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Nactation – Algorithm for the Hit Convention

Posted By: Taper_Mike
Date: Wednesday, 19 November 2014, at 10:23 p.m.

In Response To: Nactation – Algorithm for the Hit Convention (Taper_Mike)

 White is Player 2 score: 0 pip: 156 9 point match pip: 160 score: 1 Blue is Player 1
XGID=-a----E-CAA-fC---c-e----B-:0:0:1:55:1:0:0:9:10
Blue to play 55

eXtreme Gammon Version: 2.10

## 43D-65R-55

In November 2011, I wrote a Procedural Description of Hit/Most/Six. It includes algorithms for all three parts of the Hit-More-Six Rule. Although I did not check my old work, the algorithm I wrote for the Hit Convention last week is identical to the one I wrote in 2011. In some places, they eerily match word for word.

Unfortunately, Nack wrote me over the weekend to say that I was wrong back in 2011, and that I am wrong today!

My error was a no-so-subtle one. According to Nack the Hit Convention should not be applied at all when two plays make the exact the same hits. More precisely, the Hit Convention results in a tie when two such plays are compared with one another.

Here is how the Hit Convention is defined on page 48 of the Nactation Tutorial:

Hit if possible, and on the higher point.
[Exception: An extra point in the home quadrant overrides any hit.]

In the position David posted, 43D-65R-55, my mistake was to apply the exception. In the Attack family, all four members make the same hit (on the 1pt). That’s the end of the story. Whenever any two are compared, the Hit Convention results in a tie. The only time one should consider the exception is when two plays being compared with each other do not make the same hits.

For 43D-65R-55, that means that David’s original ranking of the Attack family is correct. The Hit Convention is tied, and the More Points Convention, i.e., the second part of Hit-More-Six, also results in a four-way tie. All four members of the Attack family give Blue four owned points, so no play has “more points” than any other.

The next convention is the 6pt Convention. It has two parts. The first compares the locations of owned points, giving preference to those that are closer to the 6pt. Under this convention, the top three plays are still all tied. In fact, the top three plays all own exactly the same points, so they must be tied. The fourth, however, 8/3(2), 6/1*(2), trades the 8pt for the 3pt, thereby falling into last place. That’s because the 3pt is farther from the 6pt than the 8pt is.

To break the three-way tie at the top of the family, the second part of the 6pt Convention is used. It deals with the destinations of checkers that become blots or spares when they are moved in a play. Preference in given to destinations that are closer to the 6pt, except in the outer board, where the so-called wrinkle gives preference to destinations that are farther from the 6pt.

As the table below shows, the top play has blot and spare destinations on the 5pt and 4pt. In second place, just a little bit worse, are destinations on the 5pt and 3pt. Third place goes to destinations on the 4pt and 3pt.

Attack Family
Rank Traditional Notation Nactation Inside Points Hits Owned Points Blot & Spare Destinations
1 10/5, 9/4, 6/1*(2) A 2 1pt 6pt, 8pt, 1pt, 13pt 5pt, 4pt
2 10/5, 8/3, 6/1*(2) a 2 1pt 6pt, 8pt, 1pt, 13pt 5pt, 3pt
3 9/4, 8/3, 6/1*(2) A 2 1pt 6pt, 8pt, 1pt, 13pt 4pt, 3pt
4 8/3(2), 6/1*(2) a 3 1pt 6pt, 3pt, 1pt, 13pt [none]

### Updated Algorithm for the Hit Convention

Follow these steps to compare two plays in the same Nactation family, and determine which, if either, ranks higher under the Hit Convention.
1. If the two plays make the exact same hits (or no hits at all), then they are tied under the Hit Convention.
2. Otherwise, if one play results in more inner-board points than the other, it ranks higher. This is true whether it hits or not.
3. Next, if the plays are still tied, count how many hits each play makes. The play that makes the most hits outranks the other.
4. If both plays make the same number of hits, then the one that hits on the highest point wins.
5. If the highest point is a tie, check the second-highest point where each play hits. Once again, the play that hits on the higher point wins.
6. If the plays are still tied, continue checking the third-highest point where a hit is made, and so on, until a winner is determined. Eventually, you will find one. This step cannot result in a tie (since that was covered in step 1).

Mike

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