11pt 9pt* 2pt n

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


Position 2


1O1O ' ' '5X '3X ' ' '4O

1X ' ' ' '5O '4O1X ' '5X

51S-62R-22


In Position 2, there are 2 ways to make two moves down:
  • 13/11(2)
  • 13/9*

In the same position, there are 2 ways to make two moves inside:

  • 6/4(2)
  • 6/2

By forming all the possible combinations, we generate the 4 members of the N (Near) family. In no particular order, they are:

  • 13/11(2), 6/4(2)
  • 13/11(2), 6/2
  • 13/9*, 6/4(2)
  • 13/9*, 6/2

In order to rank these 4 plays, first remember the home-board exception in the Hit Convention. More owned points in the inner board beats any hit (inside or out). Thus, the two plays that make the 4pt both outrank any hitting play that does not, and we can make the following cut immediately:

Making the 4pt:

  • 13/11(2), 6/4(2)
  • 13/9*, 6/4(2)

Beats any hit that does not make the 4pt:

  • 13/9*, 6/2

To break the tie between the two plays that make the 4pt, the Hit Convention gives preference to hitting. The final play, 13/11(2) 6/2, neither makes an inside point nor hits, and is the runt. This is the lowdown on the runt:

  • 13/11(2) 6/2 ranks below 13/11(2) 6/4(2) by the More Points Convention.
  • 13/11(2) 6/2 ranks below 13/9* 6/4(2) by the Hit Convention.
  • 13/11(2) 6/2 ranks below 13/9* 6/2 by the Hit Convention.

The following table gives the breakdown for the top 4 members of the family.

Traditional
Notation
Far
0
Down
2
Jump
0
Inside
2
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
13/9*, 6/4(2) 13/11
11/9*
6/4
6/4
9pt 4pt 9pt* N
13/11(2), 6/4(2) 13/11
13/11
6/4
6/4
4pt* 11pt n
13/9*, 6/2 13/11
11/9*
6/4
4/2
9pt* 9pt 2pt N
13/11(2), 6/2 13/11
13/11
6/4
4/2
11pt 2pt n

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


Position 3


1O1O ' ' '5X '3X '1X '4O

1X ' ' ' '5O1X3O1O ' '4X

41S-63S-22


In Position 3, there are 3 ways to make two moves down:
  • 13/11(2)
  • 13/9
  • 13/11, 9/7*

In the same position, there are 2 ways to make two moves inside:

  • 6/4(2)
  • 6/2

By forming all the possible combinations, we generate the 6 members of the N (Near) family. In no particular order, they are:

  • 13/11(2), 6/4(2)
  • 13/11(2), 6/2
  • 13/9, 6/4(2)
  • 13/9, 6/2
  • 13/11, 9/7*, 6/4(2)
  • 13/11, 9/7*, 6/2

In order to rank these 6 plays, first remember the home-board exception in the Hit Convention. More owned points in the inner board beats any hit (inside or out). For plays that have the same number of inner board points, hitting trumphs making a point. Otherwise, making a point trumphs leaving a blot or spare.

Making the 4pt puts you in the top 3:

  • 13/11(2), 6/4(2)
  • 13/9, 6/4(2)
  • 13/11, 9/7*, 6/4(2)

Hitting comes next:

  • 13/11, 9/7*, 6/2

Followed by making an outside point:

  • 13/11(2), 6/2
  • 13/11/9, 6/2

To rank the top 3, note that they all make the 4pt, so the main tie-breaker is hitting. After that, making the 9pt beats making the 11pt.

The following table gives a breakdown of the top 4 members of the family.

Traditional
Notation
Far
0
Down
2
Jump
0
Inside
2
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
13/11, 9/7*, 6/4(2) 13/11
9/7*
6/4
6/4
7pt* 4pt 7pt 11pt N
13/9, 6/4(2) 13/11
11/9
6/4
6/4
4pt 9pt* n
13/11(2), 6/4(2) 13/11
13/11
6/4
6/4
4pt* 11pt N
13/11, 9/7*, 6/2 13/11
9/7*
6/4
4/2
7pt* 2pt 7pt 11pt n

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


Position 4


2O ' ' ' '5X '3X1X ' '3O

1X ' ' ' '5O1X3O1O1O '4X

43D-64S-22


In Position 4, there are 5 ways to make two moves down:
  • 13/11(2)
  • 13/9
  • 13/11, 10/8
  • 13/11, 9/7*
  • 10/8, 9/7*

In the same position, there are 2 ways to make two moves inside:

  • 6/4(2)
  • 6/2

By forming all the possible combinations, we generate the 10 members of the N (Near) family. In no particular order, they are:

  • 13/11(2), 6/4(2)
  • 13/11(2), 6/2
  • 13/9, 6/4(2)
  • 13/9, 6/2
  • 13/11, 10/8, 6/4(2)
  • 13/11, 10/8, 6/2
  • 13/11, 9/7*, 6/4(2)
  • 13/11, 9/7*, 6/2
  • 10/8, 9/7*, 6/4(2)
  • 10/8, 9/7*, 6/2

In order to rank these 10 plays, first remember the home-board exception in the Hit Convention. More owned points in the inner board beats any hit (inside or out).

Making the 4pt beats any hit, so these plays form a group:

  • 13/11(2), 6/4(2)
  • 13/9, 6/4(2)
  • 13/11, 10/8, 6/4(2)
  • 13/11, 9/7*, 6/4(2)
  • 10/8, 9/7*, 6/4(2)

Next come the plays that hit, but do not make the 4pt:

  • 13/11, 9/7*, 6/2
  • 10/8, 9/7*, 6/2

Below that comes the single play that makes a new outside point without hitting:

  • 13/9, 6/2

Followed by the two runts:

  • 13/11(2), 6/2
  • 13/11, 10/8, 6/2

Of the plays that make the 4pt, the pair that hit are ranked 1st and 2nd. To determine which gets top billing, use the “wrinkle” in the 6pt Convention. For blot and spare destinations in the outer board, the checker that is moved closest to the 6pt should be as far back as possible. Thus, moving a blot to the 11pt beats moving a spare to the 8pt.

Still with the group of plays that make the 4pt, by the More Points Convention, the single play that adds a new outside point ranks 3rd. By the 6pt Convention, switching from the 13pt to the 11pt earns 4th, because an owned 11pt is closer to the 6pt than an owned 13pt. Fifth place goes to 13/11 10/8 6/4(2), the sole remaining play in the bunch.

The following table gives a breakdown of the top 4 members of the family.

Traditional
Notation
Far
0
Down
2
Jump
0
Inside
2
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
13/11, 9/7*, 6/4(2) 13/11
9/7*
6/4
6/4
7pt 4pt 13pt 7pt 11pt* N
10/8, 9/7*, 6/4(2) 10/8
9/7*
6/4
6/4
7pt* 4pt 13pt 7pt 8pt n
13/9, 6/4(2) 13/11
11/9
6/4
6/4
4pt* 9pt* 13pt* N
13/11(2), 6/4(2) 13/11
13/11
6/4
6/4
4pt 11pt* n

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

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