Comments/Ratings for a Single Item

Could it be possible to remove now the line saying:

Some of the rules that were not clear from the original description on Jean-Louis Cazaux's website were derived by Fergus Duniho from the Zillions-of-Games implementation of Metamachy.

As soon as I saw it, I asked what was not clear and I have clarified the original description. 

Many thanks

@Kevin: Human play is far from perfect, even for GMs. Misconceptions about piece values is just one of the contributions to imperfection. So, yes, GMs can have opinions, and the can afford these opinions to be wrong and still be at the top, because their competitors have their flaws too.

If the value of pieces depended on the general level of play, they would be meaningless concepts. We don't teach beginning chessplayers other piece values as those that GMs are using. Only if a player has a misconception applying to a specific piece, such as that knights are best moved to the board corners and should stay there, it can affect the value this piece has for them.

It's nice to hear different opinions. Perhaps I am somewhat biased due to the demolition work my Gryphon has done in the tournament game.

I also do not subscribe to formula.  I've been here long enough to watch at least a half-dozen well-thought-out systems be disproven.  The killer is that, not only has it not worked for pieces (e.g., the Archbishop is significantly stronger than anticipated), but also because it depends on the entire army (e.g., the individual pieces of the Nutty Knights aren't that strong, but together, they are totally overpowering.)

Regarding Griffon vs. Queen.  I am firmly in the camp that the Queen is better.  The case has been made that the larger board favors the Griffon - which is true to a point - but the difference is microscopic.  The Griffon suffers more in the corner or the edge, especially if blocked at the key points.  The larger the board, the fewer squares are edges/corners.  But the difference is small and the Queen and Griffon are active, attacking pieces that aren't likely to be there anyway.  Far more important is the fact that, while the Griffon has 8 rays, they emerge from 4 choke points where they can be blocked.  This limits mobility measurably.  Additionally, the Queen can slide along all 8 rays while continuing to attack the ray.  The Griffon cannot do this at all.  If it attacks even files, and makes a file-move, it now attacks odd files.  Same with ranks.  The result is that the Queen can triangulate - if it wants to attack a square, and is threatened and forced to move, it has several options of other squares to relocate to while still attacking the desired square.  The Griffon has a much harder time with this - for squares outside short range there is no option at all.  Also, it has problems with asymmetry.  One Griffon can attack another and the other may not be able to attack back because they follow different paths.  These sorts of anomolies do weaken peaces to some extent.  FInally, a Queen cannot be attacked by a King because it attacks all adjacent squares.  The Griffon can be approached.

All that said, the Griffon has some neat capabilities.  In particular, in the endgame, the ability to attack two files (or ranks) and trap the king between them is pretty good.  A Griffon plus a Rook is deadly.  Get the King betwen the Griffon's forks and then move the rook in between and that is checkmate, even if the King is in the middle of the board!  (When is the King ever checkmated in the middle of the board?)  So maybe, just maybe, a Griffon can be better in the very endgame, but I'm not even sure that is clear.  (King + Queen vs. King is much easier to carry out than King + Griffon vs. King, which is kinda tricky although still possible.)

I don't know the difference in value - a pawn sounds like a good starting point - but there is no doubt I will trade a Griffon for a Queen in even trade.

By coincidence or not, H.G., that's about 87% of a queen (on 8x8, at least) which is in line with the 85% ratio offered by the old ZoG article (for 8x8), as well as the 88% (if I read right) offered up by the Betza article. I didn't check everything he's ever written so as to see if Betza thought the ratio applied on all board sizes, though. Last night my own quick sketchy re-calculations came up with a 90% ratio for on 12x12 (at least), not too different, but I would be less confident if not comparing it to ZoG and Betza's percentage figures.

One thing calculations based on theory do have the advantage of is offering up something quick, if computer analysis has yet to be done due to awkwardness of board size, for example. Players can always take calculated (or even computer-generated) piece values with a grain of salt, and/or treat them as ballpark figures, everyone should understand that, at least for CVs that aren't much explored. There is also the question of exact board size/shape being tested, exact armies used in a starting setup being tested (and the exact squares the pieces start on, as Chess960 might even show). Not only that, but the strength of an engine being used for testing, IMHO.

Dax00 didn't so far offer up a way to numerically estimate the value of a piece like the Gryphon (on 8x8, or 12x12), but rather something that looked like opinion to me. That's fine, if a number can then be offered up as at least a guestimate based on it (unless one prefers to keep it secret). Aurelian has done a kind of calculation already, based on some sort of premise(s), so it seems for 12x12 he agrees with the conclusion that it's better than a queen for that board size - what his exact number for it could be, I don't know.

P.S.: Even the best human chess players still cannot agree on even the exact values chess pieces should have, computers be damned. The current world chess champion values a bishop slightly more than a knight on average, as is tradition for a long time. I may be an exception, in that I think a knight is almost fully equal to a B - and in my days as a young man I reached 2400 USCF chess rating, and nearly 2300 FIDE (later 2400 Canadian rating, in my early 50s). Some would say I'm still pretty weak, since I blunder badly now and then. :)

@Dax00: I agree completely that calculatory methods for piece values are usually no good. They qualfy as 'fact-free science'. The known values of the six orthodox pieces can be reproduced by infinitely many numerological recipes, which can be designed to give arbitrary values for any fairy piece.

I therefore do always determine piece values in an empirical way, by having a computer program play games in which the pieces are pitted against a combination of pieces of known value, and measure their performance. Through such measurements the Gryphon turned out to be worth about 8.3 on 8x8 (IIRC), on a scale where Q=9.5.

In the early versions of apothecary chess I have done these caculations. A Griffin is a pawn weaker than the quenn on a 10x10.About the same results I got for a marshall.  But increased board helps the griffin! Dax is correct!

It seems upon re-checking, I made an error in my calculations for the Eagle's value, then reinforced that by reading Betza's article the wrong way. For now I'll go back and use a value based on the old ZoG article's exact ratio that's found between a gryphon (Eagle, here) and a queen, if only for the sake of providing a quick and dirty numerical estimate, even though it may prove to be too low later on (with much experience). The value of bent riders is something I hadn't tried to calculate on my own before.

P.S.: If I am now reading the Betza article right, he values a gryphon (i.e. Eagle) as worth 88% of a queen, which is almost exactly the value that the old ZoG article implies it has.

Where the Queen provides distributed pressure, the Gryphon provides concentrated pressure. Against reasonable play, where you expect your opponent to try to make his pieces work together (reasonable to assume pieces are relatively close together), I assert that the Gryphon is a better piece for pressuring the opponent overall. Even when kicked away, it can often still maintain distant defense. And the forking potential is massive.

I was never one to subscribe to a calculatory method of evaluating piece values, rather in favor of practical analysis through actual play. 

Even if I were to concede that a Gryphon is about a pawn less in worth than a Queen on an 8×8 board (which I do not), it makes sense that the Gryphon's initial diagonal move would mitigate its strength more so on the smaller board than on the 12×12 board of Metamachy, so for this game its value should be at least comparable if not superior.

Before finalizing my own tentative estimate for the value of the Eagle (quite a bit less than a queen), I read Ralph Betza's article on Bent Riders, in the Piece Articles section of this website. If I understood his writings right, I'd already arrived at a similar value to what his would be for the Gryphon (what is called the Eagle in this game), even though I used a sketchier form of calculation. However, Betza worked out his theories for piece values before people began to try to estimate fairy piece values with the aid of computers.

P.S.: In the Piece Articles section, too, the Article 'Who is Who on Eight by Eight' puts ZoG's value for a Gryphon only about a chess pawn's worth less than a queen, so quite a difference in value, although those are old ZoG values that need to be taken with a grain of salt in many cases.

Pretty sure I prefer the Eagle over a Queen. So much versatility.

Confirmed.  Thanks!

That's now fixed. The function was testing whether a rankname equalled a filename, which would always return false. It was supposed to compare the ranknames of two coordinates.

In my game here, I want to capture En Passant.  It does not show as a legal move, although if I tell it to make the move anyway, it does work.

For what it's worth, here's my tentative estimates for the piece values of this (12x12) variant, at least in the endgame phase:

Pa=1.6; El= 1.76; Cam=2; N=2.6; Can=2.75; Pr=3.58; B=3.75; R=5.5; Li=8.12 Ea=9.23; Q=10.25 and K's fighting value=1.77.

So just to be absolutely sure: when moving Kf1-f3, with a black Knight on g4 attacking f2 (but pinned on the black King on g5 by a white Rook on g3), this would be illegal if f2 was empty or occupied by a white piece, but legal if it was occupied by a black piece (assuming f1 and f3 not under black attack)?

Thank you for all these explanations and feedbacks. I will correct soon the description on my own page. 

• The end-o-game rules, checkmate, stalemate, etc. are identical to standard chess
• King's jump: you guessed well. At his first move, the King may jump to a free square at 2 squares' distance. It does not matter if the square jumped over is occupied or not; however, the jump os forbidden if that intermediate square is threatened by an enemy piece. When jumping like a Knight, at least one of the two intermediate squares must be free of threat. The King's jump is not permitted if the King is in check.
• The King cannot capture with its initial jumping moves (it may jump to a free square only)
• En passant: any time a Pawn or a Prince takes a double step and passes through the capture square of an opposing Pawn, that Pawn may capture the Pawn or the Prince as if it had only moved one square. This en passant capture must be made in the immediate move following the double step. Only a Pawn may capture en passant; the Prince does not have this option.

Not clear from your description at http://history.chess.free.fr/metamachy.htm was:

• Whether stalemate is a win, draw or loss.
• What the "overpassed squares" are in case of the initial King move to the second ring. In particular whether moving like a Knight (from f1 to g3, say) passes over f2, g2, neither, either or both. And what it means for those squares to be "under attack" when they are occupied. (For D or A move it can be assumed that these are the W and F squares in the same direction, respectively.)
• Whether the King can capture with its initial jumping moves.
• Whether a Prince can capture en passant, in addition to being e.p.-capturable. Especially since, in the description of the Pawn, you present its ability to capture e.p. as a "consequence" of its ability to capture diagonally, rather than as an additional rule that could very well have been different. Since the Prince can also capture diagonally, does this have the same (but this time unmentioned) 'consequence'? And is this then a consequence just of being able to capture, (so that the Prince can also e.p.-capture orthogonally), or does the direction matter (and how about backward diagonal then)?

Note that my remark on the non-royal nature of the Prince is not meant as criticism on you piece naming, but just as a warning to the reader that the Metamachy type of Prince is not like the Shogi Prince (which also moves like King) in that it has to be captured / mated too in order to win the game and cannot expose itself to pseudo-legal attack. I would have said the same for Queen where it not that the Queen is an orthodox Chess piece that can move into check, and would automatically be assumed the same in other variants. Note that in your Metamachy description you use 'royal' in exactly the same meaning as I use it here, when you describe the Prince as "a non-royal King".

The term "royal" in this context specifically means the "capture/mate me to win" property. The term "prince" has been used both for pieces with the King-move but no such property (Tempête sur l'Échiquier comes to mind) and for pieces that serve as a backup royal (Chu Shogi, Tamerlane). Prince is a reasonable term for either, but the clarification is also reasonable.

Hello friends,

Two things. I would like to know what was not clear in my description of metamachy? I could make corrections.

Second, it is a bit severe against me as the inventor to write about the Prince "Despite what its name suggests, it has no royal properties". It moves like a King, I think this is a strong royal property. It can be checked, and this is logical, the capture of the Prince should not be the end. A Prince is not a King. Its name is well chosen or I miss something.

Best regards

Ideally, I want to treat Metamachy as a game in which White has the first move of the first turn but Black has a special setup move before White moves. The trouble is that the more complicated Game Courier has gotten, the more difficult it has become to change how it behaves. I have some ideas for what to do, but I also worry about breaking things to get it done. It also takes a lot of inspection of the code to figure out how it works and what can be changed. Some of my ideas might also be useful for supporting multi-player games, but that's another thing I have not added yet because of the difficulty in doing so.

Well, I guess black logically is the first player in Metamachy. Don't you have the same problem in Shogi?

I have made good progress toward making a rule-enforcing preset for Metamachy. The last thing to do is to enable Black to place pieces before White moves. Game Courier is not currently set up to allow anyone to do anything before the first player moves. One way to handle this would be to give the first move to Black, but this would involve inverting the board, switching the sections coding for each side, and listing White as the second player in the movelist. I would rather avoid all that, but that means working out a way to allow the second player a pre-game move.

I made a GC preset for Metamachy here.

Oh, it seems I broke something when making it possible to have multiple diagrams on one page: all collapsable legends now get different HTML IDs, so the test whether the legend table is open or closed, which decides whether you automatically get the default piece, now looks for a legend with the wrong name, and as a result considers it closed.

[Edit] OK, I fixed the JavaScript, and now you will have again promotion choice. (In the legend table, when it is open. When it is collapsed, you get the default piece, which is Queen here.) Don't forget to hold Shift down when you reload the Metamachy article, to also force loading the new .js file instead of using the cached one.

There's a problem here. The Pawns and Princes promote only to Queen, and never to Lion or Eagle.

Ah, but this is new information. You can also not make the jump when in check. I did not get that from the description on Jean-Louis' website.

Btw, it seems that this in-check business has been a seriously disputed issue at one time in the history of orthodox Chess, whether you could be in check by a pinned piece, or whether you could step your King next to an enemy King when you were protected (so that the opponent King could not legally move to the square your King was on to capture the latter). In Tai Shogi there is a similar issue, because there is a rule that says an Emperor (which is a universal leaper) cannot capture a protected piece, and it is not clear whether a piece is protected by the opponent Emperor (as he is also subject to this rule, and might thus not be able to recapture your Emperor if you had a second attacker to the square).

But I understand that this 'attacked' test in Zillions would never say that a piece is attacked by a piece of the same player.

Here's how the function works. It starts with the piece on the space it was already on before moving. It then verifies two things, that the piece hasn't moved, and that it is not attacked. The first checks an attribute of the piece, and the second checks whether an enemy piece could reach the space using its powers of movement. If these are both true, it continues to process the move. The $1 is a variable standing in for the first argument passed to the function. This will be a direction, and it will move in that direction to a new space. It then verifies that this space is not attacked. If this is true, it then proceeds in the direction provided by the second argument, $2. The one thing it verifies here is that the space is empty. If it is, it continues with the rest of the function. The next line sets the piece attribute "never-moved?" to false, which will stop the piece from making a second move of this type. The line after this is commented out. It would have set an attribute that appears to be redundant and unused. With the last line, the add command makes this an official legal move, understood in terms of the piece's powers of movement, but not in terms of whether the move would create an illegal position.

Consider the game of Chess. A King cannot legally move to a space the other King could otherwise move to, because then it would be moving into check. This implies that each King can attack a space it cannot actually legally move to. And this is what attacked means in Zillions-of-Games. It identifies a space that the King would be in check on if it moved there.

Well, I don't understand Zillions coding. But do you mean 'legally' as 'also not leaving the player in check'? I.e. would player A be allowed to move his virgin King from f1 to d1 if e1 was attacked by a Rook of player B that was pinned on the King of player B?

For orthodox Chess being in check is defined in terms of pseudo-legal moves, and 'not passing through check' would also forbid castling when a pinned piece attacks the square through which the King passes, and thus does not have a legal move to that square.

Capturing your own pieces is not even pseudo-legal, however, so I guess it is would never be a problem to jump over an enemy piece.

The code for the King's skip move looks like this:

  (define skip
( 
(verify never-moved?) 
(verify not-attacked?)
	   $1 
	(verify not-attacked?)
	   $2
		(verify empty?)
	        (set-attribute never-moved? false)
	   ;     (set-attribute never-skipped? false)
		 add
	 ))

The only condition on the first step of this move is that the space is not attacked. A space is considered attacked in Zillions-of-Games only when an enemy piece could legally move there.

OK, thank you for clearing this up. I will make the article conform to the Zillions implementation.

Perhaps you could try the following as well? (I don't have Zillions):

Is the not-passing-through-check rule also enforced when the square jumped over is occupied? And does it depend on the player to which the occupying piece belongs? Logically, if the King tries to move f1-d1, and e1 is attacked (by a Knight, say), it should be forbidden when there is a friendly piece on e1, but allowed if there is an enemy, as the Knight cannot capture the King on e1 when there also is a piece of his own on e1. (At least, I think so; it is not very logical in the first place that the King could be on a square already occupied by another piece, to be checked there...)

Thanks for putting this up. You didn't mention that the Prince moves as a non-royal King, one space in any direction.

I played both sides with Zillions-of-Games to get the ambiguities in the rules clarified.

When I attacked a space vertically in front of a King with a Knight, it could not leap as a Knight to the space the Knight was actually attacking, but it could still move as a Knight to the other space. So it looks like the overpassed square applies only to orthogonal and diagonal moves, not to hippogonal moves. But looking at the code, I see that the King is given two paths for each hippogonal move. So I setup a position where both the Mao path and the Moa path of the King to a particular space are attacked, but the space itself is not attacked, and the King could not move to that space. So the rule is that a King may make a Knight leap if there is at least one two-step path to the space with an unattacked space, and this path may be like the move of a Mao (Chinese Chess Knight) or a Moa, which goes diagonally, then orthogonally outward.

Also, while a Camel is attacking a space near the White King, it's within a Knight's leap away from the King, nothing is attacking any space the King would have to pass over, and nothing is protecting the Camel, yet the King cannot capture it. So it looks like the King's two-space leap must be non-capturing. Looking at the code, this is confirmed. The King may make its skip move, as it is called in the code, only to an empty space.

Finally, I setup a stalemate position, and Zillions reported that it was a draw. So it looks like stalemate is a draw.