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| Blue to play 66 | |||
| Position ID: 8M7BAWDLrMEAJg Match ID: QQkbAAAAAAAE | |||
31P-22E-61E-64H-31Z-41D-52Z-32K-53-431-51E-C-41H-42C-21K-2-51H-F-66
Nactation is a two-step process. First, you have to figure out exactly which plays belong in a given family. Second, you have to rank those plays.
In the underlined F (Field) family, membership is based on the board areas where checkers move.
- 2 dice are played on the far side
- 1 die is played down (to a destination in the outer board)
- 1 die jumps from the outer board to the inner board
- 0 dice move entirely within the inner board
The ratios Run:Down:Jump:Inside are 2:1:1:0. The location of the 2 (in the first position) tells you to select the first word in the mneumonic “Field Glasses Magnify Yosemite.” This is the F (Field) family. The pattern 1:1:0 tells you it is underlined. (If the pattern were 1:0:1, this would be regular, non-underlined F. The families for G, M, and Y use the same patterns, but the 2 is inserted in a different place.)
In this position, the underlined F family is relatively large. It has 10 members. The table below makes it easy to see how the Hit-More-Six Rule is applied to rank them.
| Rank | Traditional Notation | Nactation | Inside Points | Hits | Owned Points | Blot & Spare Destinations |
|---|---|---|---|---|---|---|
| 1 | 22/16(2), 13/7, 8/2 | F | 4 | [none] | 6pt, 7pt, 4pt, 2pt, 1pt, 16pt | [none] |
| 2 | 24/18, 22/16, 13/7, 8/2 | f | 4 | [none] | 6pt, 7pt, 4pt, 2pt, 1pt | 16pt, 18pt |
| 3 | 22/16, 22/4 | F | 3 | [none] | 6pt, 4pt, 8pt, 1pt, 13pt | 4pt, 10pt, 16pt, 16pt |
| 4 | 24/18, 22/4 | f | 3 | [none] | 6pt, 4pt, 8pt, 1pt, 13pt | 4pt, 10pt, 16pt, 18pt |
| 5 | 22/16, 22/10, 7/1 | F | 3 | [none] | 6pt, 4pt, 8pt, 1pt, 13pt | 1pt, 10pt, 16pt, 16pt |
| 6 | 24/18, 22/10, 7/1 | f | 3 | [none] | 6pt, 4pt, 8pt, 1pt, 13pt | 1pt, 10pt, 16pt, 18pt |
| 7 | 22/16(2), 13/1 | F | 3 | [none] | 6pt, 4pt, 8pt, 1pt, 16pt | 1pt, 7pt |
| 8 | 22/16, 22/10, 8/2 | f | 4 | [none] | 6pt, 4pt, 2pt, 1pt, 13pt | 10pt, 16pt, 16pt |
| 9 | 24/18, 22/10, 8/2 | F | 4 | [none] | 6pt, 4pt, 2pt, 1pt, 13pt | 10pt, 16pt, 18pt |
| 10 | 24/18, 22/16, 13/1 | f | 3 | [none] | 6pt, 4pt, 8pt, 1pt | 1pt, 7pt, 16pt, 18pt |
Note first that none of the members hit, so we can skip the Hit Convention.
The next convention is More Points. Evaluating it just means counting how many points result from a given play.
- The top-ranked play results in 6 owned points. It gets the capital letter.
- Ranks 2-9 all have 5 owned points. The 6pt Convention will be used to break the ties.
- The 10th-ranked play holds only 4pts. It is ranked last.
The 6pt Convention ranks plays based on proximity to the 6pt. The first part gives priority to owned points that are closer to the 6pt. If that results in a tie, the second part ranks the locations of blots and spares that are moved in a play. Let’s start with Part 1. We are concerned only with ranks 2-9. Ranks 1 and 10 have already been decided.
- All plays own the 6pt, so that is a tie.
- The 2nd-ranked play owns the 7pt, just 1 pip away from the 6pt. The other plays in ranks 3-9 all own the 4pt, which is 2 pips away. Rank 2, therefore, has been determined.
- Ranks 3-6 all own the same set of points: 6pt, 4pt, 8pt, 1pt, 13pt. The second part of the 6pt Convention will be used to break the ties.
- Rank 7 is almost the same as ranks 3-6. At the end of the list, however, it holds the 16pt instead of the 13pt. Farther away from the 6pt means this play follows ranks 3-6.
- Ranks 8 and 9 both hold these points: 6pt, 4pt, 2pt, 1pt, 13pt. Their relative ranking will be decided by the destinations of blots and spares. Note, however, that both rank below the 7th-ranked play. That’s because the third point in the list, the 2pt, is farther from the 6pt than the correspoinding point, the 8pt, that is owned by the 7th-ranked play. The 8pt beats the 2pt.
Part 2 of the 6pt Convention rates the locations of checkers that end up as blots or spares when they are moved in a play. Checkers that are used to make a point (i.e., the checkers that are first and second to land on a point) are not counted. The third (and subsequent) checkers that land on a point are the spares that count here. So do checkers that end up as blots. Midway stopping points also count. That means that a checker moved, say, from the 13pt to the 1pt (where it ends up as a spare), generates two “destinations” under the 6pt Convention. Those are the 7pt and the 1pt.
Ranks 3-6 are determined first.
- Rank 3 and 4 both put a spares on the 4pt. That’s closer to the 6pt than the checker moved to the 1pt in ranks 5 and 6.
- Rank 3 and 4 are similar, but the 4th destination in rank 3, the 16pt, beats the 4th destination in rank 4, the 18pt.
- For the same reason, rank 5 beats rank 6. It’s the 4th destination that breaks the tie.
Ranks 8 and 9 come last.
- Once again the blots landing on the 16pt and 18pt make the difference. Other blot and spare destinations are tied.
- The 8th ranked play lands a blot on 16pt.
- The 9th ranked play lands a blot on 18pt.
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| Position ID: M7tdAACbWQDgTA Match ID: QQkGAAAAAAAE | |||
31P-22E-61E-64H-31Z-41D-52Z-32K-53-431-51E-C-41H-42C-21K-2-51H-F-66f-3-61H-3-41H-3-52H-53-F-22N-1-62P-32U-63H-32H-555-53Z-54r-64Z-54P-52r-646-41D-53H-41
This is the original position of this thread. Although a long Nactation sequence like this can appear daunting, it is really quite easy to play. The only really tricky play is the 66 describe above. I played the move that is ranked 8th in the table above, but which is the best backgammon play for the position.
This was a fun game. I posted the full sequence so you could see how the cube ended up on top. The 41 in the lower diagram has a wonderful, quiz-factor option that turns out to be not quite correct. See my explanation here. Nack produced two variations where the QF play comes out on top.
This post corrects the Nactation given here.
Mike