George Duke wrote on Tue, Feb 21, 2012 04:46 PM UTC:
TABLE OF SOVEREIGN VALUES (IX) Take a really Meshuga compound of duals,
P/T P/V Mate# meaning any such bi-compound beyond Gnu and
WOLF-RIDER 5.0 1 and Man, the first two. Add Knight to it,
WARRIOR 2.25 4 say the third dual-compound Zebu is chosen to
JAGUAR 2.25 4 get (Zebra + Zemel + Knight), who is Knighted
PANTHER 2.25 4 Zebu, a tri-compound more practical than awkward
COYOTE 2.25 4 Zebu bi-compound. Because of the spacing of
WOLF(ii) 2.25 4 three supposedly cooperating legs, it still
LION 2.25 4 takes the three of the Knight to describe
TIGER 2.25 4 SOVEREIGN Knighted Zebu(8.0, 3), tested by
BEAR 5.5 1 mobility. Sovereign Boards are 64-144, and this
CHEETAH 2,25 4 tri-compound of (N+Z+Zemel) all-leaping really
practically needs 121-256, so will not be tabled formally.
How about plain vanilla Zebu? Squared and squired on 100-256 is Sovereign Zebu(6.0, 4). To justify the piece-values, Knighted Zebu on 100 centralized reaches 24 squares matched to Rook's 18 there; and Zebu leaps to 16. Yet Rook Mate# is 1 and the higher piece-value ones have Mate#s 3 and 4. So piece values can be high, or higher, over 5.9, and accompanying Mate#s over 2.
Looking at examples upsets somewhat the first impression of some kind of reciprocal, or inverse, relationship P/V to Mate#. As piece value rises Mate Number often or usually falls as generality, but there is no simple relationship that always holds. Mate# is positive integer and piece value rational number.
Another example from the only five at most significant compounds of duals follows. Antelope has dual Namel, and the bi-compound Namu looks like Sovereign Namu(5.0, 4) suiting boards 100-256; the leapers involved are (3,4) and (1,7) for squares they reach.
Eventually after several hundred p/ts, M&Bxxs themselves beginning with the Ungulates chapter p/ts the afore are representative of, can be computed for sovereign tables. ''Lions and Tigers and Bears'' above are Fantasy Grand Druids as well as 'The Wizard of Oz'.*
Many, many questions are raised for follow-up how V piece value, M mate number, and Z board size interrelate, with opposing King inviolably eight-directional. For all we know, there may be a relationship to chemical valence numbers, where 1,2,3,4,5,6,7 are the values, 7 maximum the main groups, and 1 to 4 predominating -- exactly like these Mating Numbers.
*Caution: cozy(?) 'tWoO' author Baum's virulent racism towards genocide, http://en.wikipedia.org/wiki/L_Frank_Baum.
Http://www.wendyswizardofoz.com/script8.htm.