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MatPlus.Net Forum General chameleon-hopper
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(21) Posted by Kevin Begley [Saturday, Oct 1, 2011 00:23]; edited by Kevin Begley [11-10-01]


You had me, until we came to the King's file, where it became difficult to anticipate the direction you would take; and, only more difficult to understand your choice.
I was starting to think that the Royal might be a kind of file-transmuting 'querquisite' -- normal K powers on their own 'e' file, and absorbed powers (Q/R/B/S or G/RH/BH/NH) on other files...
But, then I remembered how much I disfavor using the initial game array (which is completely arbitrary, and does not universally translate for different board sizes/shapes) as a means to govern fairy elements.

This may seem a strange philosophy, when you consider that the rules of chess do not universally translate either (e.g., double-steps, castling, en passant, promotion, etc)...
So, why should I dogmatically avoid fairy elements which rely upon this arbitrary arrangement?
And, -- coming from somebody who rarely encounters a good justification to vacation beyond the 8x8 -- why should I particularly care how this translates on a 10x10?
Finally, why should I be any more tolerant of the arbitrary cycles that chameleons pass through (S -> B -> R -> Q -> S)?

I never found satisfactory answers for any of these questions.
I could offer some excuse for chameleons (at least their cycles can be easily altered, in a small space below the diagram), but this would never be sufficient to prove my case.
The truth is, I have a personal predisposition to avoid the initial game array... maybe I'd like to forget how to set up an orthodox chess game. :)

Hopefully, some insight into my philosophy (where my predisposition is rooted!) may provide satisfactory answers...

Consider the original billing for Mars Circe -- this was somebody's interpretation of how chess might be played by Martians.
I can certainly imagine that these Martians probably discovered Kings, Rooks, Bishops, and Knights (the Queen, of course, would be a simple combination).
I can imagine they might have discovered pawns too (and promotions would seem a natural extension).
I am willing to suspend disbelief for double-steps, en passant, and castling -- I'll even allow that the Martians might agree with our arbitrary board size.
But, I could never accept how unlikely it would be for Martian's to employ our same initial arrangement (exactly).

The odds are very low that some non-Earthling -- even in this vast universe -- would have invented Mars Circe.
By comparison, consider the odds that some E.T. has discovered the concept of King opposition...
What are the odds that an E.T. (or an N.B.E.!?) was first to compose Forsberg's famous helpmate (well, maybe four-fifths of it, anyway)?
If I had to "guesstimate" what the ratio would be (Probability of Mars Circe divided by Probability of Forsberg), I'd say less than: 1/googles.

In my view, the best fairy chess elements (for problem chess/variant chess) are those which attempt to make a quality prediction about the fairy chess elements that other intelligent beings (even if only theoretical beings) might employ.

[aside: Beyond this, I would add only two things: First) ideally, all changes in a position should be entirely determined by three things: the game history, the departure square of the moving unit, and the arrival square (not necessarily equal to its final destination, ala AntiCirce forms) of the moving unit. Perhaps some exception must be made in the case of promotion choices, but any additional exceptions (movement choices) incurred would be the product of a sub-optimal element (e.g., Super Circe, Optimal Replacement, Cage Circe, Chess-960 etc). Second) ideally, the resulting position should be unique to all choices made in a complete turn (not true in Progressive Chess, nor in Arimaa -- though perhaps it might be interesting to compel a unique turn in these games). Some have attempted to extend this theory, to insist upon unique departure/arrival squares (e.g., a Rose should not move from e2 to e2), and others claim a unique path must be laid out from departure to arrival (and on, to destination). Further, the Game-Theorist's term "perfection of a game" can be seen as inversely related to its reliance upon "game history" -- except in explicitly retrograde problems, this too is a fine point, worth consideration. Finally, the super-optimal elements would minimize positional repetition (inherently, rather than by decree, as in Arimaa), would reduce draw probabilities (while maintaining a fair balance for both sides), would maximize branch factors per square, and would maximize non-reciprocal attacking mechanisms. The more of these criteria you achieve, the closer you are to playing the game of the little green men.]

The inventor of Mars Circe starts out by providing us this wonderfully rich philosophical perspective, but then fails to follow through in his invention (he shows us how Martians might play Earth-Chess, instead).
If E.T.'s are operating under the same philosophy, clearly they, too, would deliberately strive to avoid arbitrary rules (if only to match what they must expect from us)!
In fact, I often wonder if it might be worthwhile to shake off a few arbitrary chess rules (castling, en passant etc) -- regardless what wonderful asymmetries these may provide.
I suppose a few arbitrary rules (specific to chess evolution on Earth) must be tolerated. :)

ps: Some well known variant chess theoreticians -- Bird, Capabalanca, and others -- seem to have shared this philosophy (as is demonstrated by their efforts to balance the disharmony of the Queen's redundant powers: R+B, but no B+N / R+N). This may help explain the motivation behind my own fairy invention: "psycho-units." Unlike the Queen, psychos have no imbalanced redundancies, and unlike the Chameleon, they have no arbitrary pattern of metamorphosis. It remains to be seen how well this philosophy will translate in to interesting problems/games. And so, if only to discover where it leads, I am predisposed to avoid that which leads me off this path.

Maybe some day -- just maybe! -- we might have an opportunity to directly compare problems with E.T.
Wouldn't it be wonderful if we could point to some mutual experiences!
If they landed tomorrow, I would expect our commonality might be limited to Knight-Tours and "n-Queens" problems.
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(22) Posted by seetharaman kalyan [Saturday, Oct 1, 2011 14:19]

Sorry to go offtrack. I am curious. How do the immensely popular Circe rules apply on a 10x10 board? Probably they dont apply :)
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(23) Posted by Kevin Begley [Saturday, Oct 1, 2011 14:53]; edited by Kevin Begley [11-10-01]

They might actually apply -- many circe problems have even been composed on smaller boards.
So, maybe rebirths go to the first/last 2 ranks, and only pawns/fairies are reborn on columns beyond the h-file.
But, it's such a hack when orthodox units are present.

I favor universal circe/acirce forms, w/ uniquely determined rebirths: Parrain, Contra-Parrain, PWC, Eqiupollents (basically this is Contra-PWC), Antipodean, Vulcanic, Diagram, File, Symmetric, ...
You could argue that Bughouse and Crazyhouse also belong in this category, because rebirths require a drop, and that drop is always unique.
And, you could argue that "Swapping Kings" is an unusual form of Circe (with King rebirths, based upon checks, rather than captures).
Ibidem Circe too, but this is an odd one -- in its orthodox form, only en passant captures are reborn; otherwise, capturing fairy units are turned into hamster-hybrids.

Almost equally good are the other universal forms, except that here rebirths are not uniquely determined: Super, Cage, optimal replacement, Take & Make...
Plus, the new one, Memory Circe, should fit this category too, if my reading of French is any good.

All these conditions tend to increase branch factor (for the latter group, the difference can be astonishing).
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MatPlus.Net Forum General chameleon-hopper