Comments by GeorgeDuke

Of course Larry Smith and Michael Nelson are right that predilections rank
high in importance. No one yet addresses multiplicity of chess game-rules
sets, more than anyone can absorb at the level of play. Maybe would-be
designers could curb or arrest addiction to design.  Or, a change in rules
of a long-established game like Ultima, for ex., should be a very cautious
act, as a recent Comment under Ultima advises.  David Pritchard from Introduction
to Encyclopedia of Chess Variants: 'Anyone can invent a new CV within ten
seconds and unfortunately some people do' and 'Probably most CVs are
best consigned to oblivion.'

Moises Sole asks about G Exchange Gradient in move equation. See my comment here 
'To go with Depth-Clarity....'  Heuristically, G is average of all the
possible ratio-pairings of piece values, King included.  Informally: to avoid
'infinities,' put smaller value always on top, normalizing. 
In specific case of Isis with piece values 1,2,3,4,8, it becomes:    (1/2
+ 1/3 + 1/4 + 1/8 + 2/3 + 2/4 + 2/8 + 3/4 + 3/8 + 4/8)/(10) = 0.425. 
Then (1-G) for right directionality with the other factors in #M equation
is 0.575.  The first use of G, or (1-G), is to predict average number of
moves in a game-concept. This predicts closely game length for those tested so far: 
 M = 4(Z)(T)/(P)(1-G), where M #Moves, Z board size, T piece-type density, 
P Power density, G Gradient as above.

Jack & Witches design analysis:
# squares: 84
# piece types: 9
Piece-type density: 0.101
Est. piece values: P1,L2,N3,B2,R5, J1(in hand), K2,C7,W12 [Probably Pawns
are less than 1 and Witch greater than 12, but convenient to stay at these
limits]
Initial piece density: 48%
Power density: 122/84 = 1.45
Exchange gradient: 0.444; (1-G) = 0.556
#M = (3.5(84)(0.101))/(1.45(0.556)) = 37 moves [Still fine-tuning constant
now 3.5 instead of 4]
Other features: Transporter cells do not disproportionately affect piece
values.
Comments: Power density is high substantially from number of pieces
paired, five(5).

Rococo design analysis:
# squares: 82 [counting rim squares as 1/2]
# piece types: 8
Piece-type density: 0.098
Est. piece values: P2,W3,K3,C4,S5,L7,A8,I10
Initial piece density: 32/82 = 39%
Power density: 126/82 =1.54
Exchange gradient: 0.69; (1-G) = 0.31
Ave. Game Length: #M = (3.5(82)(0.098))/(1.54(0.31)) = 60 moves
Other features: Reasonable to count as 1/2 border squares, reachable only 
               by capture.  The high exchange gradient (low exchange 
              potential) reflects steady continuum of piece values.
Comments: Long games, high # moves predicted, and Rococo is game that 
          player can recover from being down in material.

Predictions for the length of games (#M) is not the main goal for looking
at CVs analytically. Yet results from Courier completed games
interesting:
               -predicted ave.#M-        -Game Courier-
Jacks&Witches       37                   11-03-04 23 = 24 Moves,     
                                               (anticipating checkmate)
                                         07-10-03 14 = 16 Moves
                                         28-10-03 26 = 36 Moves,
                                         checkmate maybe 10 moves ahead
Rococo              60             15-12-03  44 Moves
                                   16-01-04  55 = 60 Moves,
                                         (checkmate five moves ahead)    
                                   23-12-03  53 = about 58 Moves played out
  The trend is apparent that, with Z Board size more or less constant,
Exchange Gradient especially has high predictive value for length (#M).

Wildebeest Chess design analysis:
# squares: 110
# piece types: 8
Piece-type density: 7.27%
Est. piece values: P1, N3, B3, R5, Q10, K3, C4, W8
Initial piece density: 40%
Power density: 1.27
Exchange Gradient: 0.499; (1-G) = 0.501
Ave. Game Length Projected: #Moves=((3.5)(110)(0.0727))/((1.2727)(0.499))
                             =    44  Moves
Features: Unbalanced initial positioning suggests a hundred more 
          variations on the same board with the same pieces.
Comments: Despite large Z board size,low PTD suggests average-length games.

Antoine Fourriere mis-reads Larry Smith's idea, which I agree with, that
potential for advantage in the exchange comes from significant differences
in piece values, regardless whether many an exchange may appear equal. I
incorporate these piece-value disparities numerically in what is called
Exchange Gradient. In Antoine's words, 'a useful variable' of 'over-all 
strength by piecetype variance' is exactly what EG is.

Note that M = 3.5ZT/P(1-G) is useful form of Move Equation because T,
piece-type density, will figure in the Positional-advantage Potential
Equation, yet to be posted. Use of T, piece-type density, in both enables
other comparisons later. Actually, of course, for Game Length, #M =
3.5N/P(1-G), N simply number of piece-types, is all that is necessary,
eliminating Z Board Size from numerator. Z still contributes to
determination of Power Density. So, original equation reduces to M =
3.5N/P(1-G)

Bad enough that CVP editor no less lifts 'Horus' from major theme of 600
lines of Falcon Chess poetry since 2000.  Peter Aronson also puts out 
misleading description of Falcon move beginning, 'Falcon moves
like a Bison.'  Hardly correct. Falcon is a Rider with one or two
45-degree turns. 'Bison' appears nowhere in 2000 Pritchard's
'Encyclopedia of CV' games or 2000 more games in CVP (4000 total games so
far). Fitting into no false, preconceived template, Falcon does not jump
like Knight (1,2), or Camel (1,3) or Zebra (2,3).  Whereas, theoretical
Bison is a (1,3)(2,3)Leaper defined in very rare couple of problems.  My 
Patent Disclosure in January 1995 cites three(3)Pritchard ECV games with (Z+N)
compound and three others with (C+N). 
'Actual Bison' (as Zebra plus Camel), even if it appeared in any game, would not
particularly elucidate Falcon move, since they are from wholly different
families of pieces, Leapers and Riders. Aronson goes on that Falcon (US
Patent 5690334) has greater piece value than 'lame Bison.' What is that? He never 
defines it.  What to make of describing a fundamental Chess
piece (Falcon, with R, N, B the other three such) in terms of what it is
not?  It's like playing a game of twenty(20) Questions: is it this, or is it
that, until what is left out of everything possible is what it is.

Coined in 2003 by Ralph Betza (and never used by anyone else)the term 'Lame' is applied to 
Dabbaba, where from e4 it can move to e6 if and only if e5 is empty. 'Lameness' to him makes a 
leaper not a leaper, since it requires unobstructed pathway.
Yet Falcon uniquely has three(3)pathways to each square 3 steps away not reachable by Knight 
or Queen. So neither lameness nor leaping describe Falcon. Aronson goes on: 'One result is that, 
unlike with Lame pieces, if Black's Falcon attacks White's Falcon, White's Falcon also attacks 
Black's Falcon.' [Later I delete here some lines speculating what a 'lame Bison'is. 
Who knows? Aronson refuses to define it; as of April 2004, no one has 
used 'lame' for any oblique mover at all. The uncomplimentary term originates with Aronson. 
He just wants pejorative adjective attached to Falcon, and succeeds to the extent  
others now start calling F 'lame'--after Aronson writes that Falcon is not lame.  
Altogether a worthless, deliberately misleading move description.]
It is not worth delving into these 20-Questions-like what-it-is-not
snapshots of F move.  Just go to original articles, where Falcon defined affirmatively
in terms of Rook, Knight, and Bishop, and those four standards' mutuality
and accompaniments are honestly and systematically related.

US Patent 5690334 for Falcon Chess is about seven years past the challenge
stage, so patent's claims are solid having been unchallenged. Games
patents go back over 100 years, including Scrabble, Monopoly; Peter
Aronson mentions under Complete Permutation, Ed Trice's Gothic Chess
Patent 6481716. Lost on Aronson is that 'Horus', while perfectly obvious, is
already used extensively in Falcon Chess poetry for the same patented
novelty. Having searched for just the right wording for Falcon-Horus
images, I think of it as expropriation for this miniature chess: no
commercial consequence would be issue, just common courtesy for those who
may not be singlemindedly obsessed with churning out new sets of game
rules.  Patenting is wholly different sphere than mere names of games:
about five US Patents for Chess issue per year, down from a peak of ten a
decade ago. As stated in Complete Permutation Chess comment, because
well-schooled in variants myself, I deliberately excluded 8x8 from my
claims, so CVist may experiment and welcome to use Falcon there without
infringement. [One could] relate these ideas to Fergus Duniho's Enneagram
under Game Design.