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More nactation: 31P-62S-22

Posted By: Taper_Mike
Date: Tuesday, 18 October 2011, at 2:42 a.m.

In Response To: More nactation: 31P-62S-22 (Nack Ballard)

Thanks for your answer. I, too, have a preference for letters over numbers (especially in nacbracs), so I am switching to L as the nactation of 13/7*/5 in the third move position 31P-62S-22.

Your explanation of ratios and the fact that O could also be used intrigued me. In the family hierarchy, underlined O is fifth in rank:

  1. O — Upper case
  2. o — Lower case
  3. O — Upper case, italic
  4. o — Lower case, italic
  5. O — Upper case, underlined
  6. o — Lower case, underlined
  7. O — Upper case, italic, underlined
  8. o — Lower case, italic, underlined
  9. O — Upper case, bold face
  10. o — Lower case, bold face
  11. O — Upper case, italic, bold face
  12. o — Lower case, italic, bold face
  13. O — Upper case, underlined, bold face
  14. o — Lower case, underlined, bold face
  15. O — Upper case, italic, underlined, bold face
  16. o — Lower case, italic, underlined, bold face

If 13/7*/5 is fifth, I wondered, then what are the plays that precede it? My best solutions are described below. Before continuing, fellow reader, see if you can figure it out yourself.

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. If that is so, then there are 4 plays that might be ranked 1st. All maintain the half-in/half-out ratio.

  • 13/11(2) 8/6(2)
  • 13/11(2) 8/4
  • 13/9 8/6(2)
  • 13/9 8/4

As a tie-breaker, we can turn to the hit/most/6pt convention. As none of the candidates hit, we must examine the most-points convention. Two of the four plays make a new point (the 11pt), while all of them sacrifice the 8pt. Thus, the top rank must be assigned to one of the plays that makes the 11pt.

  • 13/11(2) 8/6(2)
  • 13/11(2) 8/4

To decide which one, we fall back to the closest-to-the-6pt convention. By this measure, 13/11(2), 8/6(2), which puts two checkers right on the 6pt, is the winner. Second place goes to 13/11(2) 8/4. It gets lower case o.

In order to determine 3rd and 4th place, we must also fall back to the closest-to-the-6pt convention. The play that puts two checkers on the 6pt, 13/9 8/6(2), is 3rd, and 13/9 8/4 is 4th.

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. Of them, the hitters rank highest:

  • 13/7*/5
  • 13/7* 8/6

Under the most-points convention, the former, which keeps the 8pt, is awarded 5th place, and the latter is given 6th.

If all this is correct, then the following table describes most of what I know about the nactation of 31P-62S-22.

31P-62S-22

SymbolMeaning
5 – Five13/7*/5 — L is preferred
L – Lift13/7*/5
O – Outer13/11(2), 8/6(2)
o – Outer13/11(2), 8/4
O – Outer13/9, 8/6(2)
o – Outer13/9, 8/4
O – Outer13/7*/5
o – Outer13/7*, 8/6

Mike

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