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A Procedural Definition of Hit/Most/Six

Posted By: Taper_Mike
Date: Wednesday, 16 November 2011, at 11:24 p.m.

In Response To: Nactation Questions — Clarifying Parts of Hit/Most/Six (Taper_Mike)

I think I have finally come up with a procedural definition of the Hit/Most/Six Rule. I hope you'll have time to carefully consider it. You may find it overly verbose – it may be! – but my interest is only in its accuracy. I believe this procedure fully describes the Hit/Most/Six Rule as it is currently written.

### Hit/Most/Six Rule

Use the following procedure to compare two plays within a Nactation family, and determine which ranks higher.

1. First, compare the plays using the Hit Convention.
2. If the plays are tied under the Hit Convention, compare them using the Most Points Convention.
3. If the plays are still tied, compare them using the 6pt Convention. It cannot result in a tie.

### Hit Convention

1. If neither play hits, then the plays are tied under the Hit Convention.
2. Otherwise, if one play hits in the inner board (call this play H), while the other play (which we designate play M) results in more owned points in the inner board than play H, then play M outranks play H. This is true whether play M hits or not.
3. Otherwise, if one play makes more hits overall than the other, then it ranks higher in the family.
4. Otherwise, the two plays make the same number of hits. Compare the highest points where each play hits. If one play hits on a higher point than the other, then it ranks higher in family. If the two plays are tied by this measure, and both plays make a second hit, compare the second highest points where each play hits. If one play hits on a higher point than the other, it ranks higher in family. If the plays are still tied, and supposing that a third and/or fourth hit was made, compare them in a like manner.
5. Otherwise, if the plays are still tied, then they are tied under the Hit Convention.

### Most Points Convention

1. If one play results in more owned points than the other, then it ranks higher in the family.
2. Otherwise, the plays are tied under the Most Points Convention.

### 6pt Convention

The locations of owned points are compared first. Any ties are resolved by comparing the locations of blots and spares. In general, being closer to the 6pt is better. Blots and spares in the outer board, however, rank higher when they are farther from the six point.

1. First, compare the Locations of Owned Points.
2. If that results in a tie, compare the Destinations of Blots and Spares Not in the Outer Board.
3. Finally, if the plays are still tied, compare the Locations of Blots and Spares in the Outer Board.

### Locations of Owned Points

1. Begin at the 6pt, and search outwards in both directions one point at a time until you find a point that is made in one position and not in the other. The position in which the point is made outranks the other.
2. In the event that the positions have points made at equal distances from the 6pt, but the made point is located in the inner board in one position and in the outer board in the other, then the position with the inner board point ranks higher in the family. The 5pt and the 7pt, for instance, are tied distance-wise, because both are one point away from the 6pt. By this rule, owning the 5pt outranks owning the 7pt.
3. Otherwise, the set of owned points must be the same for both plays. They are tied according to the Locations of Owned Points.

### Destinations of Blots and Spares Not in the Outer Board

The destinations of blots and spares in three quadrants of the board are examined here. We're talking just about the checkers that were moved in a play. The inner board and both far side quadrants are tested. The outer board is not.

1. Begin at the 6pt, and search outwards in both directions one point at a time (skipping over the outer board) until you find a blot or spare destination that exists in one position, but not in the the other. The position which has the blot or spare ranks higher in the family.
2. Otherwise, the two positions are tied by this measure.

### Locations of Blots and Spares in the Outer Board

1. Begin at the 6pt, and search outwards in outer board until you find a blot or spare destination that exists in one position, but not in the the other. The position which has the blot or spare ranks lower in the family.
2. In the event the two plays under consideration are still tied, then they are identical! A tie is not possible.

### A Concern about Owned Points

I have not had time yet to construct actual board positions, but I suspect a blotty postion similar to the Zare position might afford the possibility of a conflict when 1-1 is played. Consider these three positions:

1. Play H: Hits in the inner board (without making a point there). Play H also moves outside, but without making a point or hitting.
2. Play M: Makes a point in the inner board (without hitting inside) Play M also moves outside, but without making a point or hitting.
3. Play O: Makes two outside points, without hitting anywhere. At least one checker is moved inside.

Can three such plays be devised with all three belonging to the same Nactation family (perhaps the E or E (Each) family)? If so, there is a problem. By the Hit Convention, play M outranks play H (when the two are compared to each other). Also by the Hit Convention, play H outranks play O because play H hits, and play O neither hits nor makes an inside point. Finally, by the Most Points Convention, play O outranks play M when they are compared, because neither play hits, and play O makes more points than play M.

In summary: M > H > O > M.

Mike

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