Comments/Ratings for a Single Item

'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.