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Actually though, can 2 quads per turn trap Rook or Bishop? Or under what
conditions? This gets as mathematical as it is strategic, and does depend
on the board sizes and what n is, n being #Rook or Bishop squares maximum
allowed per move. Understand there is no capturing either way, only
blocking, and that the piece starts from the center or one of the central four. It turns out from research of Conway and Gardner that board size
2n+2 sides (4n+3 for Bishop) with 2 quads per turn and n being that maximum
allowable move for either of these two pieces, traps them. That's why I was looking for the
sawtooth board in CVPage, and found it only at Gilman's Nested Chess and
related ones. Moreover, for a next step abstractly -- looking variously at 1,2,3 -- there are proofs incredibly that just one quad per turn is sufficient against Bishop or Rook now once again back to an infinite board. Strategy is to create corners, based on n, and work inward, progressively capping advance, if YOU ARE THE QUAD, even against some dramatically huge n. Result: certain eventual entrapment. If you have the chess piece, YOU'LL NEVER WALK AGAIN. Can Knight escape against one Quad on an infinite board? Unknown and unproved as of Gardner's writing twenty years ago. Now for CVs the interesting cases will be short-range pieces, rather than the sliders, on visualizable boards 12x12, 20x20, 30x30. I have not thought about these much yet, so the Rook/Bishop cases simply set a context for what would promise to be very extensive recreational-math treatment. Gardner does not take up any other pieces than K,R,B, and Conway in 'Winning Ways' only a few other for follow-up. Then we'll advance the subject to what we know now are more important CV pieces than British mathematician Conway could ever have dreamed of.

The rules of Chess by Rabelais(1494-1553) are in Chapter 24 of Book V:
http://ebooks.adelaide.edu.au/r/rabelais/francois/r11g/book5.24.html,
http://en.wikisource.org/wiki/The_Fifth_Book?ChapterXXIV.
King must be local rules. Contemporary is Copernicus(1473-1543). North and South American indigenous population in 1492 was 125 million, the same as Europe then, at the beginning of European expansionism. Year 1496 in Spain has publication of Lucena's(1465-1530) 'Repeticion de Amores y Arte de Ajedrez', the same Chess of Italian term regina rabiosa, and described by Rabelais about 1540, originated and spread no earlier than 1490s.  
Two prior comment leads: 
http://www.chessvariants.org/index/displaycomment.php?commentid=26827,
http://www.chessvariants.org/index/displaycomment.php?commentid=26823.

CDA Contest to submit by 1 May 2011. Chesss Different Armies is to be
up-slotted from #30 at NextChess.  Included are all 8-10 established Armies by Betza, Aronson's Fighting Fizzies, and Lawson's Pizza Kings
under one banner. Several more Armies by any author, if close to 31.0 piece-value total, will be included fulfilling:
(1) Unremarkable Rookies may reach an edge/corner square only by a
one-step, interiorly 6x6 the same as usual.  Add feature to reclaim total
back to 31.0, and clarify whether Knight/D/A-component ever reaches an edge.
(2) The Walkie-Talkies are calcified low tech and either walk or talk.  Walk is regular move, and talk is flip of Jacks & Witches' Cannon/Canon. 
(3) The Colourbound Clubbers whereever they end each time, push all pieces one step away along the arrival file up and down. They are to be rather kin to Ultima-alternate Repeller who omni-directionally captures that sort of way.
(4) Fuddy-duddy Knights and Pawns are immune to capture mutually.  They just block each other.  Keying off the Nutty Knights of Betza, decide how many types should have the quality and how to assure near-31.0 points.  
(5) Trifling Trojans are pitting a rifle piece constantly missing the mark, 
http://www.chessvariants.org/d.betza/chessvar/missmark.html.  Fulfill the complete rules-set.  
(6) Stingy-Wingies are Betza Avian Air Force, 
http://www.chessvariants.org/piececlopedia.dir/ideal-and-practical-values-3.html, that disable any adjacent opposite in whay way?  Again, equlibrate weakening this time back down to 31.0 points. 
(7) The Sinister Ministers are to be all well-known ecclesiastics each of a different religion/order.  Make rules that novitiates play right away. 
(8) Open-and-Shutters pre-specify the say 2/3 of future moves they are subject to check/mate.  A counter-balance to get needed 31.0 might be that the other 1/3, any check the other way is Mate. If those are off, find and justify the center of gravity of such two opposing features. Or vary some similar format for most any ''same'' Different Armies where the rules for check/mate make the ''difference'' between them, instead of the piece-types' doing so.  Basically, bring the two differing checking-rules into balance, a la Betza/f.i.d.e. 31.0, somehow so it is a fair game Black-White.
(9) The Thunder Wonders move by sound not sight; finish the rules, noting this was begun before by John Smith,
http://www.chessvariants.org/index/displaycomment.php?commentid=22352.
[JSmith is answering '2' and '8' at the same time from: 
http://www.chessvariants.org/index/displaycomment.php?commentid=22344. Number '8' there becomes Number '9' here for C.D.A.]

Here to follow are a few hundred piece-types left over from Land and
Water Rook, the best two of them, at C.D.A.,
http://www.chessvariants.org/index/displaycomment.php?commentid=28066.  Below 'neutral' or 'passive' describes a move without capturing
-- mostly the same Divergent concept of Lennert and Gilman now going on for Pawns.
(1) Firstly, there are hundreds of ways for Rook to capture: just make it
move as Rook passively and capture divergently as Man, Camel, Zebra, Knight, or any
other standard. Most of those divergent pieces are never used or described
yet. (2) Secondly, some Cannons. Cannon-Colour-One and Cannon-Colour-Two.
Both move neutrally as Rook and actively Cannon-style with a screen before along some orthogonal.  However, these are Cannon-types subtly
weakened from 5.0 to about 3.0 for C.D.A. use. C-C-One requires the
captured to be on light square and C-C-Two requires captured on dark
square. They are two different piece-types identifiable by unique
definition and ideal for reaching C.D.A. 31.0 target points. (3) 
Thirdly, back from Cannon to regular Rook, the main idea for damping values to about 3.0 points, working just as well as for Cannon, involves Rook-Colour-One capturing only on light, and Rook-Colour-Two capturing only on dark.  No indication of ''binding'' can merge the two types into one really in their also have a somewhat different 'divergency' concept than usual, that is, by square-type. Rooks-One and -Two are passively the same and actively different. These processes are endless.  Staying with regular Rook, let it move normally and capture by means other than displacement. Then there are: (a) Custodial Rook, capturing with any own Pawn across capturee radially adjacent; (b) Advancer Rook rococo-style but never diagonally; (c) Long Leaper Rook ultima-style but never diagonally; (d) Dawson-grasshopper style Rook is passive-standard Rook, thus making another new divergent piece; (e) Jacks & Witches,  http://www.chessvariants.org/large.dir/contest84/jacksandwitches84.html, mode of cannon/canon can combine above 'a' and 'b' by the p-t changing from move to move, or else 'a' and 'c' the same ''flipping'' way, and so on; (f) Custodially with a given specific piece-type belonging either side; (g) By usual coordination double-orthogonal with own King, a concept not used before Rook-exclusive; (h) Coordination with one of any paired piece that still has its double somewhere on board. All these particular 'a' to 'h' are combinable several other ways for more and more piece-types, and easily expandable to 'aaa' and 'aaaaa' eventually and 'hhhhhh', most falling within sensible meaning of Divergency, which is just moving and capturing differently -- like the f.i.d.e. orthodox Pawn. 
Then there still are many more combinations for piece-types to be made having plain displacement capture. Make one up quickly now on the spot:
Only where the line joining two Kings intersects can there be capture, for a very weak rook Pawn-value of discussion Charles and Jeremy.

The idea of one Cannon capturing only to light and one only to dark squares is an interesting one. It is more complex than a twice-Pawned Rook capturing only on the colour thst it happens to be on, or a Panda-style-capture Rook capturing only on the other colour. The idea can easily be further extrapolated to two other pairs. One pair would be Rooks (i.e. no intervening piece) similarly restricted. Another would be a Cannon that has to Hop a piece on a light square, and one a piecee on a dark square.

The Man and Beast series offers a way of constructing names for some of the pieces mentioned by Jeremy Lennert and George Duke, but they are spread over pages 19 and 21 as well as 16. I could make it more explicit. For example, a Rook capturing as a Knight is a Caddied Stewapacifier, and a Queen capturing as a Knight is a Caddied Ajaxrider Ferz. I will work out the rest and add them explicitly to the relevant page.

Gilman's singling out what are called Rook-Colour-One and Rook-Colour-Two
suggests they are better than Land Rook and Water Rook. That is probably
correct. I change my priotizing between the two pairs as of now, in case of
ever putting them into a CV or using the C.D.A line-up. If Gilman wants to re-name
them, that is fine too, just so please continue noting they are invented right here. Recall
Land Rook and Water Rook are not divergent. Land Rook just stays on dark
both modes and Water Rook on light. They both have Ferz one-step option and
remain colourbound -- Rook-counterparts to Bishops. Contrastingly, Rook-One
and Rook-Two are divergent in passive Rookwise and active only on
respective squares light and dark. Their passive mode makes them not colourbound.
There could be a sort of lesson. Water and Land Rooks seem more basic in their not having divergency, but divergent (hence more complicated) Rooks-One and -Two seem to be the 'better' piece-type pair.  Forget Thoreau's ''Simplify, simplify, simplify.''

Well I can certainly claim the twice-Pawned Rook as my own, and I know of no prior mention of a Rook capturing as a Panda. For the latter I would suggest Cubbed Rook, in reference to the Pandacub, Bearcub, et cetera. Conversely a Dabbarider capturing as a Rook is a twice-Yeomanned Dabbarider, and a Panda capturing as a Rook an Uncubbed Panda.
	When I refer to other CVP members' creations I prefer to do so with a link to an indexed page rather than a comments thread. This could be either a piece article (e.g. Bent Riders, Rhino) or a variant (e.g. Ajax, Balaklava), depending on what you prefer. A piece article can be posted by making your intention clear in the introduction (this guidance can be dropped once the page is well established) and leaving the Setup and Rules sections blank. Alternatively you could post a variant, or series of variants, even if they are just FIDE Chess with each pair of piece types in turn replacing the standard Rooks.
	I realise that I can add to my examples - a Rook capturing as a Knight is a Caddied Stewapacifier, and a Queen capturing as a Knight is a Caddied Ajaxrider Ferz - ones going the other way. A Knight capturing as a Ferz is a Contracaddied Knight and it can be extraplotaed from there. Thus a Knight capturing as a Rook is a Yeomanned Contracaddied Nightsnatcher, and a Knight capturing as a Queen is a Xajarider Contracaddied Knight.

Changing the colours. There are now the four Water, Land, Yellow and Green
Rooks for considerations of many chessboards coloured red and black, the
problem of intermediate bad-pick 'White' as already representative of one
entire side's pieces etc. I.e., panning all this out, improved names for
the divergent ones are now Yellow Rook and Green Rook, where Yellow
captures only on White, Green only on Black; passively both are full-fledge
Rook. Okay, correspondingly, for the present quartet of Rookies (3.0-point
Rooks) are name-unchanged Water Rook and Land Rook, both non-divergent of
respective White and Black-square restriction, having also Ferz one-step
choice. So original Rook-Colour-One below is become Yellow Rook, and
Rook-Colour-Two Green Rook.  Generic type-marker ''Rookies'' is convenient
irrespective of Betza's C.D.A. remarkable rookies. For also besides that
''Rookies,'' any of Rooklets, scalar-rook, Rook-less, Rook-light, and
Brooks for B-Rooks will do for all these scaled-down-power Rook types, of
which there are more possible to announce -- and ultimately name.
So further, the same C.D.A., the Rookeries, are initial-to-name by starting
array: F_G_L_Q_K_W_E_F, where E is Yellow. 
The four are unquestionably brand new p-ts invented this fall here a couple comments back Green and Yellow and the Water and Land at C.D.A. in September:
Http://www.chessvariants.org/index/displaycomment.php?commentid=28066.

Http://en.wikipedia.org/wiki/Shannon_number -- it can be demonstrated that the number of cvs far, far exceed the Shannon number and the number of piece-types potentially do too. This is part of computer science and ought to develop for cvs as well.
Here before latin scientific names intruded into CVPage,
http://www.chessvariants.org/index/displaycomment.php?commentid=18396. That excercise got up to number of CVs clearly identifiable having complete rules equal to number of atoms in the Solar system, 10^57, callable on demand. For example, CV#3,254,355,999 -- here it is or would be among the running total up to 10^57 so far. The mere running total of 10^57 happens to be over ''halfway'' by orders of magnitude to number of atoms in universe; that second half is not yet completed to get #CVs equal number atoms in universe, 10^80, but easily attainable by only another 33 good mutators superimposed on the method.  Much the same could be done for piece-types themselves alone by generating them formulaically beyond, say, convenient M&Bxx's less than 10,000 to ten million and more. Thus logically CVs and CV piece-types are easy as pi. Http://www.mayhematics.com/v/gm.htm -- as Jeremy Lennert points out, Panda is Parton's Slip-Rook. From around 1960 Panda is Rook that must change colour each turn; see M&B06.
So there are mentioned already 3.0-Rooks-downsized, call them B-Rooks, four new Water, Land, Green, and Yellow and one ancient Parton Panda.
Http://www.madsci.org/posts/archives/1998-05/892502124.Ph.r.html.

In the Rookery C.D.A. line-up F_G_L_Q_K_W_E_F, 5.0-point Falcons take
cornered mounts, and the many Rooks are subtly down-valued to 3.0, all of
Green Rook, Land Rook, Water Rook and Yellow Rook. Water and Land are
Bishop-counterparts in never leaving White and Black respectively.  Green
and Yellow move Rookwise, however capture-mode only allowed on black and
white respectively. Betza's Nutty Knights versus the Rookery will be
interesting, basically several different Knights playing several different
Rooks with Falcons the glue. Betza embodies C.D.A. on 8x8 and Peter Hatch
Fantasy Grand different armies 10x10, suggesting reasonable intermediate
8x10 too. That would enable inclusion of vintage Parton P Panda, added, who
moves passively Rook-like and actively same way but only colourbound, the
Pooka-eries, as F_P_L_G_Q_K_E_W_P_F. Now you see them, now you don't,
Pooka-eries their polysyllabic ten letters for 10-wide preferred 8x10.
Next, would the Pooka-eries match well with the Druids,
http://www.chessvariants.org/large.dir/druid.html, Elves and Evil Horde?
After 5125 one year to 21.12.12, http://news.discovery.com/space/the-2012-mayan-calendar-doomsday-date-might-be-wrong.html, the Long Count's great cycle reaching completion, Tortuguero Monument 6 cites the end of the 13th b'ak'tun, the distance number's best calculation zero date.