Ahh ok, thanks Fergus, interesting to know, much earlier than I thought. Thank heavens Wikipedia wasn't wrong lol.

1979 is the date of invention recorded in our database. Betza’s games became better known in the 90’s thanks to the arrival of this website,but he is from an older generation and did not wait for the arrival of the web to start creating chess variants.

I have always thought this game was first created in 1996 by Ralph Betza, however, I notice Wikipedia says this ..

Chess with different armies (or Betza's Chess[1] or Equal Armies[2]) is a chess variant invented by Ralph Betza in 1979.

Is that right.

I was thinking of the Friend as one who could copy the moves of a friendly piece guarding it; conversely, the Orphan copies the moves of an enemy piece attacking it. With modifications, that might be able to do what you're thinking of.

Unless you're thinking of combining move borrowing with relay, or something like that.

@Bob Greenwade

O don't see the connection between the friend and what I had proposed!

Intriguing idea, Aurelian. Maybe once we can get the Friend coded in?

Meanwhile, I'm contemplating a back row with one each King, Queen, Candlestick, Knife, Lead Pipe, Revolver, Rope, and Wrench. I haven't quite figured out the XBetza for those last six yet; my intent can be found here. (I hope to build a full-fledged mashup some time in the future.) I have a suspicion that my descriptions may unnecessarily overpower the FIDE set. (Maybe a Wazir instead of a Queen?)

PS: I'm quite fond of the Lame Duck and Half-Duck from the Sliders set, and the Dragon Fly from the Dragons.

Nobody curious about this?

I'm thinking about adding an imitator in a chess with different armies environment.

But I don't like the idea of having access to the powers of the opposite armies.

So I came up with the idea of the transferer, which it would be a piece transferes the power of the enemy piece just moved to it's counterpart in the player's to move army.

For example in CC vs NN if white CC have just move a waffle (phoenix) the black NN player would have a fibnif power for the transferer. Any thoughts on this?

@H.G., I've been trying to use Kingslayer/CwDA for playtesting but I have one issue regarding the notation for promotions. I believe the ' should be used to indicate a piece from the opponent's army, but when Kingslayer plays black, it puts the apostrophe on the notation even when promoting to a piece from its own army. I haven't had an opportunity to look through the source code yet.

@HG: would you agree that the chiral Aanca of the Bent Bozos could be renamed Left and Right Manticore now?

For aesthetic reasons I would  like to avoid divergent and asymmetric pieces. So if there is a 'full-atom' alternative, I would prefer that. And symmetry breaking would be preferable over divergence. (Because it is what the Nutters do. None of Betza's armies had divergence, though.) Tinkering with the super-piece is also less course than with pieces of which you have a pair.

A 58% result against FIDE is not out of line with what the other established armies do. (In fact they all have worse advantage.) One can also argue that in human play it is a good thing to disadvantage FIDE a bit, because of its familiarity. So I think A or D moves on the Squire are a satisfactory solution. And it doesn't alter the Squire's 'footprint'; it would still be a sliding version of a Squirrel.

It is just a matter of choosing between A and D, which appear to give an equal boost. The army already has D moves through the Diamond. So perhaps I should go for the A moves on the Squire; it seems to me the ability of pieces to attack each other without being automatically attacked back contributes a lot to making play interesting.

Or maybe replace the Diamonds with DAmK?

I finally finished playetesting the Silly-Sliders army with Fairy-Max, against the Fabulous Fides. Unfortunately the army is a bit too weak. As a whole it loses by about 58%. This is unacceptable, since all other established armies are sinificantly stronger than the Fides. The Onyxes are a bit stronger than their orthodox counterparts, the Bishops (even against the B-pair). The Lame Ducks and Rooks are equally strong. But the Squire is about half a Pawn weaker than a Queen, and the Diamond is also weaker than the Knight, probably because of its color binding. Although replacing it by a Frog (WH) only made it worse.

So I have been looking for ways to enhance the Squire. Making the diagonal moves reular ski-slides rather than lame ones made it too strong. On such a mobile piece it turns out to be of great value to be able to attack other pieces from behind a cover, so they canot attack you back. Only making the sideway orthogonal slides ski-slides made the armies about equal; it is difficult to attack from the side. But I don't like to break the 8-fold symmetry that all other pieces of the army have.

What is a good option is to add A or D moves to the Squire. The SiIlly Sliders then  beat the Fides by about 58%. I have not decided yet whether to use the A or D moves.

I do not know if there is a game with Dabbabarider Fers piece, possible but yeah, I'm not sure. I can't recall seeing one myself.

I never meant for you to change name, I was just giving info. I understand though you might want to change, and Lame Duck is interesting name!!

If I do see a game with the piece I'll let you know.

The Silly Sliders are one of the weirdest Chess experiences I have had. They are so strange: One attacks by retreating and unlocking the far range moves and one escapes from attack by approaching the figures. I'd suspect that the army is a bit weaker than the FIDEs because the ranging pieces can be stuffed. A blocking piece on the ski square doesn't even need protection. The rotated short range moves of the Onyx and the Duck have unusual interactions with the pawn formations.

All in all: A great design worth trying.

Thank you. I admit that of the armies I designed I like the Silly Sliders best, aesthetically. Unfortunately I couldn't do much testing, as my main PC broke down. I would really like to do some testing on the Onyx; in fact that piece is what gave me the idea for this army. I was looking for a non-colorbound version of the Bishop, for measuring whether the B-pair bonus would really disappear in that case. Because there is an alternative explanation for this bonus, namely that two diagonal slides on opposit square shades cooperate exceptionally well. Playing Bishops against Onyxes in pairs or singletons could decide this matter.

A second point of interest would be whether the penalty for a leap being lame depends on whether the square where the leap can be blocked is attacked by the piece itself, or not. In a sense all distant slider moves are lame leaps, but they cannot be blocked without exposing the blocker to one of those. Playing Onyx + Duck vs Bishop + Rook would be a 'low-noise' experiment for investigating this. Between them they have exactly the same moves, which can be blocked the same way, but the Onyx and Duck do not attack the adjacent blocking squares, while the Bishop and Rook do.

Interesting that the name Duck was used for FDD by Jelliss. This has a very similar footprint. Is it known which variant employed this piece? If i is imporant to keep the distinction between these pieces, I could  change mine to 'Lame Duck'.

Great work on 'Silly Sliders', new pieces are interesting. Onyx, Duck and Squire are all original are they not.

They are nice. I would say I'd rather have a Squire than a normal Queen, with the Knight jump. The name 'Duck' is used by George Jelliss with his 'All the King's Men' listings though, but this is ok. Duck .... Fers + Dabbabarider.

Have you played it with someone or a computer, I'd say it must play pretty well. Great work!!

The Silly Sliders

I have an idea for an army themed on a class of pieces not often encountered in variants: lame ski-sliders. The Picket of Tamerlane Chess is such a piece: it moves as a Bishop, but must minimally move two steps. So it lacks the Ferz moves, but the more distant moves can still be blocked on the F squares. (Unlike a true Ski-Bishop, which would jump over these squares, ignoring completely what might be there.)

The idea is to turn all sliding moves of the orthodox Chess pieces into such a lame ski-slide, and compensate them for the lost moves by giving them equally many leaps in other directions. So the Bishop loses its F moves, but gets the W moves instead. This makes it a sliding version of the Phoenix (WA), like the Bishop is a sliding version of the Ferfil/Modern Elephant (FA). I will call it an Onyx. The Rook likewise loses its W moves, and gets F moves instead. It is the sliding version of the Half-Duck/Lion, and I call it a Lame Duck.

The compound of an Onyx and Duck would be a normal Queen, and is not suitable. To stay within the theme it has to lose all K moves, and should be compensated with 8 other moves. The N moves are the obvious choice for this. That makes the Queen replacement a sliding version of the Squirrel (NAD), and I call it a Squire.

The Knight isn't a slider, and its move is already in the game through the Squire. That leaves a lot of freedom in choosing a move for the Knight replacement. A totally symmetric 8-target leaper that (AFAIK) is not used in any of the other established armies is the Kirin (FD). This is a color-bound piece, but the Onyx isn't, so this doesn't seem to be a major drawback. A Kirin easily develops from b1/g1 through its D move, (and the Onyx from c1/f1 through its distant B moves), so that castling is no problem. I am just not very happy with the name 'Kirin', as it has no western meaning, and starts with K, which collides with King. In modern Japanese 'kirin' means giraffe, but that name is already associated with the (1,4) leaper. Perhaps I should call it an Egg, as its moves are a sub-set of those of the Half-Duck, and make a somewhat round pattern. This piece is called 'Diamond' in Jörg Knappen's 'very experimenal' army the Sai Squad, and since this goes very well with the name Onyx (and perfecly describes the move pattern) I will adopt that name here too.

Note that the total set of moves of the army is nearly identical to that of orthodox Chess. The same moves are just redistributed differently over the pieces. The only difference is that there is a D move on the Egg; if that would have been a W move (i.e. if we would have used a Commoner instead), the correspondence would have been perfect. (But there would not have been a color-bound piece then, and perhaps that is worth somethin too.) So I expect the army to be very close in strength to FIDE.

I did some more work on the CwDA version of KingSlayer, and finally put the source code on line. The latest version now also supports the Daring Dragons army. This was not a trivial addition; this army needed several unusual features that were not implemented yet. For one, the Dragoons (KimN) need a divergent virgin move, and neither divergence nor virgin moves were implemented (other than in the hard-coded Pawn). The Wyvern has a ski-sliding move, which thoroughly affects the way we have to test for check, and what evasions to generate. It introduces a new mode of checking (which I call 'tandem check'), which is a double check where both checks come from the same direction. These can not be cured by capture of the checker, but unlike normal double check, it can be cured by interposition.

The Dragonfly is a tricky piece, with binding to odd or even files. It requires special evaluation to handle it well in the end-game. One of the unusual properties is that it is a 'semi-major': it can force checkmate on a bare King, but the KFK end-game also has fortress draws. Which of the two it is, is about an even call, like a promotion race in KPK: If the bare King can reach the b-file before the Dragonfly gets there, he can take safe shelter on the a-file, and it is draw. Otherwise it is a win. From the material composition alone, you cannot make a good guess. So I put in a routine that makes a reasonable guess based on the actual locations. (Not perfect yet, as it doesn't take account of the bare King hindering the Dragonfly in its attempt to reach the b-file, or vice versa, but that only happens in a minority of the positions.)

When the weak side still has Pawns (e.g. KFKP), I classify the end-game as drawish. (But not as bad as for KBKP, where you have no chance at all.) This assumes that the Pawn can act as a sufficient distraction for the strong side that the weak side has a very good chance of reaching safety with his King in the mean time. In fact a fair amount of positions in this end-game are won for the Pawn! If the Dragonfly cannot visit the file the Pawn is on, you only have the King to stop it, and the Pawn can easily be outside its reach as well. So Dragonfly endings, like Pawn endings, should really test for 'unstoppable passers' in their evaluation. (At the moment, KingSlayer doesn't do that for either, with as a consequence that is sometimes trades the last (non-Dragonfly) piece in a near-equal position, and on the next move (where it can search much deeper) sees the score dropping to -8.xx because the opponent's promotion can no longer be prevented.

The version I uploaded has the announcement of equal-army sub-variants commented out. With all combinations of the 5 supported armies, the list of variants in the CECP variants feature had become so long that it crashed XBoard!

I also started implementing limited configurability: it supports a variant 'custom', for which the user can specify (in a file gamedef.ini) the armies as an arbitrary selection of all the supported CwDA pieces. In addition there are two user-configurable pieces that can be selected too. These pieces can be built as an arbitrary combination of the move sets used to construct the standard CwDA pieces, plus one user-specified set of leaper moves. I am still thinking about a way to also allow specification of divergent or lame moves on these pieces. It might also be useful to allow redefinition of the set of leaps that is only used for the Charging Knight, in cases where the latter doesn't participate. And perhaps to redefine one or two slider moves, e.g. by making the range of R4 configurable, or perhaps replaceable by B3 or B4, or fB.

[Edit] I now uploaded a Windows binary of the latest version to http://hgm.nubati.net/CwDA.zip .

While watching a cpu vs cpu game of eurasian I had noticed that vaos do not seem to care either about color binding as in the early game color binding is compensated by the other pieces and in the late game lack of platforms probably damages them more.

Cool analisys HG!...

Well, it is difficult to asses whether this capability for a pair to statically create an impenetrable barrier for a King is really important. Actually I think that Wizards can just do it (on 8x8), when standing next to each other in the center. But very often pieces can inflict a 'dynamic confinement' on a King. As long as you have to spend fewer moves to maintain it than the King needs to escape, you have moves to spare for other pieces to approach. Besides, FAD complement each other in a different way: standing next to each other the completely cover a 5x6 area, As a result they can drive a King to the edge with checks, and checkmate it there, without any help. This makes them very, very dangerous.

Even a King + Bishop can dynamically confine a King on boards of any size. The King has to cover the hole through which the opponent threatens to escape, and has to follow the bare King as long as it keeps running in the same direction to renew the escape threat. But when it reverses direction, to try an escape on the other side (which he eventually must, as he bumps into the edge) you have one free move. Therefore a Bishop can checkmate together with an arbitrarily weak piece (as long as that can go everywhere) on boards of any size.

@HG,

Also there is another effect that amplifies pairing bonus or color bonding penalty. The effect of the pair being able to block the king from part of the board. That the same way rooks do on their own. Bishops do that. Two dababahriders to that, and they only cover half the board among themselves anyway. Wizards or fads do not.

Also the case of bede and WAD on different shades who work a bit akwardly but do work together fine. Probably stronger than a charging rook+fibnif or waffle+short rook. Many pawns would help a lot the CC pair. But ChessV for example know such tricks. I did whached some games.

Well, this is the whole point of making KingSlayer play CwDA: its playing algorithm can take the effects of color binding into account. But it still requires some thought on what exactly it should pay attention to. The only things I discovered about color binding so far were obtained with Fairy-Max, which doesn't take any color binding into account. It thus might under-estimate the effects. E.g. it approximates the effect of the Bishop pair bonus by making all Bishops worth more than Knights. This biases it against trading B for N in general. Which helps to preserve the B pair, (as it should), but makes it unnecessarily shy in lone B vs N situations (which should be a self-inflicted disadvantage of having a Bishop), and it doesn't prevent it from breaking up the pair by Bishop trading in a BB vs BN situation.

But it still finds an effect of about half a Pawn. I.e. B tests about equal to N, also in 'anti-pairs' (on the same shade), but a true B-pair tests as 0.5 Pawn stronger than B+N or 2N. I also did tests with more than 2 Bishops, and concluded that with 3 Bishops (divided 2:1 over the shades) you get 1 pair bonus, and with 4 Bishops (2:2) you get 2, compared to the simple addition of lone-Bishop values. While one could argue that the number of pairs is 2 and 4, respectively, in those cases.

There is a completely different interpretation of this data, not in terms of a pair bonus, but of a binding penalty. With Kaufman values B=N=325, and the pair bonus=50, so 2B(2:0)=650, 2B(1:1)=700, 3B(2:1)=1025 and 4B(2:2)=1400. These same numbers would be obtained by setting B=350, and giving a penalty of 25 when they are not equally distributed over the shades. The remarkable thing is that the penalty doesn't seem any higher for a shade imbalance of 2 than for an imbalance of 1. So it doesn't seem to matter how much power you have on your strong shade (with non-color-bound pieces you could aim them all at the same shade anyway), but it hurts when you lack power on a shade. This would mean the magnitude of the bonus is not really dependent on the value of the color-bound piece, as it is mainly expressing the disadvantage of absence of a piece. Indeed a preliminary test with Pair-o-Max (a Fairy-Max derivative that takes pair effects into account in a primitive way) suggested that the bonus for Bede was also just 50. (Pitting 2 BD on like or unlike shade versus 2 BmW + Pawn.)

The situation in the Clobberers army should be pretty much like the 4B(2:2) case; after trading one BD or FAD you incur the penalty, which you lose again after you then trade BD or FAD on the opposite shade (making that effectively worth 50 less than the first), but which you would keep after trading the second of the same shade (effectively giving that the 'average' value). This is how KingSlayer treats it now.

But pair bonuses / binding penalties are relevant in the middle-game; in the late end-game you could be in a much graver danger than the penalty suggests, vulnerable to tactics that would destroy your mating potential. Like sacrifycing a Rook for the piece on the 'minority shade' in a 2:1 situation. (Similar to what makes KBNN-KR a draw in FIDE, while KBBN-KR is a general win.) But this weakness would only be fullly exploited if the defending engine would know about it; otherwise it would just randomly trade the Rook for a member of the pair that threatens checkmate, with a 50% probability that it leaves a 1:1 distribution, and will be checkmated later anyway. (Like that it should know in KBNN-KR that it should leave NN, and not BN.) Failing to fully exploit an advantage might lead to underestimation of the value of that advantage.

@HG,

But the issue of an game with different armies where one player has more color bound pairs of pieces is an rather difficult one. The more color bound side has stronger pieces (in order to compensate for the color binding). The issues you mentioned are also strongly related to the fact the the playing algorithm does not understand it. If it does then it will play differently. But the problem is not gone away this way either as the game is now reduced to if early mid game tactics work for the color bound side. And from a game design point of view frankly this is not much. It lacks complexity. 

I'm wondering if the more color bound army has weaker values in the color bound pieces than it's counterparts in the other army, and then it compensates through the rest of the army it can work better. Or is the color bound army, just has more pieces be them individually weaker. Even if this is contrary to Betza's game. This last case also has problems though in the realm of the army with more pieces needing more time for coordination.

So the issue you raise is not that simple in it's depths! And quite likely something that people on the musketeer chess website have not fully considered!

@HG

Your analysys is much deeper (although treating only a nieche of the problem) than any of those made by the guys from musketeer chess!...

Indeed, these asymmetric variants from the musketeer.net website are very unbalanced. Sometimes as badly as playing 6 minors against 6 Rooks in FIDE.

I discovered that the generalization of 'unlike Bishops' in KingSlayer's drawishness detection is not satisfactory. I had it only kick in when both sides have a single piece (plus Pawns, possibly different 1 or 2 in number), and both these pieces are color bound. But from watching games with the Clobberers I noticed it still stumbles in completely hopeless draws with a huge 'naive' advantage. E.g. there was a game where it had Bede and Fad on the same shade, plus an extra passer, versus a Half Duck. All the opponent's Pawns were on the safe shade, ('passively' blocking his own, i.e. without the possibility to offer trades or a majority to create new passers), and the enemy King was blocking the passer on a safe square. All the Half Duck had to do to block all progress was neutralizing any King attacks on its Pawns. Which it could easily do sitting on the safe shade, though its F and D moves. A single Bishop on the safe color (which can also protect from a safe distance) would also have done.

So I guess any situation where you have only to like-shaded color-bounds plus Pawns should be classified as drawish when the opponent has a piece with significant diagonal power (so it can keep a Pawn protected against King attack) that is not bound to the same shade as the attacker. Under some conditions a Ferz would even do (e.g. a Pawn and the Ferz mutually protect each other, and block two opponent Pawns, while the King blocks the third (which is a passer). Tempo moves can be done with King or Ferz, depending on which of the two is far away from the attacking King. No way Bede + Fad + 3 Pawns would be able to beat Ferz + Pawn. While the naive advantage would be about +9 (Bede, Fad being worth 4-4.5, Ferz 1.5 Pawn)! Of course there is no Ferz in CwDA, but there are pieces with F moves. (They are of course worth a bit more, but then you are still at +7 instead of +9.) A or D moves could sometimes do too, when two connected Pawns and the piece cyclically  protect each other (although with D moves you can then only block two Pawns, rather than three).

So end-games with same-shade color bounds can also very drawish even with many Pawns, even when not just Pawns ahead but also in pieces. I guess these must be heavily discounted in order to play well with or against the Clobberers. Having a Knight as defending piece would probably not do very well, though, due to its color alternation. So it would depend on what pieces exactly the opponent has.

This link with different armies opposing the black orthodox army from the musketeer chess website could be of interest. To me it seems that much effort has not been put in the balancing of the 2 armies.

http://musketeerchess.net/games/castellum/rules/rules.php

http://musketeerchess.net/games/castellum/rules/rules-marsu.php

http://musketeerchess.net/games/castellum/rules/rules-jumpers.php

End-games: more armies

The Nutters

I adapted FairyGen to handle also two-fold symmetry (at the expense of the EGT being twice as large, and generation twice slower). This was a bit tricky, as this required distinction between retrograde and prograde moves, and flipping the orientation of the black pieces (neither of which was needed with 4-fold symmetry). But for 3-men EGT it finally gave identical results to the mating app here (which doesn't assume any symmetry). This means I could now do end-games with the Nutters majors as well. To keep everything together as an easy reference, I added the results to the tables in the previous comments.

The 4-men endings of light pieces were already interesting: it turns out the Charging Rook is very adept at beating other light pieces, much more so than an ordinary Rook. It has a general win against B, N, FAD, WA, and Fibnif single-handedly, while wins against BD and WD can in general be forced, but are then almost always cursed. I guess this success can be explained by that checkmating with Rook requires zugzwang, and will not work as long as the opponent has another piece to dump a tempo on. So you have to gain the other piece first, and in most cases this isn't any easier than checkmating (unless the additional piece is much weaker than a King, such as Ferz or Wazir), with the additional handicap that the piece can be protected by its King. Checkmating a bare King with the Charging Rook doesn't require zugzwang, however. So the mere possession of an un-involved defensive piece at a safe distance is no help. The piece must actively engage the Charging Rook, and the weaker pieces will perish in this combat. I did not calculate any 5-men EGT with Charging Rook + other vs defender where the Charging Rook would already beat the defender on its own; these should obviously be won as well.

A Charging Knight as defender behaves like a typical light piece: it loses against pairs of majors and (unlike) Bede/Fad pairs, and draws pairs of minors. Also for the Nutters, pairs of majors typically beat any single light piece. Apart from the WD the Charging Knight is the weakest major, though, and a pair of it has similar difficulties to beat a Rook, or its replacements Charging Rook and Dragon Horse. It does slightly better than the WD in this (as might be expected from the fact that it has one more move target), and has a cursed win against the Rook rather than a plain draw, etc.

The Nutters add new pairs of major + minor. These are interesting, because their ability to win depends on the possibility of the defender to choose which of the two pieces he will trade away. Charging Knight + Fibnif have similar difficulties here as Rook + Knight, against the Rook(-replacements) except Bede (which due to its color binding is apparently easy to dodge); the comparative weakness of Charging Knight compared to Rook is apparently compensated by the relative strength of the Fibnif that was already noticed before. Charging Rook + Fibnif does even better than Rook + FIDE minor, and beat almost anything, although its general wins against Rook or Charging Rook are partly cursed.

End-games with the Colonel are difficult to classify. Because of the extreme forwardness of this super-piece, the outcome will depend very much on where it is placed on the board. End-games where both players have a Colonel thus always contain a fair number of wins and losses, even if one would expect them to be draws. This even holds for the 4-men case Colonel vs Colonel: 15% of those are lost even when you have the move! (For comparison, for Queen vs Queen this is only 0.27%.) A Colonel beats most light pieces; it has mixed results against R, R4 and the charging Rook, while the Commoner (and thus the Dragon Horse) can hold a draw against it.

The Dragons

I also added the pieces from the Daring Dragons army: Commoner, vRsN (Dragonfly) and BW (Dragon Horse). This didn't really require any modification of the existing code for 4-fold symmetry, but to make a more accurate judgement on end-games containing more than one Dragonfly I put in some code to split the statistics in a 'like' and 'unlike' cases of the Dragonfly's special form of color-binding, and only report the result for the unlike pair here (as that is what you start with, and it is not a likely promotion choice).

The BW is quite strong, which should not be surprising, as its middle-game piece value is also slightly above that of a Rook. As a defender it can stand up to the Bede/Fad pairs in addition to pairs of other minors, probably because the Bede cannot easily sneak up on it from a diagonal, as it can against a Rook. (Note two FAD, which lack the distant diagonal attacks, can also not beat a Rook.) The BW is upward compatible with the Commoner, so in cases where a pair containing a Commoner already wins, replacing that Commoner with a BW should win even easier, and no EGT for these end-games were generated.

The Commoner (once under protection of its King) can keep a draw against a Queen and an Archbishop, because it cannot be approached by the enemy King. The Chancellor beats it, however. FairyGen cannot handle the ski-slide of the Wyvern yet.

End-games part 3: Super-pieces versus a pair

This is a very murky problem. I have generated the relevant 5-men EGT, but they seem very hard to interpret. Take for example Queen vs Bishop + Knight. This has 98.56% of all positions won when the Queen has the move (including 40.42% immediate King capture). The weak side is lost in 49.08% of the positions where it has the move, 28.44% of such positions are instant wins by King capture (so really illegal positions, that one could choose not to count). And 17.88% are wins by other means, which has to mean in this case gaining of the Queen and a subsequent mate with Bishop + Knight (obtained from generating the reverse EGT), or (rarely) a checkmate with the Queen still on the board. Almost all of these (98%) capture the Queen (or mate) on the first move, and none in more than 5 moves. These should not really be counted as Q vs B+N, they are tactically non-quiet positions in the process of converting to a simpler end-game. The remaining 4.61% of the positions with the weak side to move must be draws.

This looks as much as a general win as one could hope for. Nevertheless it is well known that B + N can make a 'fortress' that even resists the onslaught of an Amazon (Ka1, Bb2, Nd4). The resulting fortress draws are hidden in those 4.61% (which amounts to 8.5% after disrecarding the illegal and non-quiet positions). So in most cases the end-game in a quiet position (where chess engines evaluate) would be a win for the Queen, so it seems reasonable not to excessively discount it. (The factor 2 applied to all pawnless advantages would already do justice to the difficulty of winning this, as the 'raw' advantage is equivalent to a single minor, which after discounting translates to 1.5 Pawns, which is only marginally above the threshold for winning advantages.)

This makes it impossible to avoid the fortress, however. The problem with fortresses that are not recognized by the evaluation is that the engine continues to count itself rich for the almost indefinite duration the defender can maintain the fortress (until the 50-move rule puts an end to it, but that will be seen only after 100 ply, way beyond the horizon when you first enter the fortress). The alternative is to always discount end-games that contain a fortress draw heavily. That would be wrong in the majority of cases, but the won cases will eventually convert to another end-game (KQ-KB or KQ-KN), or checkmate outright. And once this gets within the horizon the score will be corrected. Basically this puts the 'burden of proof' for that an end-game with a fortress draw is a win on the winning side, even when it is the most likely case, because that case is easier to prove. E.g. 26.75% of all positions (=49% of the quiet ones) converts in 5 moves or less, and the search can presumably find that. This still leaves more cases where it is in error than just ignoring the fortress, though. In addition to such a 'passive' fortress there can also be draws due to perpetual checking. But these usually lead to repetitions quickly, so that the search has no difficulty recognizing those without any special discounting.

It is kind of hard to devise a satisfactory algorithm here without actually probing the EGT, or putting in dedicated code to recognize the fortress. The latter doesn't seem feasible for CwDA, where in most end-games we really have no idea at all whether there is a fortress or not, let alone how it looks. When embedding a single exotic piece in, say, a FIDE context, it does seem feasible to generate the Q vs 2 minors EGTs (6 of those, for all combinations of B, N and the exo-piece) in advance. Even an uncompressed 5-men EGT only takes 160MB, so with today's memory sizes a number of those can easily be kept in memory (possibly shared between several instances of the engine).

Fortunately in many cases of super-piece versus a pair of light pieces the discounting is not really important, because the 'raw' advantage is already pretty small to begin with. E.g. with Q vs 2R the difference is only 0.5 Pawn in favor of the Rooks, and for Q vs R+B it is only 1.25 in favor of the Queen. And the general factor 2 penalty for pawnlessness already would reduce that to 0.25 and 0.625, respectively. So it would always shy away of these end-games in favor of an advantage of a healthy Pawn, even when they are not listed as drawish. The drawishness discounting is only important for end-games that have a large raw advantage, possibly only super-piece vs pairs of the weakest minors B, N, WA, WD and Fibnif.

I will publish a table here when I have figured out how to best present the calculated statistics.

[Edit]

I made a useful addition to my EGT generator: when it is done generating the normal staticstic for a 2-vs-1 end-game, it declares all drawn positions in the successor 2-vs-0 and 1-vs-0 end-games a win, and then continues generating from there, effectively calculating whether King-baring can be forced (and in how many moves). This is a great help in investigating end-games like KQ.KBN, by generating the 'reverse' end-game KBN.KQ with King-baring victory. That makes it possible to recognize draws achieved by trading B or N for Q, which otherwise would show up as draws, indistinguishable from any fortress draws with all material, but now are reported as wins. This leads to the conclusion that almost all draws in KQ.KBN are due to shallow tactics that loses the Q against one or both minors: of the legal positions with the weak side to move only 0.14% are fortress draws. The known fortress is apparently very difficult to reach. This is in sharp contrast to Q vs two WD, which has 46.93% wins (38.12% converting within 3 moves), 28.5% forced losses of Q or K (the large majority in 1 move) , leaving 24.57% for fortress draws. Indeed the WD pair has a huge capacity for setting up fortresses: a mutually protecting pair can confine the enemy King on boards of any size, trapping it behind the file or rank they are on. You either gain one of the WD by checking/forking before they connect, or it will be a dead draw. Such end-games deserve heavy discounting, as the search (using check extension and capture search) will easily find the won or lost cases. Queen vs two WA has rather similar statistics, although I don't have a clue as to how the fortress looks there.

[Edit 2]

OK, I finally compiled a table, by combining info from the super-piece vs pair end-games themselves, the reverse end-games, and the reverse end-games under the baring rule. I extracted the info from the positions with the pair on move. This shouldn't really paint a different picture from when the super-piece was on move, except that in the latter case the large majority of positions (>80%) captures a hanging piece on the first move, altering the material balance from the intended one, so that the interesting results are much diluted there. Of course when such a capture does not happen, the other player gets to move, with the statistics presented here.

I only considered end-games where the advantage based on piece values would be large enough to reasonably suspect it could be a win even in the absence of Pawns.

The table list 6 numbers, all percentages:
1) win by shallow tactics (conversion in first 3 moves)
2) win by deep tactics (conversion in move 4-6)
3) lengthy wins
4) fortress draws
5) forced loss of super-piece (or checkmate)
6) immediate loss through King capture

           Q                  C                   A                   Colonel
NN  26-4-13-11-21-25  21-10-25-.1-19-25     9- 5- 2-40-19-25     16-9-14-15-20-25
BN  21-7-21-.1-23-28  18-10-21- 1-22-28     6- 2-15(~8)-27-22-28 10-7- 8-23-23-28
BB  15-7-18- 1-24-35  14- 5-20(~6)-.1-26-35 3-.2- 0-38-24-35      7-3- 4-25-26-35
XX  31-4- 5-15-19-26  26- 9-14- 5-20-26    10- 8- 3-32-20-26     16-9- 9-20-21-26
FX  21-5- 5-19-21-29  18- 6- 4-20-22-29     7- 4- 2-36-22-29
FF  22-7- 1-14-23-34  29- 5- 1-15-26-34     6- 2- 1- 2-54-34
WW  27-5- 2-18-20-28  23-11- 3-14-21-28    12- 9- 2-28-21-28     15-9- 4-11-32-28
II  30-5- 4-16-20-26  23- 9- 5-17-20-26     9- 8- 5-32-20-26     16-7- 3-28-21-26
YY  18-4- 1-13-27-37  11- 8- 3-15-26-37     6- 3- 1-19-34-37      8-5- 1- 7-42-37
KK                    15- 4- 2-30-20-28                           6-5- 2-13-45-28

The relevant statistics for classifying the end-game are highlighted in bold. (Note '.1' means 0.1!) These are the lengthy (i.e. non-tactical) wins versus the fortress draws. The other cases resolve fast enough to simpler end-games for the engine to base the score on static evaluations outside this end-game. A smart evaluation strategy for these end-games could be to initially classify them as a (pawnless) win, but for those that are mainly fortress draws increase the discount factor to a drawish value when the 50-move counter goes up, reflecting the observation that when you cannot make a winning exit from the end-game in the first 3 moves, your chances for a win will be pretty bleak. When looking ahead from end-games with a single Pawn in jeopardy (e.g. Q+P vs F+2X) they should be treated as drawish, as after sacrifycing X or F for P the remaining F and/or X will typically be tactically safe (or they would have been picked off before).

The Archbishop vs two Fads sticks out because in 54% of the cases the Fads can force capture of the Archbishop. (More typically the chances to force super-piece capture are only 20-25%.) One should not conclude from this that the game is mostly won for the Fads, though. The Archbishop is only rarely captured without compensation, and even trading it for a single Fad leaves no mating potential, and thus causes an instant draw. Only 7.46% are genuine losses (Archbishop lost without compensation, or an immediate checkmate). The Fads do dominate the game, however. Where in the other end-games gaining the super-piece in almost all cases happens on the first or second move, here that happens in only 10% of the cases, and takes on average 25 moves otherwise (worst case even 57 moves). The Fads will just methodically tighten the mating net around the enemy King, keeping their own King safe from perpetual check, and at some point the mate can only be averted by sacrificing the Archbishop.

In two cases (A vs B+N, C vs B-pair) a large fraction of the lengthy wins was cursed, and the table mentions the number of cursed wins in parentheses. We see the Archbishop doesn't perform very well; the only case where it has a good number of wins is against B+N (which is the weakest defending combination). A Queen beats the FIDE minors; even the pair of Knights, which still puts up a fight, manages to reach a fortress in less than half the cases, after disregarding all initial tactics. It doesn't manage to beat any pair from the other armies, though. The Chancellor does better: it also beats two WA, and thoroughly crushes the pair of Knights, but has some difficulty with the B-pair because the wins take too long.

[Edit 15-4-2019]

The Colonel is also weak, and only has some success against a pair of Knights. But because it is quite poor in delivering perpetual check, it actually runs a large risk of losing against pairs of majors, where sacrifycing it for one leaves a lost 3-men ending. Even against the weak ones, where the piece values suggest it has an advantage (Woody Rook, Commoner and Dragonfly). The large part of the forced conversions against these pairs are indeed mostly losing conversions, and especially for the Commoners most of these are lengthy.

End-games part 2: Super-pieces

The super-pieces are in general so much stronger than the light pieces, that they will almost always beat the latter in a 1-to-1 situation. Only the strongest light piece (Rook) manages to hold a draw against an Archbishop, while its result against a Chancellor is a bit unclear. (The Chancellor can win if its King is already advanced so much that the Rook cannot cut it off at a safe distance from its own King, so that the Chancellor can attack it with its N move while checking with its R move, which is the case in a fair fraction of all possible positions.) The general win of Archbishop vs HFD is mostly cursed.

More interesting are the 5-men end-games where both players have a super-piece, (which in itself would be a general draw in all cases), to see whether an extra light piece can tip the balance. Unnatural pairs are not so unlikely here, as promotiong to the super-piece the opponent starts with should be reasonably common. To be complete I also generated EGT for the 'impossible pairs', where the light piece did not belong to the army of either super piece, because there were not that many, and some of those can occur in Seirawan Chess.

It is a bit tricky to interpret the statistics of super-piece end-games; their capacity for initial tactics that would alter the intended material balance is enormous. And even in genrally won positions there will be many draws due to perpetual checking. If I had a Xiangqi-style EGT generator it would detect perpetual checking and count it as a loss (so that I could judge its importance by comparing with the stats of normal generation), but alas... In theory it would also be possible to count draws through forced conversion to a non-lost end-game, e.g. by forking King + Chancellor by an Archbishop (possibly after some checks) and trade (or gain) it, by making that the 'winning' goal for the defending side in the table with all material present (as this would count as tactically non-quiet positions). But my generator doesn't do that either. How much such tactics is possible depends very much on the blind spots pieces have w.r.t. attacks of the opponent pieces, so it is hard to say what is 'normal' for a general draw or a general win, and even more difficult to recognize end-games that are part win, part draw.

I compiled the following table, which should be read as that the piece in the upper margin should team up with the first piece mentioned in the left margin, to beat the second piece mentioned there.

C = RN
A = BN

?  = probably only partially won

       WA FvN  WD  N   B  FAD  BD vRsN K   N' HFD  R4  R'  R
none   =   =   +   =   =   =   =   +?  +   +   +   +   +   +

Q-A    +   +   +   +   +   +   +               +   +       +
C-A    +   +   +   +   +   +   +               +   +       +
Q-C    =   ?   +   =   +   +   +               +   +       +
Q-Q    =   =   +   =   =   =   =   ~?  +   +   +   +   +   +
C-C    =   ~   +   =   =   +   +   ?   +   +   +   +   +   +
A-A    =   =   +   =   =   =   =   +   +   +   +   +   +   +
C-Q    =   =   +   =   =   =   ?               +   +       +
A-C    =   =   ~   =   =   =   =               +   +       +
A-Q    =   =   =   =   =   =   =               +   +       +

We can see that the super-pieces are not equally strong, but that mating potential of the extra piece in general is sufficient to preserve the win no matter which super-pieces are added, even if the extra piece teams up with the weaker one. The exception is the WD, which is rather minimal for a piece with mating potential. This is not able to overcome the Archbishop vs Queen disadvantage, while with Archbishop against Chancellor the win only seems partial, and then most of it is spoiled by the 50-move rule.

The minors show a more varied behavior. With equal super-pieces, or teaming up with the weaker one, they tend to preserve the draw. It is apparently too difficult to avoid trading of your super-piece against an equal or superior one. The exception occurs with Chancellors. These seem unusually good in cooperating with other pieces (which might have to do with their well-known unusual adeptness at perpetual checking): the pure advantage of Bede or Fad secures a win, and even together with Fibnif it makes a remarkable attempt (partial win, if it were not almost entirely cursed; worst case takes 154 moves!) Together with Bede (the strongest minor) it even gets a partial win against the (stronger) Queen. Together with a better super-piece the Bishop, Bede and Fad are good for a win, and the Knight, WA and Fibnif are if the weaker super-piece is the Archbishop.

Indeed, great work!...

Wow.  Great work!  Very interesting.

End-games: light pieces

The table below gives an overview of some 5-men CwDA end-games, based on the statistics of generated End-Game Tables. I don't have a generator that can handle pieces with only 2-fold symmetry, but a special built of FairyGen can handle 4-fold symmetry, so I did include the Fibnif as only Nutters piece. CwDA armies consist of a super-piece worth 2.5-3 typical minors (such as Knights), and 3 pairs of 'light' pieces worth 1-1.5 minors. In FIDE the Rooks really stand out amongst the latter; in the other armies the pieces are closer in value, only 1 piece being of Knight strength, the other two lying somewhere in between Knight and Rook.

These pieces can be divided into majors and minors, depending on whether they are able to force checkmate onto a bare King. All light pieces of the Clobberers are minors, all of the light Rookies are majors. The Nutters have one minor, FIDE has two. Of all these minors, the Knight is the only one that cannot checkmate as a pair; for the Clobberers the heterogenous pair Bede + Fad cannot checkmate if they are on the same square shade. All other pairs of minors from the same army can force checkmate. Even all 'unnatural' pairs (which can in theory be obtained by promotion) can force checkmate, provided that pairs of color-bound pieces (Bede, Fad, Bishop) are on unlike shades.

The difference in strength between the light pieces is usually not enough to force a win in a 1-vs-1 situation. Somewhat exceptional are Rook vs WA (which would be a general win if it were not for the 50-move rule; as it is the win is cursed) and Rook vs Fibnif (where the result is unclear; a Fibnif is easily confined by a Rook, and in positions where it is separated from its King it can probably be chased to doom). Of course only the major pieces can hope for a win, in these situations.

Because of their closeness in value, I treated the light pieces as a single group, and generated all EGT of a natural pair versus a single one. Each army has 6 natural pairs, but for the Nutters I could only handle the pair of Fibnifs, so 19 pairs in total. I did not bother with a pair of Knights, as these cannot even win without opposition. I also did not bother with a pair of Rooks, as a pair of R4 could already beat any opponent. Each of the 17 remaining pairs was pitted against the 10 light piecs, 170 combinations in total. This gave the following result.

R = Rook
B = Bishop
N = kNight
D = BD      (beDe)
F = FAD     (Fad)
X = WA      (phoeniX)
S = R4      (Short rook)
H = HFD     (Half duck)
W = WD      (Woody rook)
N'= fhNbFbW (charging kNight)
R'= fsRbFbW (charging Rook)
I = FvN     (fIbnif)
K = non-royal King
Y = vRsN    (dragonflY)
O = BW      (dragon HOrse)

+  = general win
=  = general draw
~  = cursed general win
~? = half-cursed general win
+? = mostly won, but lots of fortress draws
?  = mixed win/draw
?~ = mixed, and about half the wins cursed
*  = already won without the second piece

       X   I   W   N   B   F   D   H   S   R   K   Y   O   N'  R'
XX     =   =   =   =   =   =   =   =   =   =   =   =   =   =   =
BN     =   =   =   =   =   =   =   =   =   =   =   =   =   =   =
FX     =   =   =   ~? ~/=  =   =   =   =   =   =   =   =   =   =
BB     +   =   =   ~?  =   =   =   =   =   =   =   ~   =   =   =
II     +   ~   =   +   =   =   =   =   =   =   =   =   =   =   =
DX     =   ~   =   +  +/= ~/=  =   =   =   =   =   =   =   =   =
YY     +   +   +   +   +   +   +?  +   =   =   +   =   =   +   =
WW     +   +   +   +   +   +   +   +   +   =   +   +   ?   +   ?
N'N'   +   +   +   +   +   +   +   +   +   ~?  +   +   ~?  +   +
N'I    +   +   +   +   +   +   +   ~   ~   =   +   +   =   +   =
RN     +   +   +   +   +   +   +   ~?  ~   =   +   +   ~   +   =
RB     +   +   +   +   +  +/+ +/+  ~   +   =   +   +   =   +   =
FF     +   +   +   +   +   +   +   +   +   =   ?   +   =   +   =
R'I    *   *   +   *   *   *   +   +   +   ~   +   +   +   +   ~? 
KY     +   +   +   +   +   +   +   +   +   =   +?  +?  ?   +   ?~
DF     +   +   +   +   +   +   +   +   +   +   +   +   =   +   ?
DD     +   +   +   +   +   +   +   +   +   +   +   +   =   +   +
KK     +   +   +   +   +   +   +   +   +   +   +   +   +   +   ?
HW     +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
SW     +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
HH     +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
SH     +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
SS     +   +   +   +   +   +   +   +   +   +   +   +   +   +   +
R'N'   *   *   +   *   *   *   +   +   +   +   +   +   +   +   +
R'R'   *   *   +   *   *   *   +   +   +   +   +   +   +   +   +
OY                                     +   +   +   +   +       +
OK                                     +               +       +

We see that the Bede and Fad, despite their lack of mating potential as an individual, form quite strong pairs. This is probably because they are able to drive an unprotected King to checkmate with checks, in a way reminiscent of the 'hand-over-hand' checking of a pair of Rooks. This makes it hard even for a Rook to harrass the pieces, threatening to trade and destroy the mating potential, which is the usual way in which pairs of minors fail to win. So in first approximation a pair wins if both members have mating potential (so that trading any of them will not rescue the defender), or if they are Bede/Fad pairs of unlike color, while other pairs of minors draw against any opposition.

The case major + minor only occurred in FIDE here, (R+B and R+N), as Clobberers have no majors, Rookies have no minors, and for Nutters I could not handle the majors. Because the major is relatively strong in FIDE, only a defending Rook can truly measure up to it; any other defender is so much weaker that adding even a 'standard minor' tips the balance. Against R4 or HFD, however, it takes too long to force the win, and the latter is cursed in almost all, or about half the cases. For Rook + Bishop vs Bede or Fad it doesn't matter if the defender is on like or unlike shade w.r.t. the Bishop.

Of the pairs of minors Bede + WA stands out: it in general beats a Knight, and a Bishop when it is on the same shade as the Bede. The win they in general have against a Fad on the Bede shade, or a Fibnif, is almost always cursed. They cannot beat a WA (which is probably the weakest defender in such end-games), but beating an equal piece is always more difficult, as you cannot attack it without offering it an opportunity to trade. The Bishop pair and a pair of Fibnifs (like a lone Rook) can beat the WA. The pair of Fibnifs is surprisingly strong: it can also beat a Knight. For the Bishop pair it takes so long to beat a Knight that the win is cursed more often than not. A win of two Fibnifs against one is very cursed (it takes on average 90 moves), but in view of the remark above it is amazing that it can force such a win at all. That the Fad is just a bit weaker than the Bede is also demonstrated by that the wins Bede + WA have against Bishop and Knight turn into cursed wins when the Bede is replaced by a Fad.

[Edit 14-5-2019] The Nutters and Dragons pieces were added to the table.

A pair of WA is a general win. The rule of tumb is that one of the minors must be able to move from c1 to a1 (or their symmetry equivalents) in three moves (more precisely, for divergent or asymmetric pieces an uncapture, a move and a capture). A WA can do that (c1-c2-c3-a1), and can thus inflict a corner mate (moving c2-c3) with its King on b3 after the other minor has driven the bare King with check from b1 to a1. Furthermore, edge mates can be forced when one minor can 'fork' a1 and c1 at the the same time, and the other minor can move from c1 to b1 in three moves. But that doesn't work if the forking piece has to be on b3 (as a Knight would have to be), where it would collide with the King.

As to the level of ambition: perhaps I should start indeed a bit more simple. The general scheme is to discount a pawnless advantage by a factor 2 even if it still is a win (except for known easy wins such as KQK and KRK), to properly reflect the relative difficulty of the win. But known general draws should be discounted much more, e.g. by a factor 8 if there still is some hope, or even 16 or infinite if it is a truly dead draw. (A factor 16 would even shrink the KNNK advantage to much less than a Pawn, and when that would still make it the best option the alternatives will almost certainly offer no hope for a win either.)

That leaves room for discounting end-games with a single Pawn by 4 times smaller factor, when the opponent can afford to sac a piece for that Pawn to leave the pawnless general draw. Such a sac typically increases the advantage from +1 to +3, but the relative factor 4 makes the latter +0.75, so the leading side would be biased against allowing the sac. The remaining discount factor (2 or 4) would still discourage converting to such end-games, e.g. by trading Pawns in KBNPPKBNP.

This scheme would need a table that specifies which non-Pawn material should be considered a dead or a general draw. The simplest version of this would just list single minors vs nothing: KBK and KNK in FIDE. But having some 4-men endings in there (like non-mating pairs of minors, such as KNNK, or 'exchange'-type advantages like KRKN) would not be too demanding either. These entries would already extend their influence to KNNPKB and KRPKNN, through the sac-rule. The really tedious part would be to add 5-men end-games such as the 'minor ahead' situations KBNKN, KRBKR, KQBKQ,... But I already generated a lot of those tables; I will summarize those results in another comment.

It could also be good to discount cases like unlike Bishops with a difference of up to 2 Pawns by a factor 2, but at the moment I have no idea how to generalize that. (E.g. it seems that end-games with unlike Ferzes are not particularly drawish.)

Hard to say; perhaps 2 weeks if I would give it priority.

Ok, thanks.  I was just trying to get an idea, not asking to make it priority.  It'll probably take me a couple of weeks to get Quadrox ready.  I'm going to start with FIDEs vs. Clobberers because that will be easiest.  No asymetric pieces or range-limited sliders.

I'm glad you mentioned endgames - I was going to bring that up.  At a minimum, I need to determine under which conditions the game should be terminated immediately because there isn't enough material for checkmate to be possible.  (E.g., any number of BDs and FADs vs. a lone king if they are all on the same color.)  But, yeah, like you I also want to identify those piece combinations where the game should not be terminated because mate is theoretically possible if the opponent walks into the corner but the evaluation function should return zero (e.g., king + fibnif vs. lone king.)  Your Javascript checkmating app is really awesome and answers the question for single pieces.  I'm glad you're going to work on determining the answer for multiple pieces.  Can a king plus two WAs force checkmate?  I doubt it but I don't really know and I have no experience with endgame database generation.

It sounds like you're being really ambitious though.  Recognizing KBBPKBN as drawish is really advanced.  Throw in all the fairy pieces from cwda and the number of permutations is out of sight...

Greg Strong:

Any guess when you think you'll have your new cwda engine ready for testing?

Hard to say; perhaps 2 weeks if I would give it priority. But the Tenjiku Shogi implementation in Jocly is still not finished, and already 2 months (of 4) have elapsed on its clock in the yearly Modern Tenjiku correspondence championship in which it is supposed to participate...

Main issue is that I want it to recognize drawishness through lack of mating potential, which would include strongly discounting the score in end-games like KBBPKBN, because of the almost undodgeable N-for-P sac leaving a KBBKB known general draw. This requires the knowledge of which Pawnless 5-men CwDA endings are general draws, which I must first aquire by generating EGT for those (with FairyGen). And there are rather many of those, especially if I want to keep open the possibility to test individual pieces out of their own context (i.e. dropping the requirement that the two pieces fighting on one side must belong to the same army, so that I can test, say, WD+R vs R to see if the (winning) advantage of a WD is preserved on adding equal pieces on each side). An additional complication is that the standard version of FairyGen counts on 8-fold symmetry, although I once made a compile that can handle 4-fold symmetric pieces. But even that would not be able to handle the Nutters pieces other than Fibnif.

Otherwise there are only minor issues; KingSlayer supported only 6 piece types (1-6, code 0 being reserved for empty squares), and I already added some initialization code to set their move tables to that of the various armies. I still want to allow use of code 7 as an extra piece type, which requires a small code change because originally I used the 7th entry in the array that counts the number of pieces that is present of each type to hold the 'game phase' (minors + 2*Rooks + Queens). So I must move that to a separate array. And I still have to fix a-side castling for the Clobberers.

Neat!

Checkmating with the Dragon fly

Play with the Wyvern (The checkmating applet doesn't seem to like the jumping sideways rook component, putting the black king in check by that move.)

The Daring Dragons

I designed a new army, which in tests with Pair-o-Max scores about equal against FIDE. I named it the Daring Dragons.

Interesting feature that sets it apart from other armies is a piece with an unusual (meta-)color binding, the Dragon Fly: this is bound to even or odd board files, along which it moves like a Rook. It can switch between files through a sideway Knight jump. (It is in fact half a Chancellor.) It is worth slightly less than a Bishop, and can often force checkmate on a bare King. The other light pieces is the Man / Commoner, but to facilitate its development (which would otherwise heavily compete with that of the Dragon Fly), it has some additional initial non-capture Knight jumps. It is called a Dragoon. (Dragoons are mounted infantry, using horses for mobility, but fighting on foot.) The Rook replacement is the Dragon Horse known from Shogi (moves as Bishop or one step orthogonally), worth slightly more than a Rook.

The super-piece (called Wyvern) is a somewhat weird construct; first I wanted it to be a Centaur (Knight-Man compound), but then the army proved too weak. Then I replaced the wide Knight moves of the Centaur by a sideway Rook slide, to also have the latter in the game. This makes it a compound of a Man and a 90-degree rotated Dragon Fly. But this was not really stronger than a Centaur; with either the army scored only 40% with black. A sideway Rook slide should be worth more than four Knight moves, but the Centaur already covered the first step of it, so it did not add enough. I also did not like its low speed in the vertical directions, which was unworthy of a super-piece. After some experimenting, a compound of a rotated Dragon Fly and a Bishop proved a little too strong (60% against FIDE), although not out of line with what the other CwDA armies do. A suitable way to weaken it to exactly match FIDE was to replace the sR slide by a ski-slide, skipping the first square on the ray (jumping any occupant if needed).

Ski-sliders are interesting anyway: on a near-empty board they are obviously inferior to the corresponding ordinary slider, as they lack the moves to the adjacent square. That the more distant moves cannot be blocked on that square is of no import if there is nothing around to block them. But on a crowded board, where slides almost always are blocked before they hit the board edge, the ski-slider will have the same number of moves as the normal slider, each target just being moved outward one step. Which should make them nearly equivalent. So ski-slider strength will depend in a different way on game phase as the other pieces, relatively decreasing towards the end-game.

Hi, H.G.  It's good to hear from you and to hear that you are working on another engine to help test these things!  I got distracted on other things and never got around to following up.  I have far too many different projects that attract my attention - usually chess variant stuff, but sometimes other things as well.  I found this programming language for writing interactive fiction (think Zork) where source code reads like English called Inform7.  I would not have thought it possible for a real programming language to be a subset of English.  Wild stuff.  But yeah, anyway, I get sidetracked a lot :)

First, I did complete the FIDEs vs. Nutters test with the FIDEs given added incentive to move forward through the PST.  This helped a tiny bit, but not much at all:

Nutty Knights: 261
Fabulous FIDEs: 84
draw: 55

My next thought is to reduce the value of the knight and bishop when facing off against the Nutters.  This will give the FIDEs a strong desire to trade off and the Nutters will have to limit their options to prevent that.  Once the minor pieces are traded off I think the FIDEs are fine.  I don't believe a charging rook is better than a normal one, although a colonel may be a little better than a queen.

I have recently switched back to trying to get the next version of ChessV out.  I have several new features that are mostly done that just need to be closed out.  (Of course, I don't always finish a feature before starting on the next ...)  The most siginificant of these is that I have added a stand-alone ChessV CECP engine so it can be run without the GUI.  This code is all written but almost completely untested.  I admit I've been procrastinating on that.  In the whole scope of this project, there is nothing that is less appealing to me than trying to plan/code/debug for inter-process communication.  The other side of the coin - ChessV's ability to host other XBoard engines is not 100% bug-free either, although it is certainly good enough to be usable.

The material hash is something else I've added but am not making much use of yet.  It is implemented as you describe, and will handle binding of any kind such as your even/odd file example.  I think it was here I described the recursive algorithm I used to find all the different 'slices' of the board for any given piece.  (I'm calling them slices rather than colors because colors becomes confusing when different pieces have different bindings - the knight in Alice Chess being a wacky example.)  It will be interesting to see what scientific testing determines colorbinding bonuses/penalties should be for multiple color-bound pieces.  Currently, ChessV starts discounting the value of pieces heavily starting with the second piece bound to a slice if there are no pieces on a complimentary slice.

Regarding enabling CwDA for inter-engine play, yes, I am definitely interested in figuring out how we can do this.  I am certainly of the opinion that both our GUIs and all our engines should be as inter-operable as possible.  I will post some thoughts about this shortly.  (I'll start a new thread for it.)

@Greg

Any progress on this? I am contemplating to also return to piece-value measurements. Because I want to measure the more subtle effects, such as mating potential and pair bonuses, this will require a less course approach than Fairy-Max. I have started to extend the capabilities of my engine KingSlayer (originally released as 'Simple', until I was told that name was already taken), which I wrote a few years ago as a demo source code for orthodox Chess somewhat more advanced than TSCP, to also support fairy pieces. And in particular CwdA. So I changed the move generator to support limited-rage sliding/riding on a per-move basis. (For Chess it was done on a per-piece-type basis, and the range could only be 1 or infinite.)

As that engine only supports 6 piece types per side (which, with a little bit of work, could be expanded to 7), I implemented this by initializing the tables with piece properties it uses during play from a larger table that contains descriptions of all supported piece types. (So far the 16 piece types of the 4 classical CwdA armies.) For a particular game it then just picks up to 4 of these in addition to the always participating P and K. Unlike Fairy-Max, this engine has a dedicated check test (rather than just trying a null move and wait for a King capture), and this had to be extended too in order to handle the new moves. Basically it works by having a 15x15 'board' indexed by the relative distance, where for each step a bitmap indicates which piece type in principle could make such a step, where for sliding moves a contact threat is distinguised from a distant one (to easily see if you need to test for blocking). By making use of the fact that some pieces are compounds of others (like Q=R+B), and decomposig some pieces into 'primitives' to make even better use of that, the number of different primitives needed to support CwdA was 13, too large for the byte originally used for this purpose, but less than half a 32-bit integer, so that I can now even use separate bits for white and black attacks, eliminating the need to test the piece for being an enemy by other means. This type of check test would become more cumbersome with hoppers (where you don't only have direct and discovered checks, but also have to deal with 'activation' by interposition), and very awkward in the presence of bent sliders (like the Gryphon). So this engine will probably never support those kinds of moves. Divergent pieces would still be a realistic possibility, though.

Unlike Fairy-Max this engine does have an advanced Pawn-structure evaluation, (e.g. passer recognition), which is directly usable in CwdA, as that uses the same Pawns. It did keep track of the number of pieces of each type that are still present, and used this to award a Bishop pair bonus (if there were two), or discount the static evaluation score when mating potential gets into jeopary for lack of Pawns (i.e. with 1 Pawn or less). This will have to be substantially refined, though, as with multiple color-bound types cross bonuses are to be expected, and you cannot conclude from the piece counts alone whether you have a pair or not. Also drawish cases similar to 'unlike Bishops' cannot be recognized this way, which was already a weakness in regular Chess. So I plan to add a 'material hash', which uses a hash key that depends on the present material, but counts color-bound pieces of the same type but on different square shades as different. (This can be done through a Zobrist-like hashing scheme that doesn't assign a different key to a piece type for each board square, but just one for each 'meta-color' relevant for that type.) Which piece combinations will have mating potential will now depend on the army, and will thus require a more complex analysis, but if the results of that analysis are kept in a hash table, this will not impact engine speed.

BTW, other types of (meta-)color binding can be interesting as well. E.g. odd/even file binding, such as for vRsD, which does have substantial mating potential. (Although a fortress draw is possible when the bare King cannot be cut off from the safe edge. A vRsDD would even be better in preventing that.)

You mentioned lack of standardization presenting a problem for having XBoard engines playing CwdA in ChessV. What would be needed here? Now that I am making KingSlayer into a CwdA engine, it might be good to have a closer look at the specific problems, and try to find ways to remove those. At the moment I have KingSlayer report in the CECP variants feature that it supports variant 'fairy', and gave it engine-defined combo options 'White Army:" and "Black Army:" that can be used to select the flavors FIDE, Clobberers, Rookies or Nutters, and will determine what variant fairy means. But in addition to that I could allow setting of the default value of those options through arguments in the engine command (so that you would never have to bother setting the option).

I have a bit of discomfort as the game did not had any lame leapers before but that borders on nothing. I'm more concerned how the change affect the balance against the two other armies. As this seems to me that will lead to a wave of interconnected changes that are probably not easy to pull through. Some sort of logical system of equations needs maintaining and I honestly doubt such and endevour is even doable, little to say about feasible. This because you don't have many options for tunning while keeping the initial flavour on

This is a valid concern, but I'm hoping this does not become a problem.  And a tiny bit of rock-paper-scisors effect is acceptable so long as things are balanced against the FIDEs.  Obviously, the FIDEs are the one army that cannot be modified.  For an example of a board game that has significant R-P-S effect but is still an awesome game, see tournament Star Fleet Battles.  I should say this as I was probably not clear - I am NOT proposing making this change until testing of all combinations is complete, along with some testing of evaluation terms changes...  This is just what I'm leaning towards given what we know so far.

It is a pity that test takes so long (a common problem in computer chess...)

Indeed it is, but I can scale up quite a bit.  I actually have quite a few i5 and i7 PCs that can be pressed into service to do testing (6 or 7 of them.)  The longest part, which is largely manual, is calculating out all the starting positions so I can feel very confident that my tests aren't playing the same games over and over.  But when this is accomplished I can scale up testing quickly.  I have just finished generating 20 positions of FF vs RR and am just starting on those with the colors reversed.

I suppose that the new ChessV is stronger than Fairy-Max? Have you ever measured by how much?

My current builds are definitely stronger than Fairy-Max, at least at the various 10x8 variants, but I have not done formal measurements.  I intend to test that with my new "batch mode" capability also, but I've been focused on CwDA tests instead :)  ChessV will control XBoard protocol engines for many games, but CwDA is not one of them because it would require more standards than presently exist.  I should also mention that Fairy-Max is an absolute speed demon, in terms of nodes-per-second, compared to ChessV at approximately 4x the nodes.  ChessV's strength comes from smarter search (using ideas stolen from Stockfish and other GPL engines - I take absolutely no credit for this) and better evaluation.

What TC are you using for these tests?

The 400-game sets use different time controls as one way to get more varied results.  They also modify the new Variation setting from None (which is completely deterministic) to Small (for most games) to Medium (for a few games.)  The fastest time controls I'm using are 25 sec + 2 sec/move.  The longest are 5 minutes + 1 sec/move.  Typically a 400-game set on one computer takes about 2 days.  I will post a new (unofficial) version here shortly along with all my opening positions and batch mode control files so everyone can see exactly what I'm doing and run tests of their own.

Regarding the NN vs FF test with the FIDEs given more encouragement to advance through the PSTs, the test is half done.  The 200 games where the NNs are white and the FFs are black are done.  The Nutters won 136, the FIDEs won 36, with 28 draws.  So it doesn't look like this is making the situation any better although these are all games where the nutters have the first move.  Tomorrow we should know the final results.

@HG&@Greg

We have discussed the matter of possible rock-paper-scizors effects with negative conclusions so maybe my idea involving musketeer chess gating was an overreaction, but maybe may be kept in the back of the mind if such problems arise. Good luck everybody :)!

It is clear that the change BD -> BnD should weaken the Clobberers against any opponent, which would be undesirable against opponents that already have the upper hand. But usually such opponents would also be stronger than FIDE, and would also have to be weakened. My earlier testing with Fairy-Max suggested that the performance of armies was reasonably 'transitive', in the sense that when A > B, and B > C, then A > C by an amount approximately equal to the sum of the first two. The only anomaly was that the Nutters under-performed against the Clobberers. I conjectured that this could again be a strategic issue, namely that the more forward-directed strategy and slow backwardness of the Nutters backfires when the army has pairs of pieces (or single pieces) that can easily checkmate a King.

It is a pity that test takes so long (a common problem in computer chess...). I suppose that the new ChessV is stronger than Fairy-Max? Have you ever measured by how much? What TC are you using for these tests? Have you tried how far you can push that, without significantly affecting the result? Large depth is only needed to bring the eventual tactical punishment of strategically bad moves within the horizon, so a more advanced evaluation (e.g. for Pawn structure and King Safety) should allow faster games without play becoming so unrealistic that it is no longer a representative sampling of the pieces their tactical abilities. People are nowadays tuning their engine's evaluation at ~0.25 sec/move (e.g. 10 sec + 0.1 sec/move). It would surely save a lot of time if that would work for piece-strength measurements too.

The danger is that playing at a lower level reduces all 'excess scores', even though the ratio of these scores keep constant (so that you get the same value in terms of centi-Pawn when you divide them by the Pawn-odds score). For a twice-lower Pawn-odds score you would need 4 times as many games to get the same resolution in centi-Pawns. So I suppose there will be an optimum there. Too high a quality of play is also not good. btw; you want the typical evaluation lost per move compared to prefect play to be so large that over the duration of a game it typically accumulates to a range wider than the draw interval (say [-150cP, +150cP]), so that small departures from equality in the initial imbalance already significantly sample the won/lost range.

@Greg,

First, I'm on the tip of my toes about your next trial with conditions adapted to HG's observation.

"Again, I don't think changing BD to BnD changes the flavor or removes any spice.  Do you?  "

I have a bit of discomfort as the game did not had any lame leapers before but that borders on nothing. I'm more concerned how the change affect the balance against the two other armies. As this seems to me that will lead to a wave of interconnected changes that are probably not easy to pull through. Some sort of logical system of equations needs maintaining and I honestly doubt such and endevour is even doable, little to say about feasible. This because you don't have many options for tunning while keeping the initial flavour on

But I'm very much for any CWDA game. It is just that a sequel to Betza's game should borrow off his elements otherwise it is another chess with different armies game. A better one quite likelly.

"On this we must disagree[about the game not needing rescuing].  Sure, it is playable.  It is one of the most popular games on Game Courier so certainly people can play it and have fun.  But if the armies are way out of balance, as it has become clear that they are, then it fails at its stated goal.  If the game were played and studied even more as time goes on, people would learn exactly how to exploit the unbalance and the game would no longer be playable. "

The game is good enough at my level. It is probably good enough at any current human level (although this could be a stretch) but there is always the quest for even better (I am an engineer after all). And the endeavor of making another game sequel or not is great. I'd venture the idea we may need to make a distinction about it, but if we don't make it other future people will surely do, if it's the case, so much bothering could not be needed here either.

What I was actually insisting about it was that maybe my musketeer technique is and easier goal to achieve without sacrificing any design principles(besides making the board more crowded which is something I actually like, even if 36 pieces on an 8x8 tends to be too much even for me). But we can easily go on our merry way if this back and forth can't advance in an useful way and maybe History will decide. Or not, as currently chess variants don't seem to catch on! The space of possible chess variants is so vast that there is more than enough room for all of us. I remember you actually agreeing to help, so that is cool. So it is a math debate actually: the way I like it :)!

It occurred to me that the Nutters are unique amongst Betza's armies in their forward-backward asymmetry. I wonder if this could have an unexpected effect on the outcome of self-play games of engines with an evaluation that is not highly tuned. In a random mover Nutter pieces would tend to diffuse forward. Perhaps this makes the nutters a bit more aggressive than the others, which would benefit them if the others are not aggressive enough. Perhaps the others would benefit from a piece-square table with a larger forward-gradient, while the Nutters automatically play like they have one.

Good observations as always.  ChessV has a more sophisticated evaluation than FairyMax but it is certainly not "highly tuned."  I can definitely re-run the FF vs. NN test with the forwardness component of the FIDE's PST increased.  I'll kick that off and see how much it affects the results.  The test will take a few days to complete...

And balance is the primary goal but to me the flavor is what bring the spice :)!

Again, I don't think changing BD to BnD changes the flavor or removes any spice.  Do you?  You seem clearly opposed to this change, but I do not understand why.

I don't say CWDA needs rescuing it is a good game.

On this we must disagree.  Sure, it is playable.  It is one of the most popular games on Game Courier so certainly people can play it and have fun.  But if the armies are way out of balance, as it has become clear that they are, then it fails at its stated goal.  If the game were played and studied even more as time goes on, people would learn exactly how to exploit the unbalance and the game would no longer be playable.

@HG,

In CWDA army tunning is most definetly a thing for any AI, epeacially in the context of flavor I was discussing with Greg earlier. In machine learning that should come rather easy but unfortuneatly I have not god that far. In the end the army is just another variable (be it some multidimensional properties). What I mean is that it should not be more difficult than any other desing of such algorithms.

@Greg,

We can very much leave Betza's game as is and invent a improved version ourselves. There is nothing wrong with that. And balance is the primary goal but to me the flavor is what bring the spice :)!

" If you want to make such a game, I would encourage it and I would try to help if you wanted, but I don't see this as a valid approach to rescuing CwDA. "

I don't say CWDA needs rescuing it is a good game. But I also see it as a good lesson, we could use.  The musketeer chess approach is meant to offer a way to balance the imbalances in a specific way to each match, because yes it is about armies and not the individual pieces but there is that old libertarian saying that society is made out of individuals which I think goes well here. A pair of minors or a rooklike and a bishoplike piece would at least open more doors which is hardly done otherwise, as far as I can see!

It occurred to me that the Nutters are unique amongst Betza's armies in their forward-backward asymmetry. I wonder if this could have an unexpected effect on the outcome of self-play games of engines with an evaluation that is not highly tuned. In a random mover Nutter pieces would tend to diffuse forward. Perhaps this makes the nutters a bit more aggressive than the others, which would benefit them if the others are not aggressive enough. Perhaps the others would benefit from a piece-square table with a larger forward-gradient, while the Nutters automatically play like they have one.

On two occasions I noticed issues that could be related. In Fairy-Max white seems to play better than black, even when I average out the first-move advantage by having black start in half the games. This must be due to the direction the board is scanned during move generation; for white this typically first encounters the Pawns, for black the pieces. So if a Pawn move and a piece move have equal score, white would likely play the Pawn move, black the piece move. As Pawn moves are always forward, this makes white play more aggressively.

The second case was when I was measuring the value of KNAD. I was not sure whether it would be good to give a bonus for centralizing such a valuable piece, so I did the measurement both with a neutral PST and a centralizing PST for the KNAD. In the latter case the KNAD cae out about 1 Pawn more valuable! Normally misconceptions on the evaluation (such as the piece value) hardly affect the outcome of such measurements, as long as both players share the misconception. But not in this case. Without an incentive to centralize the side with the KNAD too often left it unused, in a place where the profitable things it could do stayed beyond the horizon.So strategic errors only one side can make (because of the imbalance) can affect the outcome.

There could be a solution but first remember the the state space of the possible solutions is linked to the choosing of the pieces out of a small possible set, is it is probably non-neglijable likely to plainly not be able to succeed as the demands ar pretty tight.

I agree that absolutely perfect balance between all combinations of armies could be very difficult, but I also think it's not necessary.  Even if they are not balanced enough for computer vs. computer matches to come out exactly even, so long as the goal is to make a game good for humans I think we absolutely can get sufficiently balanced armies.

My take from cwda is not about balance but aboutsomething i'd call "dinamic balance" as each army seems to "mean" something.

It is unfortunate that Betza hasn't been heard from in nearly 15 years now and may not even be alive.  But he has written a lot of content on this site about piece values, his struggles to determine them, and his goals for Chess with Different Armies, and his previous failed attempt at it.  I believe we know enough from these writings to feel confident that an even balance between armies was THE primary goal and, if he were here, he would be continuing to work toward it.

Yes, each army does have a unique "flavor" that absolutely should be preserved to the maximum extent possible.  But making the BD's leap a lame leap is a very, very tiny change that doesn't change the flavor at all, at least in my opinion.  I can't really see an argument against this change unless one believes that it is Betza's game and only he can update it and, consequently, if he's dead we are stuck with it forever.

The fact is we have learned a lot since this game was made and Betza was unfortunately wrong about some things.  The Archbishop is worth a lot more than he thought as just one example.  If he had known what we know now, he would have made different decisions.  There's a page here somewhere where he talks about the Short Rook and trying to decide what the range should be and how he used computer vs. computer test matches to help validate the decisions exactly as we are doing.

The Musketeer Chess approach is problematic.  For one thing, you are taking about a radical change that makes a completely different game.  You no longer have armies with themes that "mean" something as you put it.  And, we have determined that the strength of an army depends heavily on the specific combination of pieces, not just the individual pieces.  If you want to make such a game, I would encourage it and I would try to help if you wanted, but I don't see this as a valid approach to rescuing CwDA.

I thought a bit about Greg's proposal of weakening the charging rook (and his earlier proposal of weakening the Bede). I personally see big flaws with such a approach as the state space of the problem has at least 4 dimensions (16 if you consider playing white or black different things).  There could be a solution but first remember the the state space of the possible solutions is linked to the choosing of the pieces out of a small possible set, is it is probably non-neglijable likely to plainly not be able to succeed as the demands ar pretty tight. My proposal for getting out of the impasse is to combine the CWDA with musketeer chess. But instead of offering many options we may give a set of gating pieces for each of the 16 encounters (let's include FFvsFF here as they could receive slightly different pieces in order to compensate for playing white.). They can be just one piece of a general value of approximately 2 or 3 or 4 or 5 or maybe pairs of the same or different pieces. Pairs of approximately 2.5 pieces seems quite interesting to me, as 2 of them worth exactly a rook and for one of them you may capture a regular minor and give up some positional or capture 2 pawns and earn some minor positional bonus.

For example in the FFvsFF encounter which in regular Betza is banned I think white should be able to gate two ffbbNsD and black should be able to gate two ffNsDbbLbH. Maybe the second piece is actaully worse but at first glance more jumping retreats should be better, be them longer. They also add to versatility especially in the endgame. Such pieces should worth around 6.5/8 knights=0.8125 knights=0.8125*3.25 pawns=2.640625 pawns=2.65 pawns, so pretty good.

Another reason Betza's implied (and indeed not stated) principle of armies with different styles should be preserved. The gating piece would probably be counter style, though in order to compensate for the misshapen of that particular matchup.

Greg,to be honest,i'm not sure if we should plunge ourselves into piece change judgemets. It is, most likelly, more complex than just this experiment. Also the game needs to be fun. My take from cwda is not about balance but aboutsomething i'd call "dinamic balance" as each army seems to "mean" something. I'm preparing a small experiment on this, also!... And maybe a more interesting rook could be along the lines of fsR4bWbB2

I have some more results to report.

I've generated 20 balanced opening positions with the FIDEs vs. the Nutters and another 20 with the colors reversed and run the 400-game test.  Here are the results of Nutters against the FIDEs:

Nutty Knights: 272
Fabulous FIDEs: 79
draw: 49

Holy crap!!!  That is not at all what I expected.  I don't really understand why the Nutters are so dominant, given that their total piece values seem to be about the same.  Our piece values could certainly be wrong, of course.  But I don't think they are that far off - at least in terms of what a piece is worth in general.  In which case, it shows that the true value of a piece really, really matters what else is on the board.  I'm guessing they can develop very quickly and very flexibly and get early advantage.

How to fix is a hard question.  I've thought about this some and considered a few ideas.  The one that "feels" best to me is limiting the range of the Charging Rooks to 4.  Essentially, this means that instead of the Charging Rooks being regular Rooks that move backwards as a King, they become Short Rooks that move backwards as a King.  I will test this, but I'm certainly open to other thoughts.

Speaking of fixes, I've re-run the FIDEs vs. Clobberers test with the suggested fix - change BD to BnD.  Here are the results:

Colorbound Clobberers:  180
Fabulous FIDEs:  156
draw:  64

Much better, and probably sufficient for now.  Given that we don't know what a lot of evaluation terms should be, the accuracy of these results is limited and this result is probably within the "margin of error" (acknowledging that I am not using that term in the same way that statisticians do.)  With this change, I would consider this matchup balanced for all practical purposes.

H.G., I saw your question about what the results would be in pawn odds games.  I don't know but I'll work on running that test also.

Basically this is just a scaled version of the 3.25/3.25/5.00/9.50 values. Except that the Pawn was weakened by 5%.

But a Pawn is the most variable piece of all; it is really very ill-defined what an advantage of 1 Pawn means. Rook Pawns, Pawns on central files, doubled Pawns, passers, 7th-rank passers... These all have completely different values, with as much as a factor 5 between them. For this reason I always use the Queen as calibration standard.

Below is a sub-wiki that quotes many valuations for the chess piece types; I'm wondering why Kaufman in a book of his published in 2011 apparently changed his valuations to make them nearly identical to what the Dutch world chess champion Euwe gave them (notably single N=B=3.5 and Q=10, though unlike Euwe he has R=5.25 instead of 5.5), which is about what I'd use (I'd put a N at e.g. 3.49, as if to be 'precise', and use Euwe's R=5.5):

https://en.wikipedia.org/wiki/Chess_piece_relative_value#Alternative_valuations

I think this is where Betza's 'leveling effect' comes in. You can use a piece in two ways: (1) avoid trades for a nearly equivalent opponent piece; (2) don't care about such trading. In the trade-avoiding strategy (1), the opponent's counterpart will interdict access to the squares it attacks, as going there would give him the opportunity to trade. This limits the use you can make of the piece, thus depressing its effective value. In general, stronger pieces lose value due to the presence of opponent weaker pieces that they have to avoid 1-for-1 trading with.

If the value was close to start with, the value depreciation caused by adopting a trade-avoiding strategy can be larger than the intrinsic difference. In that case you would be better of using strategy (2). But there the fate of the piece is to be traded, which makes them effectively equal in value, as any difference will evaporate with the trade. So pieces nearly equal in value will see their value pulled towards each other when they oppose each other, until it gets exactly the same. I think this is pretty much the case for a Knight and a lone Bishop on 8x8. If the intrinsic value of the Bishop was somehow increased compared to the Knight, initially you would not benefit from it. Because you would have to 'sacrifice' that extra intrinsic value by limiting the use of the Bishop by stricter trade-avoiding.

Regarding the 3 tempi are worth a pawn axiom in chess, I think this was long ago originally stated with the added condition that it was a rule of thumb that applied in particular for open positions. In closed positions, there is often no rush and a player is often able to afford the time to maneuver pieces to their best positions one at a time (I have neglected to mention the added condition of an open position in Notes sections of pages on chess variants I've invented, though, regarding my suggested hints on how to play them).

To be clearer, I'd only put the average difference between a N and B within the microscopic margin you suggested, in favour of the (single) B. However I have a soft spot for knights, though many chess players would more often than not just as soon not trade a B for a N as a Cadillac for a Chevrolet. I still remember the late world chess champion Tal looking away disappointedly when I traded away a B for a N against an older Grandmaster (GM) in the last round of an international event in Canada in 1988 (the fellow soon offered me a draw, as I still had the tiny edge of a slightly better pawn structure). An untimely and inappropriate recollection of a remark Dutch GM Timman made about Ns in a book of his was my undoing. I wouldn't be honest though if I didn't mention that I had had the bishop pair already in the game in question.

Well, the equality of a lone Bishop & Knight (both 3.25 Pawns) was what Larry Kaufman found from statistical analysis of a huge database of grandmaster games. If you are talking about deviations of the order of 0.05 Pawn, I doubt that this will be measurable, or even meaningful. Because piece values are by definition averages, and it serves no purpose to know the average much more precise than the typical deviation. Total material balance also depends on how well pieces cooperate, or combat each other, as the case of 3 Queens vs 7 Knights dramatically shows. Kaufman himself already investigated how the B-N difference depends on the number of Pawns, and did indeed find a dependence, where it is better to have Knights if there are many Pawns, but better to have Bishops with very few Pawns. AFAIK he did not try to correlate it with the shade of the Pawns (probably because such a thing is not always easily defined, if the Pawn chains are not fully interlocked). The 'good Bishop' vs 'bad Bishop' probably has a much larger effect than average Bishop vs total number of Pawns.

Common wisdom has it that "3 tempi is a Pawn", which would equate a tempo to 33cP. That makes that for nearly equivalent pieces the actual difference will be mostly determined by where they are located (centralized vs on the edge), as moving them to improve their location is so costly it already defeats the purpose. The difference between having a Knight on e4 and having one on a1 would certainly be more than 0.05 Pawn.

I remember spending a lot of time on determining the value of limited range Rooks (R2 - R5), so the 400 cP I used with the Rockies is probably quite reliable. And you are right: your value for the Cardinal is definitely too low (all my tests point to A+P being slightly stronger than Q), and the unexpectedly large cooperativity bonus of the B and N move is most-likely indeed due to this concentration of attacks. If I watch games the Cardinal turns out to be extremely adept at annihilating enemy Pawn chains, and I gues this is because it can attack a Pawn, the square it can be pushed to, and a Pawn it protects, all at the same time. I am suspecting that orthogonally adjacent move targets are an asset by themselves, in addition to the individual moves. The Cardinal's 'footprint' has 16 of those, Queen and Marshal only 8. This would also explain why a Rook is still worth more than a Bishop (500 vs 400) on a cylinder board, where the average number of moves is about the same. (On 8x8 one square less for the Bishop, but one square can be rached through two paths, which should partly compensate that.)

It would be very interesting to do a more thorough investigation of pair bonuses. (Still on my ever-growing to-do list...) The only thing I tested so far is that two B-pairs seems exactly twice as strong as one pair. So it doesn't count as 2x2 pairs; the even Bishops are always worth 50cP more than the odd Bishops.

Hi H.G.

I did note in my (unchanged) Edit sentence just above the values that I gave (in my second last post in this thread) that my memory had been rather off, though I could have been more explicit about that pretty much negating my earlier remarks in the text about the ranking of the armies as I recalled it. A natural aversion to my eating crow, I suppose. :)

The effectiveness with which an army works together is indeed not necessarily reflected by the material sum of its parts.

I was happy many of our values for pieces of the 4 armies seemed relatively close to each other, with some notable exceptions (perhaps especially the Cardinal, Colonel and Short Rook). I can see how I might have underestimated a Cardinal (on 8x8 at least) since my primative formulas for valuations don't account for a Cardinal's great concentration of power within a 2 square radius around it, covering the same number of squares as a Chancellor or Queen would.

I still rate a knight as microscopically worse than a bishop on average, though I didn't bother to say so explicitly in my recent post on CWDA values. At least two chess grandmasters that have been in my area (besides some advanced chess books I read long ago) note that once a B is gone, it's harder to cover squares of its colour. I'd say that's since a knight takes at least two moves to cover a square of the same colour it wasn't already, whereas a B might often take only one move to do so. There is also that a B can sometimes trap a N against an edge of the board in an endgame. Of course, there are many other things to consider, but these things are what chessplayers have recently pointed out to me. Then there's my still not being 100% trusting of computer statistical studies/methodologies, but at times that comes down to vague doubts and my own intuition/studies as a chess player.

The values you added seem at odds with the text above it.

Note that the individual piece values Fairy-Max uses do not really add up to give the observed total strength of the army. In particular it seems to overestimate the Clobberers, and under-estimate Rookies and Nutters (which get about the same total as FIDE, which I will use as a reference). The values reported for color-bound pieces include half the pair bonus, as Fairy-Max does not explicitly keep track of such bonuses, and I always do the value determination of such pieces in pairs. This might be unrealistic for the Clobberers, as it will be difficult for them to conserve both pairs. And the color-bound pieces are significantly stronger than Bishop, so their pair bonus is probably larger too.

Another possible explanation could be that the Clobberers pieces poorly cooperate, in the sense that they do not complement each other's weaknesses, but tend to have the same. E.g. the Cloberrers have only one major piece. And 4 of the 6 minor pieces are quite valuable (about a Rook). So there is a fair chance that despite a large advantage in terms of piece value, they can often not win for lack of mating potential. That so many pieces are color bound makes it worse. You can end up with Fad + Bede on the same shade, an advantage numerically as large as 2 Rooks, but still a dead draw. And Fad or Bede + Pawn vs minor can be drawn by sacrificing the minor for the Pawn, or perhaps simply by having the King stand in the path of the Pawn on the other shade (so you could only win if you can somehow catch the minor to force that King to leave by zugzwang). If it would be a Bishop of opposite shade, it would obviously be impossible to harras it. And Fibnif or Woody Rook can always move to the other shade and safely stay there.

The Rookies might have an advantage that all their pieces have mating potential. On an individual piece mating potential doesn't seem very valuable, but when all your pieces have it, even a disadvantage as small as a Pawn might always be lost, for lack of drawing tricks. This could be worth something.

I've added some content to my previous post in this thread, with an edit (notably my own estimates of the relative material values for each army).

Indeed, I addressed this this inconsistency in a follow-up comment, at the time. Paper-Sciccors-Rock situations are very uncommon with piece values; usually the empirically determined value of a piece is highly independent on what you play it against. (Except for extreme situations such as 3 Queens vs 7 Knights; it has to be a mix of pieces of different value.) I guess that this is why 'piece value' is a useful concept in the first place.

It could be that the Clobberers are composed such that they can better exploit the most important weakness of the Nutters, namely that they cannot quickly pull back. The Clobberers have only one major piece, but they have several combinations of two minor pieces that together can force checkmate (through repetitive checking) on an unprotected King. As Kings tend to stay on the back rank until the late end-game, it is rather tempting for a naive Nutters player to abandon its King while aggressively attacking (possibly gaining significant material), to discover that a counter-strike expedition of two pieces will unescapably kill its King. I don't think any of the other armies has the ability to inflict mate with such a small force. (In FIDE there is the pair of Rooks, but that already fails when there is a Pawn to shelter behind, while the FAD can jump.)

So it seems it is more important for the Nutters to have some strategic knowledge (which Fairy-Max utterly lacks), namely that it should always keep a 'sweeper' piece near the back rank to defend its King against sudden break throughs. That the opponent also doesn't know that this is a weakness, and won't intentionally lure the Nutter pieces forward (e.g. by forcing them to make a forward distant recapture) only partly compensates this ignorance, as it will happen enough that the Nutters will just accidentally (unforced) move their pieces ahead. This is actually statistically likely, as the Nutter pieces in general have more forward than backward moves. So they tend to 'drift' forward when they would wander around aimlessly. In an engine with the required strategic knowledge the Nutters should do even better, though, and they were already one of the strongest. So if the method has a systematic error here, it is in the wrong direction.

The reason I was not so worried about 'disadvantaging' the Nutters by denying them the opportunity to promote to Queen / Marhall / Archbishop is that they already seem to have too strong an army despite this 'handicap'. Also, the disadvantage for the Clobberers that they cannot do better than Archbishop is not nearly as large as what Betza thought, as the Archbishop is unexpectedly strong. And also with this handicap, Clobberers seem stronger than FIDE. So I thought it entirely acceptable to limit promotion to each army's own super-piece.

If it would help, it would not be a bad idea to limit the Rookie's promotion choice to { Fibnif, Short Rook, Half Duck }, or perhaps even just to Fibnif. But such promotion limitations seem actually ineffective in altering the strength of an army.

I wanted to notice something in HG's old results.

I see the CC and the NN are balanced against each other but the CC behaves quite worse versus the RR (10%). So it seems same small but not insignificant rock-paper-scisors effect is taking place. This could be due to a possible need (I mentioned a long time ago in the different context) of a concept of multidimensional piece values. But it is probably more than that if any such thing is possible? The NN are a "pressure" army as they have more forward moves and the RR are usually slower as they can't turn a corner that easily. This seems a reduction of the weakness of the NN. On the other hand CC has the strategic weakness that it can be twice impaired by te lack of an counterpart of the other color bound piece.. RR can profit more easily from that as because of it slowness weakness it is a more strategic army herself. The NN don't have time for such debates. They need to "act" so they can't profit out of it.

Such lines of reasoning are most likely usefull but I can't pinpoint why I'm a bit uncomfortable with the idea of studying it exactly here. Maybe the game dimensions.

I looked up my old comment in this topic ( https://www.chessvariants.com/index/listcomments.php?id=31222 ). There I report that the Rookies were actually strongest of all. So RR >~ NN > CC > FF. This was based on the scores in 400-game matches between each pair of armies with Fairy-Max. In a comment just before it Fergus had arrived to the same conclusion based on ChessV (but with far fewer games). Fairy-Max randomizes the first 4 opening moves of each player, which should be enough to not have significant duplication of games. (I did not actually check for duplicate games.)

My experience with this kind of materialy-imbalanced testing is that the result is not very sensitive to the piece values used by the engine. E.g. if you give one player an Archbishop instead of a Queen, and assign it a value of 900 (where Q=950), the side with the Queen will score about 62%. If you then repeat the test with A=1000), the player with Queen will still score around 62%. The reason is likely that, as long as the values are different, 1-for-1 trading is not frequent, because there is always one player that thinks it is to his disadvantage, and will avoid it. And it does not matter much which player this is. The imbalance is therefore long-lived, and you measure the relative effectivity of the imbalanced pieces for doing (or helping to do) damage to the common pieces. Which is pretty much independent of how the computer values them, as they will mostly not be traded directly for other material (2-for-1 trades are also pretty rare).

So as long as both players share the misconception on actual value, the programmed value doesn't seem to be very critical. Of course it should not be totally off; if you set the value of a Queen below that of a Pawn, it will indeed get worth as much as a Pawn, because it will be immediately traded for one. There is just no way the other player could shield all its Pawns from Queen attack, before the Queen gets to see it can force a more profitable trade. If you assign reversed values to pieces that differ very much in power, the strong one will probably succeed to force it being traded for the weak one, which it mistakenly considers profitable.

Before I did the test with complete armies, I did similar tests on all individual pieces in the armies to determine their value. E.g. use FIDE as context, and then replace Rooks of one side by (say) HFD on the other, to see whether HFD is better or worse than an orthodox Rook (and by how much). In such tests I always make sure they are self-consistent, i.e. performed with the programmed value equal to the value suggested by the eventual score. If my initial guestimate of the value was wrong in this respect, I just repeat the test with the value suggested by the outcome of the flawed test. Which then usually does not significantly alter the outcome. This should have made the individual piece values more or less OK, so that the play during the whole-army tests must have been realistic, and thus must have made the sampling of what the pieces can do representative.

I am a bit surprised about the low score imbalance you get for CC-FF. My old results table says +9% for this (meaning the match score averaged over both colors was 59% in favor of the Clobberers). You get only 52.6%. What is the Pawn-odds score for ChessV (i.e. when you use equal armies, except that one of the players gets f2 or f7 deleted)?

These are the piece values Fairy-Max is using (Pawn = 100):

FIDE
Knight           325
Bishop           350
Rook             500
Queen            950

Clobberers
Waffle           320
Fad              480
Bede             530
Archbishop       875

Nutters
Fibnif           310
Charging Knight  400
Charging Rook    485
Colonel          935

Rookies
Woody Rook       310
Short Rook       400
Half Duck        480
Marshall         935

I'd rate the RR army and the FF army about the same, though the mobilitity of a Q may give an edge to the latter. The CC army would seem to be at least slightly better than either (based on material valuations) IMO, but noting, perhaps very significantly, that it seems it could often be really awkward to develop both of the two waffles (i.e. not just one) that a player has with any speed, especially with the Black pieces (the edge pawns being unprotected at the start doesn't help either, especially vs. a FIDE army, with its Q). The NN army seems clearly the best army of the 4 in theory to me (based on material valuations), except I've yet to play with it, rather than against it. Thus I find myself pretty much agreeing with H.G.'s assessment of the 4 armies' relative strengths, though perhaps for many differing reasons.

[Edit: It seems my memory of the relative strength of the 4 armies that I estimated long ago was rather off. In any case, here's my current tentative estimates of each army's relative strength (based on material valuations alone):]

FIDE:

Knight 3.5 approx. Bishop 3.5 Rook 5.5 Queen 10 Army (w/o Ps/K) 35

Clobberers:

Waffle 3.125 Fad 4.75 Bede 5.125 Cardinal 8 Army (w/o Ps/K) 34

Nutters:

Fibnif 3.125 Charging Knight 4 Charging Rook 4.9375 Colonel 8.9375 Army (w/o Ps/K) 33.06

Rookies:

Woody Rook 3.125 Short Rook 3.54 Half Duck 4.915 Marshall 10 Army (w/o Ps/K) 33.16

I think the NN despite their many weaknesses they have a wonderfull middle game. That should probably always do it!

@Greg The Bede thingie seems a good idea for me and it does sound more natural for a rook!

About the RR, I find the FDH quite akward and it sould be around rook level. It probably is not (but the R4 definetly compensates for it).

Anyway very nice effort on mister Betza part in an era when computers were much weaker :)!

BTW, I always interpreted the promotion rule in CWdA as that you could only promote to pieces of your own army. This seemed logical to me; promoting to pieces of the opponent army strikes me as unnatural and ugly. But now I believe this is not what Betza originally meant

The rule is definitely that you may promote to a piece in either army.  I know I've seen that explicitly stated, with reasoning, on one of Betza's pages here.  (There are quite a few auxiliary pages about CwDA, armies, and piece values by Betza on the Chess Variant Pages, some of which might not be in obvious locations.  This is something I've been meaning to look into cleaning up.)

But the Colonel has a major shortcoming: it cannot move backwards fast. All native Nutter pieces actually have that problem. So if it comes down to a promotion race, and they can only promote to their own pieces, the Nutters are toast.

Yes, this is exactly right.  It would make the act of pawn promotion for the Nutters wildly inferior to every other army if the they could only promote to their own pieces.

NN > CC > FF > RR

This is certainly not how I would rank them.  I would do almost the opposite.  I'm not sure whether FF or NN is better and I'm not sure if CC or RR is better, but I am confident that both CC and RR are stronger than both FF and NN.

I've started studying this formally.  I was going to wait until I had completed more testing to get into it, but since the subject is being discussed, I'll explain what I have so far, which is some solid testing of the FF vs. CC match-up.

I started by coming up with a number of different, but balanced, opening positions.  I have 20 different opening positions with FF as white and CC as black and another 20 positions the other way around.  These positions are roughly 8 moves deep into the game.  I have also programmed ChessV with the ability to play a list of games one after the other in "batch mode" and record the results.  I then played each of these 40 different positions 10 different times with slightly different time controls and settings and compiled the results:

CC beats FF: 178
FF beats CC: 157
draw: 65

So it certainly appears that the Clobberers are stronger than the FIDEs (which is what I expected.)  It is possible, of course, that these results are not perfect.  Chess programs can only "see" so deeply and then they must evaluate the position, and they do that with parameters we supply - for example, we tell the program how much the pieces are worth.  There are lots and lots of parameters, and while I believe what I have provided are very reasonble, they are almost certainly not perfect.  One important evaluation parameter for this match-up that we don't know - what should the color-bound bonus/penalties be?  In Chess, having both Bishops is worth half a Pawn.  But the Clobberers have two color-bound piece types.  What if you lose both of the pieces on one square color but still have both on the other?  This should trigger a large penalty, since the opponent can avoid both of those peices by occupying the other color, but how large a penalty?  More testing is needed to continue to refine the accuracy of the evaluation parameters ...

The bottom line is that this result should not be considered 100% conclusive, but the difference is large enough that it is almost certain that the CCs are at least somewhat stronger than the FFs.  I will post all my test positions and results sometime soon, but until I release a new version of ChessV with the batch mode people won't really be able to reproduce.

Now, next question.  If we accept this result, and we believe the armies should be closely balanced, what to do?  Obviously the FIDEs shouldn't be messed with, so the Clobberers would need to be weakened.  My thought is to weaken the Cleric (BD) by making the Dabbabah move a "lame" leap - only allow leaping to the second square if the first square is empty (BnD).  I plan to test that change and see what the results are like.

the Nutters seemed to have not much trouble beating FIDE

Interesting, this is not what I would expect.  I think this is the next match-up I'll start testing.  The challenging part of the testing is computing a number of different but balanced opening positions ...  Stay tuned.

OK, I see. I don't recall exactly anymore where the RR fitted in; it was one of the last armies I implemented in Fairy-Max (because initially it had trouble doing the R4). BTW, I always interpreted the promotion rule in CWdA as that you could only promote to pieces of your own army. This seemed logical to me; promoting to pieces of the opponent army strikes me as unnatural and ugly. But now I believe this is not what Betza originally meant; he was afraid having different promotion rules would cause the Pawns to have different values, which could easily disturb the balance, as you have so many of those.

But I once made an attempt to weaken an army by allowing Pawns to only promote to a Commoner, rather than a Queen-class piece, and it did not seem to affect the strength of the army at all! At first this seemed very strange, but then I realized that in practice you almost never allow a promoted piece to survive: you sacrifice a minor for the Pawn while you still can, or dedicate a minor to prevent it reaching the promotion square. By that reasoning the value of a Pawn is not so much determined by what it promotes to (as long as that is at least a minor), but more by what the opponent can use to prevent the promotion. This would mean that an army where the weakest piece is stronger (compensated by some of its stronger pieces being relatively weak) causes the Pawns of its opponent to be worth more. Having 7 pieces each worth 4.5 (vs FIDE with 4x3 + 2x5 + 9.5) would pose a real problem w.r.t. stopping opponent passers.

Anyway, since Fairy-Max does not support under-promotion, I had to appoint a unique promotion piece, and chose the most-valuable piece of each army. For the Nutters this was the Colonel. But the Colonel has a major shortcoming: it cannot move backwards fast. All native Nutter pieces actually have that problem. So if it comes down to a promotion race, and they can only promote to their own pieces, the Nutters are toast. Even when they promote 2 or 3 moves earlier, there is no way for them to prevent that the opponent will promote as well. Even worse, the freshly obtained Colonel might not even be able to connect with its own King fast enough, and get lost through a fork on King and Colonel. Especially when the opponent can promote to Queen. The Colonel is completely defenseles against slider or night attacks from behind.

Despite this, the Nutters seemed to have not much trouble beating FIDE. The average superiority of there pieces makes that they hardly ever get into an equal Pawn ending.

By NN I meant Nutty Nights. Sorry for the confusion. And I was not thinking about this. By definition the charging knight is a major piece. So is the charging rook, that should be obvious, and along with the colonel this means 3 major pieces. Although the colonel is probably weaker than the ordinary king or than the marshal!

The way I see it and I remember you commenting about this on wikipedia, HG (and us having this discussion a while ago) the order of the armies is NN>CC>FF>RR. But they are close. I like this game for the diversity though. In a private talk Vitya Markov has said that he think the RR are the stronger. I had never made this experiments, though.

I am not sure what you mean by that.

It stands to reason that the Charging Knight has mating potential on 8x8: the Gold General already has that, and the Charging Knight has 4 Knight moves instead of the single Wazir step of the Gold. (After you flip it, which should not matter in an otherwise 8-fold -symmetric context.) So it is bound to be a much stronger piece. I see that in Fairy-Max' implementation of CWdA I valued it as 400 cP (where R=500 and N=325).

Nice data HG!

My trouble is that I was already considering the NN overpowered :(!

There are only 98 positions (out of a total of 64*63*62 = 249984, counting also illegal positions) where King + Charging Knight is not won against a bare King, when the strong side is on move. With the bare King on move, he loses in 80.5% of the positions. In the other 20% of the positions he captures the enemy King or the (unprotected) Charging Knight on his first move, or is stalemated.

It takes at most 33 moves to force the checkmate:

        mated    mate
King captures 50168
mates      36         ( 0.00 sec)
in-1       30     126 ( 0.01 sec)
in-2       90     158 ( 0.01 sec)
in-3      138     446 ( 0.01 sec)
in-4      198     560 ( 0.01 sec)
in-5      334     772 ( 0.01 sec)
in-6      278    1122 ( 0.01 sec)
in-7      498     908 ( 0.01 sec)
in-8      770    1630 ( 0.01 sec)
in-9      808    2246 ( 0.02 sec)
in-10    1240    2274 ( 0.02 sec)
in-11    1720    3124 ( 0.02 sec)
in-12    2312    3978 ( 0.02 sec)
in-13    2606    4922 ( 0.03 sec)
in-14    2930    5294 ( 0.03 sec)
in-15    4002    5400 ( 0.03 sec)
in-16    4432    6778 ( 0.04 sec)
in-17    4966    6770 ( 0.04 sec)
in-18    5072    7006 ( 0.04 sec)
in-19    6334    6988 ( 0.04 sec)
in-20    7678    8402 ( 0.04 sec)
in-21    8512    9134 ( 0.05 sec)
in-22    9074    8836 ( 0.05 sec)
in-23   11468   10968 ( 0.05 sec)
in-24   15336   13132 ( 0.06 sec)
in-25   17800   16642 ( 0.06 sec)
in-26   20122   17610 ( 0.07 sec)
in-27   21332   18210 ( 0.07 sec)
in-28   20308   15816 ( 0.08 sec)
in-29   16108   11550 ( 0.08 sec)
in-30   10430    7332 ( 0.08 sec)
in-31    3470    1386 ( 0.08 sec)
in-32     666     174 ( 0.08 sec)
in-33     124      24 ( 0.09 sec)
in-34       0       0 ( 0.09 sec)
won:     249886 (100.0%)
lost:    201222 ( 80.5%)
avg:       23.7 moves
 

I have seen a game of CWDA where K& Charging Knight has managed to checkmate a lone king. I was first not expecting this but it now seems normal especially if the attacking pieces are "above" the defending king. I'm not sure if it works otherwise. Anyone else knows anything else on that?

On the subject of "...a difference just for the sake of being different, without adding anything new" (H.G), I've poured over various lists of chess variants on this website in search of new games that I might to try out sometime, and many times I've run into arguably just that, e.g. about a half-a-dozen versions of 10x8 Capablanca Chess, same rules for each except for the starting setups being different.

In the case of using CwDA as a kind of mutator, there might at times be an effect that's [essentially] new that is more than the sum of old ideas. For example, if Marsailles Chess works, somehow, when crossed with CwDA, it may well play rather differently than straight Marsailles Chess played using only FIDE armies for both sides. It seems a more problematical matter in the case of a 10x8 version of CwDA, as it's open question, perhaps, whether enough new fairy chess pieces could possibly be created from scratch to make for the novel and bigger armies that might be used.

Also, If, say. an archbishop is not rejected as a tired old piece type, then (kind of as Joe alluded to about rooks & bishops on circular boards) it's value/utility on 10x8 is somewhat different than on, say, 8x8, perhaps moreso depending on the pieces it's mixed with in a given army. I suppose then one could still debate whether anything essentially new is being added - I'd say there was, but instead of being something spectacular, it's subtle/'small', which many/some might find uninspiring though.

P.S.: At the moment I cannot send/receive email.

I'm having computer troubles. Hopefully I can continue on this old machine a bit.

@ H.G.: I suppose the only point to having two like armies on, e.g., 10x8 playing each other, and which aren't already in the context of a previously invented variant like 10x8 Capablanca Chess, would be that the two like armies could be designed to be close in value to, say, Capa's army. Otherwise your point on the matter many posts ago is taken, my oversight due to a hurried post.

I agree that 10x8 would not make sense for Chess with Different Armies. The all-new pieces are already enough of a change.

As for any board-size being better than another, I think that's just a matter of preference. Going smaller than 5x5 might be too small because enemy pawns would be in contact with each other, and the complexity of the game becomes severely diminished. As far as I know, there is no upper bounds for the maximum size of a good board size, and even infinitelly-large boards are easily playable and fun.

True, 10x8 boards have their attractions. Main disadvantage is that they are difficult to come by, as physical rather than virtual entities. Alteratives are Seirawan gating or Musketeer gating (new pieces can appear on a square evacuated by a virgin piece in the same move), or Gustavian boards (just adding two extra squares on each back-rank). I have also seen gating by Pawn pushing (i.e. a piece appearing on the square behind the one evacuated by a virgin Pawn), or dropping on the back rank as a separate turn.

But for Chess with Different armies there is no need to play with armies of 10 (non-Pawn) pieces rather than 8. Most armies consist entirely of exotic pieces already, the whole idea was to do away with all orthodox pieces other than King. So the specific virtue of a 10x8 board would not be used at all. So the question is just whether you want the game to be larger or smaller. And the more pieces each army has, the fewer different armies you can make without reusing the same pieces. So it seems the cons outweigh the pros.

Agree 100%. My only comment is that 10x8 boards (compared to 8x8) have something peculiar: you can add a few variant pieces without taking away any of the classical pieces.

Of course there are other ways to do this: new pieces can be added after the original ones move out, or they can be put in place of pawns, or in front of pawns, or pawns can be moved up to make space for more pieces. But I really like the 10x8 board in favor of these options.

Note that what I like or don't like is just a matter of personal taste. Reasons I don't like FRC are that it offends my sense of symmetry, and that it often leads to start positions from where developing the pieces is awkward and cumbersome. Ease of development is something I appreciate in a Chess variant, and consider a trait of good design.

Orthodox Chess is rather unique by being a very well designed game, and still having a problem, namely that it has been played so much that the opening theory is now so well known that it is too easy to achieve a draw by rote learning. OTOH, opening theory is something most players of Chess-like games do like; prepairing an opening repertoire is a relatively easy way to get better at the game. So I don't think shuffle games are the best answer to the draw-death problem of orthodox Chess.

BTW, I never wanted to claim that new chess variants should not be designed before all existing ones have been played to death. I just see no point in generating 'more of the same' when there still is so much of the same that can be explored by other openings. In order to appeal to me, a Chess variant should provide something essentially new. Shogi is great because of the drops, Xiangqi is great because of the Cannons. Chu Shogi is great because of Lion power, Maka Dai Dai Shogi is great because of contageon. Chess with Different Armies is great because of the asymmetry.

@ Everybody

Well guys, this discussion could hastily become pointless as anyway most people would do what they like. I think the best (but paraphrasing from memory- Fergus if you read this maybe you have a better memory) has been put by Fergus Duniho during my Apothecary creation discussion. He has said something like people will invent variants and the best will come out on top from many points of view like popularity (which is probably most important) or critical acclaim, in a evolutionary manner. But surely there will be always people on the fringe. For example I tend to like 8 stones chess a lot and it is a small popularity game, but still played. Crazier even, I'm playing an Atlantean Ballroom Shatranj against Erik these day which (if I can get my tactics straight) looks at least interesting. A guy/girl has to do what a guy/girl has to do, end of story :)!

Thanks, Joe, for the intelligent well-phraised defense, although I'm not sure defenese was even needed.  True, I will agree that there are too many variants, and people should spend some time playing existing variants and identifying what should be improved before making their own.  But H.G.'s position is strange - that there's just no need to invent anything more until the existing variants are played out (if I understand correctly.)  H.G. has also criticised Fischer Random Chess on the grounds that it was "not imaginative" (if I remember correctly) although I consider it a perfect example of a responsible chess variant.  Chess was "played out", the openings studied to death.  So Fischer tried to make the smallest change possible to solve that problem.  The result was FRC.  But H.G. doesn't like FRC at the same time it seems he doesn't want a new different-armies inventions until CwDA is "played out".  So it seems he doesn't like agressive variants or modest variants, although that's just my  nieve view - I'm sure his actual view is much more nuanced.

A minor quibble here about board size: it can be considered a mutator. There are variants which propose placing an 8x8 standard chess set-up in the middle of a 10x10 or 12x12 board. This does change the game a fair bit. Now, with a 10x8, you can use it a few ways. You might have a file a rook can step to on either side of the standard 8x8 set-up, or you could 'play the long way' and set up with 6 rows of 8 squares empty between the 2 sides, or even move both sides up 1 square, so they ar the standard distance apart, but there is an extra row behind each side. Circular boards have long been used, also, for example. But what you are really doing here is examining how board geometry affects play and affects the utility of various pieces (eg: on a Byzantine circular board, bishops are nerfed and rooks are enhanced. In other words, you're playing Chess with Different Boards.

Isn't that exactly what chess variants are: games with non-standard armies and/or non-standard boards? I fail to see how there is anything new in your proposal.

I also don't see the merit of trying different armies on all kinds of different boards. It seems the famous adagium "it only takes 10 sec to invent a new chess variant, and unfortunately some people do" applies here. The idea of using different pieces for each player is a great idea, but what would you get by using, say, 10x8 boards that you don't get on 8x8 boards? It seems a difference just for the sake of being different, without adding anything new. There might be an incentive to do that when the original game has been 'beaten to death', like orthochess, but that doesn't seem to be the case here at all.

Not sure how interesting they would be by themselves, but for now one might be content just with new variant(s) in which both sides use the same new armies (but a new army which is different from e.g. the standard 10x8 Capablanca Chess army) in e.g. new 10x8 variant(s).

At any rate, I'm not quite sure if e.g. a variant of Marsailles Chess based on Chess With Different Armies wouldn't work okay if just using the standard 4 armies as in Chess With Different Armies.

Oh, I make no claims about that position being good.  It was just an idea I was toying with a long time ago that I haven't tought about since Kevin's post.  Maybe I'll start thinking again ...

@Greg

I don't see why there are two queens and only one colour bound caliph. I asume it is for balance but maybe something else could be done as from an artistic point of view it does not make much sens. What about caliph's on the starting squares queen squares as you have drawn them and instead of your central caliph a more powerfull queen. If you are ok with the many bishops moves, maybe BDHN would work fine. This is obviously a first glance judging and not a thorrow investigation :)!

It is an excellent concept, and, in my opinion, an excellent game.  That said, balance is very difficult to accomplish.  There are complaints about Betza's standard armies not being balanced, and while they are not perfectly balanced, they are pretty darn close - especially given that they were developed before the advent of sophisticated engines capable of evaluating them.  This was the culmination of Betza's life's work - it is unfortunate that he disappeared right before such tools became available.  The first version of ChessV, 0.1, was pretty much a Betza engine - Chess with Different Armies and Chess with Differently Augmented Knights.  As soon as it was ready I emailed him, but he had gone dark a few months before ...

Regarding the suggetions, I think 10x8 "Capablanca with Different Armies" is certainly worthy of pursuit, and probably easier to balance than 8x8 since there are more pieces.  In fact, I made such a game of standard capablanca vs. colorbound capablanca about 11 years ago.  Here's the starting array:

/play/pbm/play.php?game=Capablanca+Chess+with+Different+Armies&settings=SS_vs_CC

An excellent concept!

Inspired by it, I can suggest many Chess With Different Armies-like variants that, to my taste, might be especially interesting to try out sometime:

That would be with the Different Armies idea used to make any number of versions of the following variants 1) 9x8 Symmetric Chess; 2) 10x8 Janus or Capablanca Chess; 3) any number of 10x10 variants, such as Grand or Sac Chess; 4) 4x16 or 5x16 Circular Chess variants; 5) Glinski's, Symmetric Glinski's, McCooeye's or Hexajedrez (91 cell Hexagonal Chess variants); 6) 4-Way Chess; 7) Crazyhouse, Chessgi or Hostage Chess; 8) Pocket Mutation Chess; 9) Backlash; 10) Marsailles or Progression Chess.

@HG Muller

It seems to me that you have placed the pieces for bent bozos in reverse order of what would it be in the opening. My take on this would be that most pieces should as much as possible move towards the center with their first move. I believe that happens only for black, i.e. the example you gave.

For example if bozos are white then the left aanca should be placed on g1 as it moves towards the center that way. But from black's point of view the right aanca would move towards the center if you place it at the beginning on g8. I think it's not that tricky what I'm saying and it goes that way for all three pair of pieces. See you soon!

Yes, castling with the corner pieces is always possible in Chess with Different Armies. The Chiral Griffons are not color bound, so this would be O2 castling. It seemed better to set up the Sastiks on c- and f-file, even though they are really Knight replacements. This suits both the move of the Satstik and Chiral Aanca better. The latter can get out of the Kings way for castling througj the trajectory g1-f1-c4/b5 after the Sastik moved from f1 to f3 or g3. On f1 the King itself would block it, and you would be forced to break the Pawn shield to get the Right Aanca out.

Good point. Fixed that now. Unfortunately the diagram will always only consider one piece royal, so it now will not mark stepping into check with the Clobber King as forbidden move. But I guess that is just a minor flaw; this forbidden-move feature was only introduced for Caissa Brittannia, to indicate the numerous forbidden moves of the Royal Queen there. For symmetry I should perhaps also switch it off for the other King (by adding "royal=0" to the diagram definition).

The king is supposed to move three squares on the queenside if the queenside rook is colorbound. This is so the piece doesn't change colors.

Thanks Fergus,

It looks like there's a big set of Alfaerie graphics. I was looking for a war machine icon that I saw somewhere, and i was able to find it. In fact, there's a few versions. I appreciate it.

Thanks! :)