I've posted very little about the extended hierarchies of underlined families, because the deep-level situations arise so very rarely.
There are 13 letters (EACONGYMDJIQ) that are "double-service:" they have both underlined and regular (non-underlined) families. The other 13 letters have only regular families.
The double-service letters skip over the underlined toggle in their hierarchic structure. For example, consider the letter O. The hierarchy of the regular family is
O, o, O, o, O, o, O, o.
Similarly, the hierarchy of the O family is
O, o, O, o, O, o, O, o.
That's right: O and O each have "only" eight members. Contrast with a single-service letter like R, which has 16 members: R, r, R, r, R, r, R, r, R, r, R, r, R, r, R, r. (Not that you're likely to ever go beyond the first few of those!)
I am guessing that maintaining the ratio 1:1 (or 2:2) is more important than any of the considerations of the hit/most/6pt convention [sic].
Right. The ratio is part of the definition of a letter itself. The hit/most/6 rule merely determines the ranking within those defining characteristics.
| |
|---|---|
| 31P-62S-22 | |
- 13/11(2) 8/6(2)
13/11(2) 8/4 Wrong.
13/9 8/6(2) Right.
13/9 8/4 Wrong.
The first of those is O, and the third is o. For the second and fourth, one of the four move portions is entirely within the inner board (those 2:1:1 plays happen to be D and d).
Only after the half-in/half-out plays are exhausted are we allowed to consider those that have ratios of 1:3 or 3:1.
Incorrect. The 1:3 and 3:1 moves (collectively) are in a different family than the 2:2 moves. The separation simplifies matters. Thus, your examples below are not 5th and 6th in the O family (as you speculated), but rather 1st and 2nd in the O family:
- O = 13/7*/5
o = 13/7* 8/6
Note how the hit/most/6 rule helps the best plays rise to the top of their families.
As you observed, while the best play 13/7*/5 can be O, L or 5 seems like a preferable choice of Nactation.
Nack