Comments by GeorgeDuke

Most likely Beyond Chess'(tm) moving squares(1) force unboundedness,
because unlimited the sequences of moves.  Once having modality of moving
squares, then new Rules-types(2) are also unlimited, as one of its
subsets, piece-move definitions(3), would then be.  So, there probably
become infinite ways to move Rook, Bishop, Knight, at least in combination
with just one other helpful Mutator like Beyond Chess'. Still to be
decided is whether one inclusive systematic definition of, say, Rook's
movement, without another Mutator and with same board size, could be
infinite.  We use up to 32 Mutators at once at '91.5 Trillion...',
exceeded by only few other (convoluted) games like Ralph Betza's
Nemeroth. The goal eventually, in understanding so-called
''inventing'' and concatenating Rules to fancy, should be to divest
99.9999% of them more systematically than mere popularity.

Altair standard, Rococo standard, Jacks & Witches.

'9x9' percentagewise has far and away the most Excellent Chesses, however it may be broken down to get subsets of 0.1% to 1.5% of the 10*4 CVs invented per grouping: whether by such board sizes, or by locale of invention(Hanga Roa is South American), or by Western or Xiangqi-based(further subdivided to get < 2%), subsets of Mutators versus new piece-types, any way that can be thought of to slice it. '9x9' is the pinnacle, however weird it seems. Among the several acme 9x9 is Hanga Roa, already analysed couple of times. Hanga Roa does so much with only three piece-types. One of the two win conditions has kinship with just-discussed Melee preceding it chronologically.

9x9.  Here's a theorem by Niels Henrik Abel (Abelian set, group, integral) on convergence of series in 1826:     
 0 = 1^n - 2^n + 3^n - 4^n + etc.,  n positive integer.  Here's a poem by Mark Stroud (slashes are lines): ''In a field/ I am the absence/ of field./ This is/ always the case./ Wherever I am/ I am what is missing./ When I walk/ I part the air/ and always/ the air moves in/ to fill the spaces/ where my body's been./ We all have reasons/ for moving./ I move/ to keep things whole.''  How to slice, like apple or pizza, the 10*3 CVs from 'ECV' and 'CVP'? Any 100 of them, like Gilman's or Betza's, are 1%. To evaluate we need subsets of 10 to 200 to compare, in other words, 0.1% up to 2%. Criteria can be any of locale of invention, board size, number piece-types, power density, year invention, gender, shape, geometry, theme, number mutators, winning conditions . Take sizing's '9x9', containing about 50 CVs, 0.5%. Surprisingly there are 25 Very Good/Excellent within 9x9, a disproportionate 50%. Previously reviewed, Weave & Dungeon   uniquely has Circle, Star, Triangle, Square, Pentagon, Diamond.

'9x9 Blockbusters'. Who know what it is? Put a 'CV' (chess variate) on 9x9, and most of the time it turns out very good or excellent. The only other category that holds for seems to be  handful of particular human inventors -- to be named later. Who characteristically has  > 10 CVs and > 50% Excellent? Only  few, and we shall go out on our proverbial limb as usual, find them, and name them. Part of the reason for 9x9-types' inherent excellence has to be that Shogi amalgums -- chiefly standard Shogi -- on 9x9 are so poorly conceived. Certainly representing excellent culturally, Shogi nevertheless has been found mostly bad for play to most clubbers, worse than also-slow-paced Shatranj. Casual players in the western world find Shogi pieces, moreover, arbitrary and drops distracting. (At least Shatranj had coherence for its time.) Anyway, here is another fine, because original, '9x9', Sissa, recreating as it does ten years ago multi-path Sissa, after Coherent months earlier, and explaining it well enough in this article.  The era was short-lived, 1995 - 2003 (when Ralph Betza left) that gave CVs  spontaneneous inventiveness, with none of today's ego-driven ''new'' (and not so new (and not new at all)) combinations of elements and, worse, rating of others' CVs not very analytically, instead even with self-described vengeance aforethought. In other words, the modern ethos within CVPage includes that if someone criticizes one's CV, it is taken personally and  calls for ''balancing the equation'' by rating the evaluaters' CVs or articles low, regardless of actual merit. Most of newer prolificists adhere to their such principle of ''vengeance rating.'' What a downturn from days of Ralph Betza's mixture of dry wit and informed judgment.

Draws in Chess would not optimally be expected to be as infrequent as a
Deadheat in thoroughbred horse racing, occurring less than 0.5% of the
time. Neither should we require several sudden-death ''extended
times'' to get an outcome 95% the time. Infrequent Draws are to be
tolerated. The right technique, i.e. Rules-set tack-ons, to reduce Draws
to acceptable level (usually 1% to 10%) depends on the game. Draws in
Rococo might benefit from the following novelty, entailing strict 100-move limit: if no capture of Rococo King by move 100, either player may declare
''DRAW'' precisely at that milestone. It would be brand-new Draw
criterion never used before. Many CVs have not determined requisite mating material, especially those CVs never yet played, even by inventors. If no
one knows minimum mating material, that standard has to be used with
extreme caution.

In ''Defining the Abstract'' Mark Thompson discovers four timeless
factors defining a CV (or game, or formal axiomatic systems if one will).  Namely, Clarity, Decisiveness, Drama, Depth. The tradeoffs are apparent.
Which are markedly like polar opposites? Which paired opposites in tension forever try to drag the other down, in the quest for coherence?  Which
reduces or offsets  the other one's effectiveness in any design? Go ahead
and guess, there being only the three possibilities. Why obviously, Depth
versus Clarity, and secondly Decisiveness versus Drama, as Thompson
enunciates. Think predator versus prey: more depth means less clarity by
and large. Or like balancing an equation: if less decisive then more
dramatic, by some rule of balance. Observe a binary star system's unending tug-of-war: an abstract game's play-offs. Two-body problems three- four-,
multi-. ''Defining the Abstract'' appears to have been written for
short-lived website 'Games Journal' in 1990's.

Hutnik's asks origin of Pawn moving NSEW and capturing omni-diagonally.
Centennial Chess Steward is also called QuadraPawn used after Centennial
invented in 1990's in number of other CVs. Offhand ''Corporal'' and Sergeant exist under other names. We are clearly at the re-inventing stage, where (almost) nothing new under the Sun.  //Second Comment: Hutnik is assuming 9 and more ranks (''rows'' is equivocal) throughout this thread. If only 8 ranks and 9 or more files, there is no need for Pawn enhancement at all. //Thirdly, Big Battle invented 1994 and patented has interesting Pawn enhancement, facing the overwhelming empty space 10x10 dumps on the players. I.e., Big Battle Pawns can move 1, 2, or 3 spaces non-capturing any time, not just from their array.

Here is another Piece Values thread from environs of 2004, but it is hard
to read before its most recent 25 Comments, because 26-50 and 51 and over
get lost in the indexing.