Comments/Ratings for a Single Item

thanks.

the charging knight can move like a king 'sideways and backwards' - does
that include a single backwards diagonal move?

ok i have my rating cap on :)
well this game is a legend in chess variant world, so i'll start here,
great fun with different armies :)

new army idea: swift splicers bishop: the deacon moves as a four square
bishop plus spacious wazir
rook; the fourfer from the meticulous mashers the fourfer a four square
rook plus ferz
knight; the waffle alfil plus wazir
queen the general a four square queen plus two square crab rider or an
alternate queen the admiral: a four square queen plus two square chinese
rider

I also thought my test set named 'Crowned Nobility',but it could be too stupid.

*The Rooks: the Crowned rook

(Rooks puls King)

*The Bishop:the Crowned bishop

(Bishop plus King)

*The Knight: the Crowned knight

(Knight plus king)

*The Queen: the Fool

(Moves like a King -- a nonroyal King)

To Jeremy Good: 

Thanks for your enthusiasm,but I have realised that my tentative set is
indiscreet. To devise is more difficile than I thought.

I decided to let 'Crowned Nobility' set have a vulnerable spot to
balance  too powerful 'Crowned Pieces'. Maybe I make an inept thing
again.

*The Rooks: the Crowned rook 

(Rooks puls King) 

*The Bishop:the Crowned bishop 

(Bishop plus King) 

*The Knight: the Crowned knight 

(Knight plus king) 

*The Queen: the Figurehead 

(It can't be moved.It also can't capture. Enemy can capture it.) 




To Andreas Kaufmann: 

Your opinion hitted the nail. Easier rule would apeal to more favorers. 
Alought CWDS would not be in vouge,CWDA is still an excellant and
interesting variant.

'Crowned Nobiliby' is abortive. 
I have an another idea :'Torrid Firework' 

The Knights: The Armed Pao

Armed Pao slides orthogonally, and captures by jumping or as Wazir.

I strenghen Pao coming from Xiangqi. Original Pao is relatively weak in
Chess because King does not live in Ninecastle. Now this more aggressive
weapon can capture enemy berfore its eyes by moving one square
orthogonally. I also did the same thing in Vao.


The Bishops: the Armed Vao

Armed Pao slides diagonally, and captures by jumping or as Ferz.


The Queen: the Armed Leo 

Combined Armed Pao with Armed Vao, Armed Leo slides diagonally or
orthogonally, and captures by jumping or as Commoner.


The Rook: the Half Duck

Borrowed from 'Remarkable Rookies', Half Duck is an excellent partner to
Armed Pao and Armed Leo. 


I have tested 'Torrid Firework' in Zillions. I thought that  'Torrid
Firework' is as equal as the other teams. Maybe it is eligible, I hope.

Half Duck in 'Torrid Firework' is probably a little power. 
I created 'Hood Rook' to instead of Half Duck. A Hood Rook jumps
two squares orthogonally , or jumps three squares orthogonally.

Hood-Rook: moves as Dabaaba, or jumps 3 squares orthogonally.

In my experience, the flexibility of the Charging-Knight in the Nutty Knights team makes it somewhat stronger then a Bishop. 

The Colourbound Clobberers' lack of a piece that moves by ranks and files makes them slightly susceptible to back-rank mate treats.

The Half Duck has a range 3 jump. It is very easy to attack King behind a
row of pawns without being threatened. I adviced that  Half Duck can't
have 3 jump as long as a piece standing on front of 2 jump square.

As for the Half-Duck, it's a popular piece used already in some other variants, notably as the Lion in Paulowich's Lions and Unicorns. The objection doesn't speak to Betza's own description of why he uses it. I myself have plans for a lame half-duck in forthcoming CDA.

[The size of an audience is not a reliable measure of the excellence of a production.]

[btw, there is no shame in losing to Paulowich and losing to him probably speaks less to the supposedly overpowered character of the Half-Duck than to the strength of Paulowich who has beaten me several times too.]

Reading back through the dicusion about this variant prompts two remarks:

1) I was a bit surprised by Ralph's Betza remark that this is 'serious, heavy-duty Chess'. Not that I doubt this is true, but I think it holds for mny other variants as well. The armies do not have to be different to make all the strategic issues of FIDE Chess carry over to it (and indeed, FIDE Chess uses 'identical armies'. Many other variants have the 'feel' of FIDE Chess. This is mainly caused by having the same Pawn, which is known to be the 'soul' of the game since Philidor.

So games like Berolina Chess, or Heian Shogi definitely have a very different feel then Chess. But Knightmate already looks very familiar to a Chess player (despite the funny 'King' moves). Capablanca Chess also strikes me as very similar. I guess it is mainly a matter of how seriously you take the game.

2) There was a very interesting remark over how long it took the FIDE army to subdue an inferior army. This might be an artifact of the evaluation function of the program handling the FIDE pieces. The effective value of strong pieces is depressed by the presence of weaker pieces of the opponent. This effect (for which Reinhard Scharnagl coined the term 'Elephantiasis correction') is tantamount to having evaluation terms that are proportional to the product of the number of (selected) white and black pieces.

Example: in normal Chess, a Queen is worth more than Rook + Bishop. But if each side would have 3 Queens, trading your first Queen for Rook + Bishop is actually a good trade! This because the removal of 33% of the light pieces of the opponent increases the effective value of your remaining 2 Queens by more than the intrinsic deficit of the trade. This is not a positional effect: it does not matter where the pieces are on the board. It is purely dependent on the material composition.

So even if the pieces of the opponent are inferior to yours in a one-on-one comparison, it could be wrong to avoid trading them. Because trading the first few creates the freedom for your remaining superior pieces to affirm their superiority, which they would not have when they have to run for their life to avoid 'bad trades'. 

A numeric example: Suppose you have 4 pieces worth 600 (centiPawn), and the opponent has 4 pieces worth 525. But suppose that the presence of one such opponent piece would depress the effective value of each of your pieces by 25, because it can interdict you access to the part of the board covered by the lighter opponent piece. With 4 against 4, this means each of your pieces is depressed by 100, down to 500, so in fact you are 4x25=100 behind, in stead of 300 ahead!

Not accepting this, and handling your pieces like they were equal to their inferior opponents, will allow us to unleash their unrestrained power of 600 against the opponent Pawns or King, so that to avoid losing Pawns or being checkmated, the opponent will be forced at some point to trade. (The opponent can certainly not avoid trading; this would depress the effective value of his army by about 400 on top of the intrinsic 300 deficit.) After the first trade it is 3 against 3, and in the trade-avoiding strategy we would see out pieces depressed by 3x25=75, for 525 each, so now we are about equal, in stead of 100 behind. But we will continue to ignore threats of further trading, so that our effective piece value remains 600. When the opponent under pressure trades us down to 2 vs 2, each of our pieces is suppressed by 2x25=50 to 550 in a trade-avoiding strategy, and even under trade-avoidance we would already be ahead by 50. Trade-ignoring we would lead by 150. After trading the fore-last piece the effective value of our remaining piece would be 600-25=575, and we would still be 50 ahead. So even now, trading would not have to overly worry us, athough we should not imagine that we can keep up the 150 advantage we have in a trade-ignoring strategy forever.

Trading the last piece would truly equalize us, and as that is not better than the +50 advantage we could reap in a 1-1 or 2-2 situation by employing the trade-avoiding strategy, we would switch to trade-avoidance only after the first two trades, where for the third piece we would still be prepared to take some risk of trading if that could increse our attack on other material. Only the last piece would have to be jealously protected.

Moral lesson: By being afraid of an inferior opponent, you give him the advantage. Treating your pieces as if they are worth more might in practice make them worth less. Don't do it, then!

I would be surprised if Zillions would know this. And that explains why it would take so long to beat Seperate Realms with FIDE. It should simply seek a few quick, nominally bad trades, and it would still be left with ennough advantage to get it over with quickly. In stead it cowers away, avoiding trading, until out of pure need it is forced to make the trades of lose other material, only to discover that after it has done so, the pressure is lifted and it can lash back with unrestrained power.

'Why not make different armies for Xiang-qi?'
I think, it's interesting idea. I think, general, pawns, advisors and
elephants should be common for all armies, as they plays special roles in
game, but horses, rooks and cannons must be different.
Shogi with different armies is also interesting idea, but it needs some
headache with promotion... I can suggest this: not only kings and pawns are
common, but gold generals also common, and first rank pieces promotes to
them. Pieces, wich replaces rook and bishop, gets 4 additional moves after
promotion. Another idea - gold generals also different, and they promotes
to normal gold generals (in standart shogi they don't have to promote, as
they are already gold generals).

Invented in 1977, Chess Different Armies initiated salvation for little customary 64 squares. Betza left us thinking it is to be Next Chess, period, 
http://www.chessvariants.org/index/displaycomment.php?commentid=614. After all, every cycle and every life ends, or re-continues, and sixty-four -- vraiment, compare its diminutiveness to big 81 Shogi and big 90 Xiangqi -- were computer-busted by the nineties if not the eighties. Busted to the point ex-player Fischer (1943-2008) proposed junking the set array RNBQKBNR in 1996, ignorant that was done by Frenchman Alexandre as early as the 1820s post-Napoleon. Fischer Random is Alexandre redux.  Now by Fischer we can have BNQRRKNB, so long as Bishops do not compete. Beautiful. Betza saw irony/inferiority there and redoubled towards perfection of CDA, obviating FRC for Next Chess, in armies: Nutty Knights, Remarkable Rookies, Colourbound Clobberers, Forward F.I.D.E.s, Amazon Army, Meticulous Mashers, pitted against each other or against the F.i.d.e. one.  The pointage of that latter, 39, is the benchmark for equality of usually different forces. There have to be subtle differences inexactly achieved, equal-valued forces being impossible when so much as a single piece-type differs side to side. There are contributors' Armies of point value also approximately 39 not created by Betza: Lawson's Pizza Kings, Aronson's Fighting Fizzies, Streetman's Spartan. The latter in current discussion has not a single new piece-type and may be adequate new combination as useful as Lawson's Army or Aronson's Army. The best Armies appear to be ones described in follow-up comment soon.
Does it matter that one Army is 38 points or 40 points? A little. When there is a disparity humans can detect, the challenge then becomes to win with White 38.5-pointed, or win with Black 39.5-pointed.  How many near-39-point Armies can be created? Hundreds. Thousands. Probably thousands of good ones, not beyond that, if computer-generated and having time allotted to devote.  How many active or finished games of Chess Different Armies are indicated at Game Courier? 105. Also for follow-up will be to find the leading player(s) Chess Different Armies over the past ten years.

I have play-tested some combinations using Fairy-Max, and it seems that both the Nutty Knights and the Colorbound Clobberers have a sizable advantage over the FIDE army.

For the Nutty Knights this advantage seems to be slightly over a full Pawn. It seems fully due to the Charging Knights. In a direct comparison all other Nutters perform slightly worse or equal to their FIDE counterparts. But replacing a pair of Bishops by a pair of Charging Knights provides a spectacular advantage. With the standard values 325 for a lone Bishop and 375 for a paired one, the Charging Knight might be 400 or even 425.

This seems unreasonably strong for a piece with only 9 moves, the extra move compared to Knight even being backwards. I guess this is one of the rare move combinations that noys a large bonus over the additive value of the individual moves, like the Archbishop (BN) or the divergent piece that moves as Knight but captures as King. In fact the Charging Knight is also a combination of Knight and King moves. Such pieces combine the speed of the Knight with the manoeuvrability and concentrated attack power of the King/Commoner. The latter endows them with mating potential, and makes them very effective supporters or attackers of FIDE Pawns, as they can protect/attack a Pawn, and at the same time the square in front of it.

The Clobberers are also significantly stronger than FIDE (advantage slightly under 1 Pawn),althogh not as much as you would expect from their individual piece values. A pair of Bedes tests better than a Rook (525 against 500 centiPawn), a pair of FADs as slightly worse (450-475), and thus provides an advantage of more than 2 Pawns over the Bishop pair. This is not dequately compensated by substituting the Queen for an Archbishop, which differs by less than a Pawn from it. (The WA is almost equal in value to the Knight.)

The names used here for the pieces are awful, of course. In the WinBoard / Fairy-Max implementation I use different names. (Or at least different letters to indicate the pieces in FEN and SAN; WinBoard never uses full names of pieces.)

FIDE      Nutters     Clobberers
N Knight  H Horse     E Elephant
B Bishop  U Unicorn   D Deputy
R Rook    T Turret    L Lama
Q Queen   C Colonel   A Archbishop

'Unicorn'seems an applicable name for Knight-King chimera, and WinBoard happens to have a bilt-in bitmap for it. For the Horse I use the WinBoard Nightrider symbol, and for the Colonel the Knight-on-Rook symbol that is popularas a representation of the Cancellor in some 10x8 variants, so that the Nutters army indeed looks quite Knight-like. For the 'Lama' I use the Promoted Bishop symbol, which in WinBoard generically stands for a Bishopwith some extra moves, (in this case the (2,0) teleports), and the WA is an Elephant variation because of the Alfil move.

References

• Index of Ralph Betza's work on piece values
• A Pawn is as Strong as the Hand that Holds It Part I
• A Pawn is as Strong as the Hand that Holds It Part II
• A Pawn is as Strong as the Hand that Holds It Part III

By taking away the known and studied board positions, it takes the chess back to its root as a test of logic and strategy. From pure information overload, players should not -- and generally can not -- rely on memorized openings or endgames, but must instead invent the process as they play.

Really, is that not the point of chess variants, giving chess players a new experience outside of the tried-and-true? I have not, nor do I have any desire to work towards memorizing opening books, beyond two or three moves. My enjoyment of chess comes from working out the best tactic as the game develops.

CWDA is my preferred variant, because of its simplicity and expandability. Really, the game play is chess. Learn the movements of four new pieces, and you can introduce a new army into the game. With just four armies, there are now 15 games you can play (not counting the FIDE vs FIDE match). Starting with a knowledge of chess, and only adding the movement of 12 previously unknown pieces. Simple! Versatile! Elegant! What's not to like?

http://www.chessvariants.org/index/displaycomment.php?commentid=614. This comment of Betza was linked before, but what ''pprilla'' says today is exactly what Betza was saying the last couple years to 2003.  NextChess will take up the C.D.A.(provisional #30) this year.

We tacitly assume that strength can be measured by one number and that the numbers can be compared using a transitive relation like 'greater than'. However, this needs not to be true, see here for a simple game with dice:

http://en.wikipedia.org/wiki/Nontransitive_dice

So here is a new chess variant challenge: Chess with nontransitive armies

Design a chess variant with different armies such that, whatever army your opponent chooses first, you can choose another army having an advantage over your opponent's army. (To avoid the first move problem assume 2 games where either army moves first once)

Muller's solution there cannot be topped, but hypothesize,
http://www.chessvariants.org/d.betza/chessvar/cvda/alice.html,
that Fabulous F.i.d.e. Army beats Maharajah, Maharajah beats Alician Army, and Alician Army beats Fabulous F.i.d.e. Maharajah army would be royal (RNB) alone.  The rules have to be tweaked properly from the several Alice-to-F.i.d.e. choice cvs Betza presents above.  The index to this old part of Betza:

Okay, Cyclic Advantage Armies can be many too. Right or wrong should assure maybe 75%-25%, with any question resolvable by Muller's or other engines. Easier to generate are Pawn armies dispensing with piece, instead 8 pawns and King . That would be the problemists' way; or problemist method would be to try very few piece-types only 1 or 2, or even only 2 or 3 pieces themselves let alone types.  (In fact, the two triads of C.A.A.s so far are that way.) This is a good topic appropriate for C.D.A. ////
Example One of Pawns only: In general, to stay 8x8 and allow flexibility, make the arrays Pawns a1-b1-c1-d1-e1-f1-g1-h1; King e2.
Example One, Pawns only, call it ''R.O.Q.'' Rock, like the Rock/scissors/paper it simulates: Quadra-Pawn army > Rococo Pawn army > Ortho-Pawn army > Quadra-Pawn army....
Ortho-Pawns have 1-, 2-, or 3-step opening option 8x8. Promotion all three types to Queen. Quadra-Pawn is like used in Centennial Chess. As per the suggestion, play this alternately on three-player board for mayhem and indeterminate outcomes, certainly not any 63-19-18, in peculiar way to back-equalize:
http://www.chessvariants.org/multiplayer.dir/three_player/three_player_chess.html. Does any program play three-players yet?
[Incidentally contrast all Pawns here to no Pawns of current fad Chieftain Chess.]

Revision. Cyclic Advantage Army, Pawns only. ROQ, ROCK Armies are the three-fold. Quadra-Pawn army > Rococo army > Ortho-pawn army > Quadra-pawn army...ad infinitum.  What was not noticed, Centennial's two-step for Quadra-pawn has to be eliminated, getting back to normal, since Quadra-pawn is not original with Centennial anyway.  Arrays have to be those 1- and 8-ranked described, promotion to Queen virtually wins, but one more tweak may be necessary.  Ortho-pawn may need 1-, 2-, 3-, or *4*-step opening option, to be sure to subdue Quadra-pawn. And that strengthening of the Ortho-pawn will not change Rococo advantage over her. And Quadra-pawn without two-step will still give Rococo fits, who has to jump-capture. At least all to the tune of 60-40 if not 70-30, best projected.  The Kings will be offensive weapons par excellence.

These Cyclic Armies definitely deserve articles or cvs. Questions like: (1) How about four in sequence? (2) Hexagonal ones. Experimenting there are found 4 Dabbabah bindings, that Gilman has not touched on yet; but I did not finish a tripartite  hexagonal army with any confidence. (3) Try one piece only and King back on squares.  This one is only preliminary for 8x8:    [Pasha/Mastodon + King] >  [(Dabbabante+Wazir)+King] > [(Quadra-leaper 1,5 1,6 2,5 2,6) + King] > [Mastodon+King] ad infinitum. ////   That (15/16/25/26) is okay to call (Ibis-Flamingo-(Satyr or Korsar)-26).

Sphinx of black quartz, judge my vow.
There are shorter ones, but contrived by use of proper nouns.

Some (tiny) steps have been taken towards CwDA opening theory. The page quoted below also has a link to a mini-tournament of CwDA games.

'The Paulowich Plan for playing with the Remarkable Rookies is very interesting.

My own first attempts at playing this army involved taking a cramped closed central position and suffering for a long while before winning; my second idea was to do a Halfduck Dance, which may work even though it goes against the general principle of developing weaker pieces first.

Pushing the b-Pawn so the WD can sit behind it is an interesting and creative idea; but in Paulowich-Aronson I'd instinctively prefer 3...a5-a4.

(My instinct could be wrong, of course.)' -- gnohmon [9 Oct 2001].

I found this comment by looking at a nonindexed page on this site: Recent Ratings and Comments, which actually covers old comments from [27 May 2001] to [31 Mar 2002]. This list is also available in another format: alphabetic by variant name, where you can more easily find the 1st Email Championship Chess w... comments. NOTE: the page name on the left links to the main page, while the three blue dots on the extreme right link to the comments.

To add an army, balance the sides because material must vary. The Immortal AntiClericals versus Fabulous F.I.D.E.s. The new idea for army is Immortal AntiClericals and they go: RNIQKbNR. There should be same-value forces where 'b' is Barrier Pawn of year 1948, http://www.chessvariants.org/large.dir/kristensens.html. 'I' is Immortal mediaeval Germanic Mann, the sub-piece variate of Man/Mamra suggested by Jeremy Lennert. 'Immortal' here moves and captures non-royal King-like and when captured belongs again to the capturee. Capturee later drops I. on line 1 or 2 vacancy. Since all Betzan Armies (unlike atoms) are equal, there can now be playable fair match-ups Immortal AntiClericals v. Pizza Kings and I. A. v. Nutty Nights, and so on, weigh in Betza willing.

'Gilman's is correct also for Hatch's Fantasy Grand though not all different-armies Chesses.'
	I was actually referrng specifically to the family of armies replacing the Queen, Rook, Bishop, and Knight of FIDE Chess on the 8x8 board with pieces designed to equal their combined values - the Nutty Knights, Pizza Kings, et cetera. As far as I am aware, the Immortal AntiClericals are the first army proposed for this system that substitutes different pieces for one kind of FIDE piece.

How many Armies? Add Immortal AntiClericals and about two dozen others since, doubling the list by Peter Hatch a decade ago of the first twenty:
http://www.chessvariants.org/index/displaycomment.php?commentid=595. Peter Hatch invented different armies for 10x10 in Fantasy Grand and contributed ideas to Betza's C.D.A.
Now Immortal AntiClericals replace Bishops with Barrier Pawn and Immortal Man, who move neutrally exactly the same as each other, as if they were the very same piece-type for 80% of moving cases, excluding the rest of capture/captured minority, the lesser 20% of moves recordable: the observed outcome units valued 0.5 and 5.5. Still, uneasiness to the C.D.A. theme of usually strict paired substitutes is being understandable. Therefore, furthering the symmetry of the two here replacing the Black and the White  Bishop, let's add necessary subvariant where Barrier Pawn promotes to Immortal Man and vice versa Immortal Man to Barrier Pawn(then I.M. will tend to avoid rank 8).  That modality in toto for the tandem in new themed C.D.A., Immortal 
AntiClericals, RNIQKbNR, is creating more alike a piece-type pair, to go with N-N and R-R than the two Bishops themselves of long standing are across the board in the orthodox F.F. -- looking at the single match-up Immortal AntiClericals versus Fabulous F.I.D.E. Two opposite Bishops are really supposed same piece-type only by convention. That is of course because Bishops Dark and Light actually never reach or threaten any same square, in contrast to Rook/Rook and Knight/Knight and contrast to these particular replacements and in contrast to any genuine fully same-types. 
Anyway for one example, Amontillado, http://chessvariants.org/dpieces.dir/amontillado.html, does not follow the structure most assume and Charles Gilman describes. Betza would immediately endorse without reservation Immortal AntiClericals too -- with or without subvariants -- delighted to see development in the Chess form he sought to supplant standard fixed-array 64 squares not too distantly. 
Http://www.chessvariants.org/index/displaycomment.php?commentid=614.

I believe you have reinvented the dababba-rider, also known as skip-rook.  Betza discusses that piece in Ideal and Practical Values part 3, and uses it as a building block in his Avian Airforce army in the same article.

I think your estimate of its value at 3 pawns is almost certainly too high, though.  Using Betza magic number 0.7, DD has about 60% of the crowded-board mobility of R, but it loses the King-interdiction power and can reach only 1/4 of the squares on the board.  Betza's 'Wader' adds Wazir move, which removes colorboundness and adds mating potential, but he still estimates it as weaker than a Rook, whereas he estimates NW as equal, suggesting DD alone would be substantially weaker than N.

I'm also curious where your valuation of the Amazon comes from, though it seems vaguely plausible.

I must say, though, I think these 'different armies' that have more pieces in common with FIDE than they have different are a bit silly.  It seems to me not so much a new army as just a single new piece.  If we're not going to try to have themes or account for value-modifiers to specific combinations of pieces, then creating a new army is as simple as using point-buy rule, and thousands could easily be created by simple enumeration.  To be worth naming and discussing, I think an army ought to have a cohesive theme and some serious thinking done about how its components interact.

Okay, let's complete the Water Rook Army. Jeremy's point is appreciated that Dabbabah-Rider is a cousin of Land Rook and Water Rook. However, the new piece-types under scrutiny are sliders and not riders.  
 The intention is each reaches 1/2 the board, one all the white squares and other all the black, as Rook-counterparts to dark and light Bishop, who also reach their separate checker-correspondent halves of the ancient 64-square board. There are different mechanisms to complete the wanted piece-types to be valued near or over the already-established 3.0 for the two differing Bishops (Notice 3.0 is a preset target to complete a 31-point army). The correction now is Water Rook slides one as Ferz to a white square or instead slides any number as regular Rook to white square. Land Rook slides one as Ferz to black square or rather slides any number as regular Rook to black square.
That way each reaches their mutually-exclusive 32 squares and can be seen as separate p-ts comprising together the complete Rook of 7th century to date (minus the heuristic/simplistic ferz one-step). That is all: a complete practical new C.D.A. like we used to do frequently and a thought experiment how both Rook and Bishop separate out into their two different component piece-types.  
Bishop can be regarded as Ferz-rider and Rook as Wazir-rider. All other so-called riders are less appealing to players. As a general rule, Riders formed
from leapers are too limited in arrival squares.
So, instead of riders, or as that above technical Wazir-rider, the Water and Land Rooks slide like a Rook with their opposite restriction on arrival squares. They could as well appear under other thread ''Piece-types,'' where M. Winther's comment happens as the last, http://www.chessvariants.org/index/displaycomment.php?commentid=26403.  Actually however, Water/Land Rook becomes radical enough C.D.A. force. Frankly a fatal flaw for orthodox-schooled players in most C.D.A. force match-ups is having 10 or 11 p-ts to keep track of. Seven or eight are far better for strategy in actual play, and future C.D.A.-type efforts are likely to evolve accordingly -- the very opposite of what Jeremy Lennert touts.  Immortal AntiClerical and Water Rook are now C.D.A. experimental line-ups along with other specific 31-point forces, exclusive of Pawns, numbering 45 or 50 as of the present moment.
Http://www.chessvariants.org/diffmove.dir/augmented.html -- several places in articles Betza says there are already thousands of Armies to choose by enumeration, such as at the end of above Augmented. The 45 or 50 total noted for C.D.A. are rather more developed as Betza's own in articles and others' from comments.

Well, in Fairy-Max I support the Clobberers and the Nutters (together with FIDE) in all asymmetric combinations. This is partly inspired by easy of implementation; I might have implemented the Rookies as well, if it were not for the fact that the Short Rook falls outside the set of meta piece types supported by Fairy-Max.

Btw, it was not clear to me what the promotion rules are in CDA. 'Every piece type initially on the board' is a bit ambiguous, because it is not clear if piece type here means colored or uncolored piece type. I assumed it meant colored, i.e. if white has a Queen in the initial setup, and black not, black cannot promote to Queen. This seemed more in the spirit of different armies. As Fairy-Max is not aware of the possibility to under-promote, I thus let it promote always to the dominant piece of the respective army.

Another observation: Armies can not only be modified by 1->1 or 2->2 substitutions, but also by changing the number of pieces. 'Charge of the Light Brigade', which is basically FIDE Chess starting from the position

. q . k q . q .
p p p p p p p p
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
P P P P P P P P
N N N N K N N N

would then also qualify as a CDA sub-variant (if we add the rule that white can only promote to Knight. It would be a light sub-variant, though, as the total value of the armies falls well below the usual 31 points.

IIRC my tests with Fairy-Max (allowing promotion only to the strongest piece of your own army) found the Clobberers to have a small edge over FIDE, and the Nutters a much larger edge, of nearly a full Pawn. (i.e. against FIDE I had to give them Pawn odds to approximately equalize).

I did experiment only once with the effect of promotion on Pawn value, in the context of Spartan Chess. The result was (surprisingly) that there seemed to be none. In particular, in an attempt to weaken the Spartan army, I changed the single allowed promotion in Fairy-Max of their Hoplite Pawns from 'Warlord' (BN, value ~8.75 on the Kaufman scale, where Q=9.5 and N=3.25) to 'Captain' (WD, value ~3). This did not seem to have any effect on the score.

My interpretation / explanation of this was that in practice unhindered promotion only occurs when a game is already decided, and normally the pawn will be captured directly after promotion, or even before, when promotion is unavoidable. So typically a promotion means the opponent loses a minor piece by sacrificing it, no matter to what you promote. But loss of even a minor piece is usually decisive.

Only in variants like Shatranj, where you can only promote to a completely worthless piece, this reasoning does not apply,and Pawn value gets depressed. (Note that the WD still has mating potential, however. Perhaps limiting promotion to a piece without mating potential would have some impact.)

Note that the Clobberers are not really disadvantaged that much, as the value difference between Q and BN is less than a Pawn. So even promotion races where both sides promote don't lead to a large disturbance of the balance of power. In fact the Nutters suffer more, because their 'Colonel', although much closer in value to a Queen, has almost no backward moves. Thus even when the Nutters do promote first in a promotion race, they have no way to stop the other side from promoting as well 2 or 3 moves later, and thus miss the win. But despite that disadvantage, the Nutters seem to havethe strongest army anyway, so perhaps this is a good thing.

Here are some comments of Ralph 8-9 years ago:
one that Clobberers are well-balanced with Remarkable Rookies and benchmark FIDEs, http://www.chessvariants.org/index/displaycomment.php?commentid=2952, and two making three points on all of levelling effect, that Remarkable Rookies have at first look highest absolute p-v, and that results should vary intrinsically as to h.v.h. or c.v.c.(or h.v.c.?), http://www.chessvariants.org/index/displaycomment.php?commentid=1282. Michael's Nelson's experimental CWDAs are from Separate Realms, http://www.chessvariants.org/index/displaycomment.php?commentid=1259, some of the first to increase Peter Hatch's list of 20 the year before.

Well, I think the remark that computers would play quite differently from humans should be interpreted in the context of the time it was made. Computers have made huge progress in their ability to play Chess since then, not in the least because of faster hardware. And Zillions, the only program at the time that was able to play such variants, is rather weak by today's standards.

Piece-value measurements with Fairy-Max on orthodox pieces reproduce the piece values extracted from human GM games quite well, despite the fact that Fairy-Max is rather weak, as Chess programs go.

Also note that I gave an alternative explanation for the slow demise of the Separate Realms army against FIDE as the one forwarded by Betza, in terms of the elephantiasis effect rather than ease of development.

Betza seemed to believe the BN was significantly weaker than Q (see cost table in Buypoing Chess, http://www.chessvariants.org/d.betza/chessvar/buypoint.html ). So Knappen's remark is at least a plausible guess at Betza's original reasoning, even if that valuation turns out to be incorrect.



Muller, it would be interesting to test your theory by letting pawns promote to something at least a full pawn weaker than a minor piece--perhaps a Wazir, or a backwards-facing pawn.  This should mean that it is no longer worthwhile to sacrifice a minor piece to prevent a promotion.

If you are correct that the power of the promoted piece has little effect because the threat of promotion rarely coerces the sacrifice of more than a minor piece, then the difference between W and WD promotion should be greater than the difference between WD and Q promotion, even though a WD is closer in value to W than Q.

On the other hand, if the difference is not noticeable simply because promotion is very rare and so its average effect is not large enough to measure, then changing the promoted piece to W should also have negligible effect.

Well, I will put it on my to-do list. Currently I am a bit busy getting my engines in shape for upcoming tournaments; in November HaQiKi D and Shokidoki will play in Taiwan for Xiangqi and 5x5 mini-Shogi, respectively, and later that month in the ICGA Computer Olympiad. Ina few weeks there is the Dutch Open Computer Chess Championship, where I partcipate with Spartacus.

I would also prefer to perform future piece-value measurements with a really strong engine, which can also be made aware of pair-bonus effect for color-bound pieces, and is aware of what constitutes insufficient mating material. Soon Spartacus will fit that description.

In a sense the measurementhas already been done, though: In Shatranj Pawns can only promote to Ferz, which is often as bad as not promoting at all (when the Ferz is on the color where you already had one). The rule there is that a Ferz is worth two Shatranj Pawns, while embedded in a FIDE context the Ferz is only worth 1.5 FIDE Pawns when part of a pair. That would make a Shatranj Pawn worth 0.75 FIDE Pawn. That is a significant weakening when you multiply it by 8. Probably the value of such weakly promoting Pawns would be much more dependent on their loation on the board, i.e. reasonably valuable in the center and as King Shield, and nearly worthless else where.

I did some tablebases with Clobberers pieces. The FAD (single-letter ID I will use here = F) and BD (= X), despite their large general strength of course have no mating potential due to their color binding, and neither has WA (= W). So the interesting tablebases here are 3-1 and 3-2. Even KWWK is a win, comparatively easy with a maximum of 27 moves. In end-games the (2,2) jump of the FAD is hardly an asset, so that the BD,which can slide to (2,2), is practically upward compatible. So what works with 2F in general also works with F+X or 2X. (And usually a bit faster.) Of course nothing works with these combinations if they are on the same color; the lack of mating potential dooms you like it dooms K+N+N in ortho-chess. But on different color a pair of them is very dangerous, able to force checkmate without help of their King, driving the opponent to the edge through checks with their (2,0) moves. KFWK also wins easily (17 moves). So the 3-vs-1 tablebases are not the most interesting; every pair wins. To make it interesting black needs a defender. So I did a few 5-men (3 vs 2 and 2 vs 3).

K+X+X and K+X+F beat K+R, but K+F+F doesn't. K+F+F does easily beat K+B and K+N, though. (And thus K+X+F and K+X+X should also do that, although I did not check it). K+F+W beats K+N, but it only beats K+B when the FAD is on the B color. Most of the power comes from the FAD here, and if black can set up a defense on the other color it is draw. K+R also draws agains K+F+W. K+W+W is too weak to beat any defender, even against K+N it is draw.

The WA behaves as a regular minor, such as N. Normally an advantage of B or N in a Pawnless ending is not enough to win. (KRBKR, KRNKR, KQBKQ, KQNKQ are all draw, and also the 2-1 minor end-games KBN-KB, KBB-KB, KBN-KN. The only exception is KBB-KN, if we ignore the fact that the 50-move rule spoils most of the fun there.) I tried non-CDA end-games KQWKQ, KRWKR, and these are also draw, like KBNKW and of course KNNKW. But KBBKW (with unlike B,of course) is a win. The B-pair is strong in such situations, and the WA performs as a Knight (but K+W+W wins, where K+N+N draws). In Clobberers-only games, KFWKF, KXWKX and KAWKA are all draws.

As Betza promised, FAD is significantly stronger than B (and other minors), and this is also noticeable in the end-game. Where an extra minor is seldomly enough fora win, an extra FAD often is. KRFKR and KFFKF are wins, as is KFBKB when the F is on the color of the B (and white's B+F ondifferent colors, of course). With the B on the same color it is too difficult to attack the defending B without him immediately trading. (This is also why drawing KBBKB is easy for black, where KBBKN is hopeless). KFNKN is again a draw, though. So F is just at the border of making the difference.

That A (Archbishop) is slightly weaker than Q is seen in KQNKA and KQBKA: these are won, where a defending Q could draw. The BD and FAD are not as strong in defending as in attacking. KQKFF is won; KQKXF and KQKXX are not clear. (Many wins for the Q, but not nearly everything. K+R+B and K+R+N beat K+X and K+F. (But note that K+R could hold them off.) Problem is likely that adefending Rook can use the distant checking weapon, while with X or F a harrassed King simply steps to the other color, and you are out of options.

A problem that just came into my head. Is castling into a check which will
be nonexistent after the move allowed?

Example 1: (where c is a cannon)
2 ........
1 R..K...c
  abcdefgh

b1 and c1 are all attacked, but when the king actually goes there it is not
checked by anything.

Example 1: (where r is a R3+, a rook that only moves 3 squares or more)
2 ........
1 R..Kr...
  abcdefgh

r3+ does not give check until K moves to b1, but the R then blocks it so
that check is removed.

Indeed, the rules for castling could need clarification. In Fairy-Max I use the rule that _after_ castling none of the squares skipped over by the King should be under enemy attack. With only ordinary leapers and sliders this is as good as any definition (in combination with the requirement you cannot castle out of check).

I agree a more logical generalization of the rules would be to specify sub-state of castling, stepping the King towards the Rook as many times as needed, and then hopping the Rook to its target square. The requirement should then be that in none of the sub-states the King would be in check, would the castling be terminated there.

Compare this to Seirawan gating, where the King is also not allowed to be in check after the development move of the piece, but before the gated piece is dropped on the evacuated square.

Indeed, this seems a case where the Fairy-Max implementation would not give the most logical ruling: it would forbid the castling.

But OTOH, one guess is as good as another. The rules should really specify exactly what to be done, in variants where cases like this can occur.

H.G. Muller, 


Many many thanks for the end games table bases. I also thought it would be similar that in QKFFK game , Q wins. Please let us know more. 

Indeed a very interesting research.

Very good question! It had not occurred to me to check that. But the result is surprising: KRKW if won for the Rook! It can take up to 75 moves (to conversion), though, and most wins take more than 50 moves. That makes it one of the most interesting 4-men end-games I have ever seen.

BTW, I released the program with which I calculate the tablebases some time ago as a WinBoard engine, so that people can calculate any 3-, 4- or 5-men ending they want, and then play black against it to see how the computer beats them. It can be downloaded from 

http://hgm.nubati.net/fairygen.zip

This contains a README file that explains how you have to install it in the WinBoard GUI. WinBoard supports 22 different piece types, when you switch it to variant fairy, and fairygen knows them all under the same letters as WinBoard uses for them (e.g. W = Wazir). But WA is not one of them. So to calculate the tablebase I just redefined the Elephant (which is used in CWDA by Fairy-Max as WA) as

E: 2,2,* 1,0,*

in fairygen's piecedef.ini file, and used a Wazir for it in WinBoard, with legality testing off.

Below you  see how Fairy-Max loses a position I dreamt up against the tablebase. You see from the mate scores (1000.xx = mate or conversion in xx) that the engine defends far from optimal:

[Event 'Edited game']
[Site 'FOM-RHKA8J2A5WY']
[Date '2012.02.28']
[Round '-']
[White 'fairygen']
[Black 'Fairy-Max']
[Result '1-0']
[Variant 'fairy']
[FEN '8/8/8/3k4/4e3/8/8/4KR2 w - - 0 1']
[SetUp '1']

{--------------
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . k . . . .
. . . . e . . .
. . . . . . . .
. . . . . . . .
. . . . K R . .
white to play
--------------}
1. Ke2 {+1000.67/1} Kd4 {-1.78/16 8} 2. Kd2 {+1000.66/1 0.1} Ke5
{-1.72/16 9} 3. Kc3 {+1000.64/1 0.1} Ef4 {-1.77/18 22} 4. Kc4
{+1000.60/1 0.1} Eg4 {-1.86/21 11} 5. Re1+ {+1000.56/1 0.1} Kf5
{-1.85/22 10} 6. Re8 {+1000.55/1 0.2} Ef4 {-1.84/21 9} 7. Kd4
{+1000.54/1 0.2} Ed6 {-1.83/23 14} 8. Re5+ {+1000.50/1 0.2} Kf4
{-1.83/22 14} 9. Re1 {+1000.49/1 0.2} Kf5 {-1.84/22 13} 10. Rh1
{+1000.48/1 0.2} Ed7 {-1.85/21 17} 11. Kd5 {+1000.43/1 0.2} Ee7
{-1.83/20 10} 12. Rf1+ {+1000.40/1 0.1} Kg4 {-1.84/21 11} 13. Ke4
{+1000.39/1 0.2} Kg5 {-1.81/20 9} 14. Ke5 {+1000.32/1 0.1} Ec5 {-1.82/20 8}
15. Rg1+ {+1000.16/1 0.2} Kh5 {-1.86/21 27} 16. Kf5 {+1000.15/1 0.2} Kh4
{-1.84/21 11} 17. Kf4 {+1000.14/1 0.1} Kh3 {-1.85/21 10} 18. Rg5
{+1000.13/1 0.2} Ee7 {-1.84/20 9} 19. Rg3+ {+1000.12/1 0.2} Kh2
{-1.83/20 13} 20. Kf3 {+1000.11/1 0.1} Ef7 {-1.81/21 12} 21. Rg5
{+1000.10/1 0.1} Ef6 {-1.78/20 12} 22. Rg7 {+1000.09/1 0.2} Ed4
{-1.82/20 9} 23. Rd7 {+1000.08/1 0.2} Ec4 {-4.89/21 11} 24. Rh7+
{+1000.07/1 0.1} Kg1 {-4.89/23 12} 25. Rg7+ {+1000.06/1 0.1} Kh2
{-4.88/23 14} 26. Rg4 {+1000.05/1 0.2} Ec3 {-4.94/23 9} 27. Kf2
{+1000.01/1 0.1} Kh3 {-4.96/25 11} 28. Rg3+ {+1000.00/1 0.2} Kh4
{-4.98/27 9} 29. Rxc3

This is where it stops, as fairygen can play only from one tablebase at the time, and does not have KRK loaded here.

Wow, this is a really intresting result. Now I wonder how the Woody Rook aka Wazaba (WD compound) does in the end game against a Rook. I felt it was too clumsy in certain endgames with some pawns against a Knight and replaced it with the Phoenix aka Waffle in the Fearful Fairies army ( http://www.chessvariants.org/index/msdisplay.php?itemid=MSfearfulfairies ).

K+R vs K+WD has the signature of a general draw, although there is an appreciable number of lengthy wins (upto 32 moves to force conversion). With white to move 62% is won, with black to move only 13%. The latter number is far mor than the expected number of forks and skewers, and indeed only about 2% of the btm positions are quick tactical wins (conversion within 3 moves). Most of the other won btm positions take at least 10 moves to conversion.

So there is plenty of trouble for the WD. Presumably mainly when the black King is pushed against the edge by the white King, although I did not check that.

KRKN has about 9% btm wins, and about 5% are within 3 moves (presumably more than with WD because R can pin N from close range, while against WD it has to keep a distance), and although wins can take up to 26 move, the number of lengthy wins tails off pretty fast, and there there is no pronounced bump in the DTC histogram at long DTC. So the character is is definitely different.

It seems that the lengthy wins in K+R vs K+WD are mainly due to hunting down a WD that is not able to connect with its King, in combination with an unfavorable black King location (near the edge), which allows you to force separation of them even when they can connect. 

Note that K + R vs royal WD is a win. So there are many wins where K+R drive the WD into a corner. But the longest wins are those where the WD can just survive by fleeing to the shelter of an unfavorably placed King, and then, under the threat of mate, can be forced away from it, to be hunted down in isolation after all. Like in the following game:

[Event 'Computer Chess Game']
[Site 'CHESS_LAPTOP']
[Date '2012.03.02']
[Round '-']
[White 'EGTgen 1.2.4']
[Black 'hgm']
[Result '1-0']
[TimeControl '40/60']
[Variant 'fairy']
[FEN 'K7/7k/2R5/8/8/8/w7/8 w - - 0 1']
[SetUp '1']

{--------------
K . . . . . . .
. . . . . . . k
. . R . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
w . . . . . . .
. . . . . . . .
white to play
--------------}
1. Kb7 {+1000.32/1} Wb2 2. Rd6 {+1000.31/1 0.1} Wc2 3. Kc6 {+1000.30/1 0.1}
We2 4. Kd5 {+1000.29/1 0.1} We3 5. Rb6 {+1000.28/1 0.1} Wg3 6. Ke5
{+1000.27/1 0.1} Wg5 7. Kf4 {+1000.26/1 0.1} Wg6 8. Kf5 {+1000.25/1 0.1}
Wg8 9. Kg5 {+1000.24/1 0.1} Wg7 10. Kh5 {+1000.23/1 0.1} Kg8 11. Rb7
{+1000.22/1 0.1} Kf8 12. Ra7 {+1000.21/1 0.1} We7 13. Kg5 {+1000.20/1 0.1}
We6 14. Kf5 {+1000.19/1 0.1} Wd6 15. Ke5 {+1000.18/1 0.1} Wc6 16. Rd7
{+1000.17/1 0.1} Wc5 17. Kd6 {+1000.16/1 0.1} Wc4 18. Kd5 {+1000.15/1 0.1}
Wc2 19. Rb7 {+1000.14/1 0.1} We2 20. Ke5 {+1000.13/1 0.1} Wf2 21. Rb4
{+1000.12/1 0.1} Wf3 22. Ke4 {+1000.09/1 0.1} Wh3 23. Rb7 {+1000.08/1 0.1}
Wh5 24. Kf4 {+1000.07/1 0.1} Wh4 25. Kf5 {+1000.06/1 0.1} Wh2 26. Rb2
{+1000.05/1 0.1} Wh1 27. Rb1 {+1000.04/1 0.1} Wh2 28. Rf1 {+1000.03/1 0.1}
Wg2 29. Ke4+ {+1000.02/1 0.1} Ke7 30. Kf3 {+1000.01/1 0.1} Wh2 31. Kg3
{+1000.00/1 0.1}
*

Rook vs Waffle also has a very unusual distribution of the DTC (distance to conversion):

Usually a won end-game has only a single pronounced peak close to maximum DTC.
E.g. for KBN.K (where DTC = DTM, as there is nothing to capture):

The maximin game is (W = WA):

[Event 'Computer Chess Game']
[Wite 'CHEWW_LAPTOP']
[Date '2012.03.03']
[Round '-']
[White 'EGTgen 1.2.4']
[Black 'hgm']
[Result '1-0']
[TimeControl '40/60']
[Variant 'fairy']
[FEN '3K4/1R6/2k2w2/8/8/8/8/8 w - a6 0 1']
[WetUp '1']

{--------------
. . . K . . . .
. R . . . . . .
. . k . . w . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
white to play
--------------}
1. Kc8 {M74/1} We6 2. Kb8 {M73/1} Wd6 3. Ka7 {M72/1} Wd5 4.
Rh7 {M71/1 0.1} Wc5 5. Ka6 {M70/1 0.1} Wc4 6. Ka5 {M69/1}
Kd5 7. Rc7 {M68/1 0.1} We6 8. Kb5 {M67/1 0.1} Wd6 9. Re7
{M66/1 0.1} Kd4 10. Re1 {M65/1 0.1} Wd5 11. Rd1+ {M64/1 0.1}
Ke5 12. Kc4 {M63/1 0.1} Wf7 13. Re1+ {M62/1 0.1} Kd6 14. Kd3
{M61/1 0.1} Kd5 15. Rf1 {M60/1 0.1} Wg7 16. Rg1 {M59/1 0.1}
We5 17. Rg5 {M58/1 0.1} Ke6 18. Kd4 {M57/1 0.1} Wf5 19. Rg8
{M56/1} Wd7 20. Rh8 {M55/1 0.1} We7 21. Ke4 {M54/1 0.1} Kd6
22. Rh6+ {M53/1 0.1} Kc5 23. Ke5 {M52/1 0.1} Wd7 24. Rh7
{M51/1 0.1} Kc6 25. Kd4 {M50/1} Wc7 26. Rg7 {M49/1 0.1} Wb7
27. Kc4 {M48/1 0.1} Wd5 28. Rg6+ {M47/1 0.1} Wd6 29. Kd4
{M46/1 0.1} Kd7 30. Ke5 {M45/1} Wf8 31. Ra6 {M44/1 0.1} We8
32. Ra7+ {M43/1 0.1} Kc6 33. Ke6 {M42/1 0.1} Wg6 34. Ra8
{M41/1 0.1} We4 35. Rc8+ {M40/1 0.1} Kb6 36. Rc4 {M39/1 0.1}
We3 37. Kd6 {M38/1 0.1} Kb5 38. Rc3 {M37/1 0.1} We2 39. Kd5
{M36/1 0.1} Kb4 40. Rc2 {M35/1 0.1} We1 41. Rc4+ {M34/1 0.1}
Kb3 42. Kd4 {M33/1 0.1} We2 43. Rc6 {M32/1 0.1} Wf2 44. Ke3
{M31/1 0.1} Wh4 45. Kd3 {M30/1 0.1} Wg4 46. Rg6 {M29/1 0.1}
Wf4 47. Rb6+ {M28/1 0.1} Ka4 48. Kd4 {M27/1 0.1} Wg4 49. Kc5
{M26/1 0.1} We2 50. Rb2 {M25/1} We1 51. Rb4+ {M24/1 0.1} Ka3
52. Re4 {M23/1 0.1} Wc3 53. Re3 {M22/1 0.1} Kb2 54. Kb4
{M21/1 0.1} Wc2 55. Re2 {M20/1 0.1} Kc1 56. Kc4 {M19/1 0.1}
Wd2 57. Rg2 {M18/1 0.1} Kd1 58. Kc3 {M17/1 0.1} Wf4 59. Rf2
{M16/1 0.1} Wg4 60. Kd3 {M15/1 0.1} Ke1 61. Rg2 {M14/1 0.1}
Wh4 62. Re2+ {M13/1 0.1} Kf1 63. Ke3 {M12/1 0.1} Wg4 64. Rf2+
{M11/1 0.1} Kg1 65. Rc2 {M10/1 0.1} Wg3 66. Rc5 {M09/1 0.1}
Wg4 67. Kf3 {M08/1 0.1} We6 68. Rc1+ {M07/1 0.1} Kh2 69. Rc2+
{M06/1 0.1} Kg1 70. Re2 {M05/1 0.1} Wc4 71. Rg2+ {M04/1 0.1}
Kh1 72. Rg4 {M03/1 0.1} We6 73. Re4 {M02/1 0.1} Wd6 74. Kf2
{M01/1 0.1} Wf4 75. Rxf4 1-0 {black resigns}

OK, I think I should indeed have explained this in the readme file. Note there are two kinds of output: what is printed during the building, and shown in the WinBoard Engine-Output window (if you are lucky), and what is written on the file rep2.txt. (Silly name; I should also change that...) The former is raw statistics after symmetry reduction. The rep2.txt statistics is the true statistics, where every position that had a diagonal mirror image different from itself which was not taken into account in the calculation to save time is counted twice. But the numbers printed are still only counting positions where the King is in the square a1-d1-d4-a4. But this always would give you a factor 4, as on 8x8 boards there never are any horizontally or vertically symmetric positions (if you have one King, that is).

Now the meaning of the output:
TOTAL = the number of positions with no two pieces on the same square
WON.wtm = nr of positions won to white with white to move
K captures = nr of the above where white can capture the black King
other = WON.wtm - K capture

Then follows a table of the number of positions that are won to white when black has the move, split out by how many moves it takes to effect the win. In (default) DTC mode this is offset by 10, so 10 means black is currently checkmated, 11 he will be mated in 1, etc. (Losing a non-royal defender is counted in the same way as losing the King, so the count already reaches 10 when the piece will unavoidably be exposed to a winning capture on the next move, and not when you have actually captured it. The position after the capture would be listed as 9, but is not listed at all, because it belongs to a different tablebase, with another number of pieces. Nevertheless, now that I think about it, this is a bit weird, and it might be better if I change it such that I count positions where the non-royal piece is 'mated' as 11, or even 12, so that it would no longer prefer to be checkmated over losing its piece and be checkmated in a subsequent phase.) 

The 0-entry of the table gives the number of positions that are not won to white (still with btm) for other reasons than black capturing the white King (e.g. black capturing a non-royal white piece, or having a fortress draw). It probably should be renamed 'nonwins'

WON.btm = the sum of all entries other than the 0-entry in the table
stalemate = number of positions where black to move is stalemated
LEGAL = WON.btm + nonwins + stalemate
W check = positions where the white King is in check (i.e. illegal with btm)

Interpreting the numbers is a bit tricky, as even dead draws usually have most positions won for white to move; a generally won end-game really have a number more than 99% of the total there. To interpret the number, the K-captures help. E.g. in the sample output for KBN_K shown below, you see that more than 25% of all positions is won to white through immediate K capture, which has absolutely nothing to do with the mating potential of the white pieces. If black would have had a piece beside King, (e.g. KBN_KB) there are approximately as many positions where that piece is hanging. (This is not separately listed, but the chances it is protected by its King are only about 10%, so the K-capture number is a good indication for it.) So you would already have about 50% 'false positive' WON.wtm positions that don't have anything to do with the end-game under study.

It is often more revealing to look at the black-to-move numbers. But there you have a large number of false negatives, where black starts with capturing a hanging attacker. The 'W check', where he captures the white King has already been taken out of the WON.btm, (and this is about 10% for an orthodox King on 8x8) but the probability black attacks each of the other white pieces is the same, and they are unprotected more often than not (and sometimes protection does not help, if attacked by a non-royal defender). So it is quite normal that 30-60% of the btm positions are not won in a generally won end-game.

What also helps is to look at the distribution of the WON.btm positions. Even KR_KQ has won positions (for the Rook), but none of those takes more than 3 moves. So the very fast wins should all be discounted as tactically non-quiet positions, that after the tactics raged out don't really belong to the end-game under study. So what really counts is the number of lengthy wins with btm.

KBN_K

WON.wtm    3798926
K capture  1093380
other      2705546
  0.        636982
 10.           116
 11.            78
...
 43.           740
WON.btm    2797042
stalemate     3222
W check     375010
LEGAL      3437246
TOTAL      3812256

Thanks, Muller.  This is a neat little tool.

Could you go into a little more detail about how the columns work when some of the pieces are colorbound?  With two colorbound pieces, I get two columns in rep2.txt, which appear to be same-color and different-color, respectively.  But with 3 colorbound pieces, I get 4 columns, one of which is all zeroes (including its total board positions), and none of them are labeled.  (Also, none of them are identical, even when all 3 colorbound pieces are the same piece-type and owned by the same player...)

I did some experimenting with mismatched royal pieces.  Interesting result:  while it is commonly known that KNN v K is drawn, it appears that NK v K (that is, a single royal knight + commoner vs. king) is generally won!  (89% won with black to move, longest win 29 moves, if I'm reading these results correctly.)  I suppose that shows the value of sacrifice.

How difficult do you think it would be to modify this code to accommodate 'lame' leapers, bent riders, crooked riders, and/or pieces with only 2-fold symmetry?

With N color-bound pieces there are 2^N possible color assignments, but thy come in symmetry-equivalent pairs. (The latter is only true for boards with an even number of squares.) So with 3 color-bound pieces, you have 4 possibilities. Unfortunately I always forget which is which, but the total number of positions is a help in identifying them. (All on the same color has fewer positions.)

If two of three color-bound pieces are identical, two of the columns would be equivalent, and I combine them into one (resetting the other to zero). If columns give different results, say one a general win, the other a draw, I usually just set up a position to see if it is win or draw to identiify them. (E.g. FAD + B vs B, if you set up a position with B on same color, wit will be a draw.)

It is not so easy for this generator to expand the move generator, because it uses the same generator for forward and retro moves (just leaving out captures for the retro moves). This was a bad idea, becaus with lame leapers in general you cannot do that.(E.g. retro Mao moves are Moa moves, etc.) This generator predates Fairy-Max, otherwise I would probably have written its move generator to work in the same way as that of Fairy-Max. 

Reducing the symetry would blow up the memory requirement. On modern hardware an increase from 128MB to 512MB for a 5-men is probably affordable, but it would also quadruple the generation time.

The Nutty Knights are weak. The fibnif is exactly 3. The charging rook is maybe slightly weaker than rook, but it's really a quantum of advantage. The Charging Knight is probably stronger, but again by a quantum of advantage. So that leaves just the Colonel. The rook part is 3.75 the knight part is 1.5 the king part is 2. 3.75+1.5+2=7.25. The Colonel is just too weak. What about fsRfhNAK? The other two teams? :)

Actually the Nutty Knights beat the *** out of FIDE. They score about halfway between when you give otherwise equal armies one extra Pawn or two extra Pawns. So they seem to have a 1.5 Pawn advantage. The Colorbound Clobberers are also stronger than FIDE, but not by as much (slightly less than a Pawn), so the Nutty Knights also have the edge over those.

It seems that especially the charging Knights are much stronger than one would expect. It seems you also don't take account of the fact that compound pieces usually are stronger than the sum of their parts. Otherwise the Queen would be worth 5 + 3 = 8, rather than 9.5. You also do not take account of the fact that forward moves are worth more than backward (or sideway) moves, so that the fsR part is worth more than 3/4 of R (more like 4/5, as forward moves approximately contribute twice as much).

I did not test the Rookies army as extensively, as Fairy-Max only recently implemented that army. (Upto then the short Rook was the problem; Fairy-Max did not implement limited-range sliders.)

Nutty Knights to me seem more powerful than Fabulous FIDEs, but the known theory of the FIDEs and the unfamiliarity of the Charging mechanic makes the Nutty Knights complicated. Also, Fibnifs should stronger than Knights. 

Players well experienced with Chess with Different Armies are likely Nutty Knights preferable, but players new to Chess with Different Armies would probably prefer the Fabulous FIDEs. This seems to be the case with the Clobberers and the Rookies as well, to a lesser extent.

One thing I don't get though, is why would Charging Rooks be a miniscule amount stronger than normal ones?

Of the experimental armies of CwDA, most work well but the Cylindrical Cinders doesn't. It can win the exchange Rook-type pieces on turn 1: if Fabulous FIDEs, Nutty Knights, or Fearful Fairies it can win Rooks without exchanging them (unless i'm missing something). Besides, they can't develop to protect pawns.

My suggestion is that they switch places with the Bishops, since as BDs show corner squares work well with Bishop-ish pieces, and all Bishops (so far, including Bakery Bombers regardless of the Queen) are protected, and because like Knights they usually develop to protect the opposite pawns.

I don't see how the Cylindrical Cinders can capture a Rook on move 1. For cylindrical chess a board glued between the files h1--8 and a1--8 is usually assumed. A cylindrical bishop can move, e.g.,  from a1 to h2, but not from a1 to, say, b8. Even though the rooks are initially unprotected, they are not directly reachable for the Cinders behind their wall of pawns.

Gluing the board the other way round, along the ranks (a-h)1 and (a-h)8 is very unusual and you would start up with the opposite Kings in direct contact.

So, I was sort of thinking of a Spherical Waffle. I see.

However, my point about Pawn protection still stands, although having an already fien... finch... thing empowered Bishop, C-Name and central Waffle placement  may make this army a bit too similar to the Colourbound Clobberers.

I think it's a fun exercise for chess variant inventors to develop their own CDAs, kind of like a poet to develop his/her own haiku or sonnet. Obviously, it's not essential for poets to adopt "accepted" (but also merely arbitrary and conventional) forms. I encourage cv inventors with time, energy and inclination to do what Aronson, Lawson, Joyce and several others have done and try to come up with their own unique blend of pieces to compete against the ortho-Eurocentric one, e.g., what CDA might employ a GW Duke Falcon? I would LOVE to see such a thing developed and I'm sure some very nice ones could be.

A fun variant design contest would be for CDAs.

I hope to see CDA developed for other variants besides the ortho-eurocentric one such as the Shatranj for Different Armies alluded to by such as Knappen and Joyce and Tripunch for Different Armies as Betza has alluded to (I have recently myself discovered a Tripunch CDA currently in Beta Testing). One hopes to see more classic, exotic, fancier CDAs developed such as those by Knappen, Maxson, Makov, I myself, others and older ones fine-tuned with the guidance of computers such as H.G. Muller has been delving into...

"Classic" is the right word because Betza invented Chess Unequal Armies, http://www.chessvariants.org/index/displaycomment.php?commentid=614, as he points out in 1976 nearly forty years ago.  The most creative ever CV inventor Betza did not "begin" the dissatisfaction though.  OrthoChess having already 300 years of pretty fixed rules from 1500 on, CVs burgeoned right after the time of Philidor (d. 1795) and continue unabated.

I have posted a nightrider cda but I think because of forking factors that makes them too strong (as with Fearless Fairies - courtesy again H.G. Muller). I have what I think is a clever idea how to revise it and only say this pre-emptively before unveiling...

Cunning Cupids is still in a very primitive state of un-readiness but I hope it will one day be a legit cda too (in the mean time, i'm preparing several new pieces in the heart theme)...I have another geometric army even less ready called Awful Alfils based on hexagonal movements.

From different perspective there is the Sovereign Values study, http://www.chessvariants.org/index/listcomments.php?subjectid=SOVEREIGN_P_Ts, determining more general mating material needed instead of value directly itself. From that we know that many well-thought-out piece-types do in fact have approximately the 3.0 value of Knight. 2.5 to 4.0 is more typical piece-value range than Falcon or Rook 5.0 +/- 0.1. For example, Peter Hatch has many devised pieces for his different armies on 100 squares near Knight equivalence. (Druids: http://www.chessvariants.org/large.dir/druid.html) 

On conventional 8x8, Scorpion would fall from Falcon 5.0 to about 4.5, and Dragon still more to 4.0. They move progressively a required 3, 4 and 5 steps.  Based on those values, and calling it the Multi-path Army,

F-S-D-R-K-D-S-F is an appropriately 31-point Chess Different Army.

Thank you. I look forward to trying it out!

George, that's a rook you put in the center there, right?

I've been inspired this morning to think of a substitute that would perfectly complement the rest of these pieces, some sort of a lame multipath queen that would have approximately the same value as the rook. Sounds funny because queens are already "lame" but I'll show you what I mean...Why don't I email you tentative details and maybe we can work out such a piece and post it here...should I use the same email address as you use in games you play via courier?

I will copy H.G. Muller on this correspondence and hope he can help us finetune for accuracy of value.

Sure on all counts.  I had to think for a moment whether Dragon can reach all squares.  Though required 5-stepping, yes it can even on small 8x8. Not all middle-distance leapers, by contrast, reach every square such as Rector(4,5) unable to reach central four.  It shows multi-path flexibility.
(http://www.chessvariants.org/large.dir/scorpionanddragon.html)

Well there can be alternative subvariants (mentioning it once and for the last time thank Muller for useful "subvariant" term) replacing King-accompanying Rook, as many subvariants as we want.  The idea of Rook here would be comparable to Betza's Colourbound Clobberers having Carrera-Capablanca Centaur, though that Bishop-Knight is the one exception not being colourbound.

5-stepping never gets you to the 4 central squares on 8x8, right? When you start in the central 4 squares, the largest step you can make before hitting an edge is 4, so you would have no moves there.

BTW, the Color-bound Clobberers also feature a Phoenix (WA), which is not color bound.

How about 'Multi-path Marauders' as an army name?

I wonder if it would be possible to base a CwDA army on Team-Mate Chess. The latter is not really conformant with typical CwDA, because all the pieces are different, in stead of occurring in pairs. It also seems a no-no that it uses some pieces already occurring in other armies, in particular the Phoenix and the Knight. It might also be just a bit weaker than FIDE, while most CwDA armies are stronger.

[Edit] I got the following idea for a CwDA army based on the same philosophy as Team-Mate Chess, that no single piece should have mating potential, but which has the same composition in terms of pairs of light and heavy pieces, plus one super-piece, as regular CwDA armies:

The lame Gnu (NC) will serve as replacement for both Rooks; Team-Mate Chess uses the slightly weaker WN as the second Rook-class piece here, but I let this piece feature here in chiral form, having only the left-handed or right-handed Knight moves, so that it gets the strength of a minor. Of course it would occur as its mirror image on the other wing. The Queen-replacement will be Aanca, as in Team-Mate Chess, while the second pair of minors could either be Modern Elphant (FA) or Mortar (AG), to tune the strength. (Mortar is weaker).

It could be called: the Tricky Teamsters.

Please describe by what routes your lame gnu gets to its camel / knight squares. Or are you saying the knight-chirality is what makes it lame?