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About piece names: F-then-DD is used in one of David Paulowich's games, with a compound with rook too (Spotted Gryphon and Chainsaw). I recently thought of a F-then-W-then-DD piece. About Man-and-Beast, those definitely deserve a rework

Ski-sliders are another example. The Ski-Bishop starts like Alfil, and then continues as Ferz-rider (= Bishop) in the same direction.

Yes, the Seeping Switchers army uses this idea. The rook you describe is called the Slip Rook there.

Last night I was thinking of bent riders that are not bent in the sense of changing direction. I suppose they are among the 25 possibilities Betza mentions, but I don't think he elaborated on them. One piece I was thinking of would initially move as a Wazir, then if it continues, continue as a Dabbabbah-Rider. Unlike the Dabbabbah-Rider, this would not be color-bound. Another one would initially move as a Ferz, then if it continues, continue as an Alfil-Rider. Unlike the Alfil-Rider, this would be able to reach every space of the same color instead of just half of them. I was thinking I might call these the Shifty Rook and the Shifty Bishop and their compound the Shifty Queen. Has anyone used these pieces before?

Iirc what happened with the diagrams was that after they were added some changes were made to Fergus' Diagram Designer which meant that the FEN Charles used no longer generates dots in the images (M&B09 actually got off pretty good here as most of the diagrams there have numbers); Charles seems to have disappeared though so noöne has fixed them.

I agree it's a long and difficult piece of writing, all the more so because of how much it has to get through; and it takes some time to get familiar with (though as you say, there's a bunch of interesting things in there, including stuff which he's thought of by exhaustion that occasionally comes up in these comment sections with questions as to whether anyone's though of this yet). Not sure how easy it'd be to rework though without making it several times longer still… (maybe it'd work as a series of videos??)

Alas this Man & Beast series for me is frustrating. For reasons I don't know, I see no moves on the diagrams, only a large chessboard and a poor lonely piece in the center. The accompanying text is so long, difficult to get something useful. Too bad because it is a huge work with probably a lot of good points inside. It will deserve a rework.

Wrt piece names, Gilman's Man and Beast series is always worth looking at if you can find your way around (it's invaluable for its comprehensiveness if equally forbidding for its density)

In particular wrt bent pieces, M&B09 suggests Anchorite for W‐then‐B (“after a kind of religious hermit” that sounds like ‘Aanca’, which he rejected for similar reasons). D‐then‐B (Osprey in another variant that came out earlier this year iirc) is suggested as Lama, and its counterpart A‐then‐R is a Zephyr.

N‐then‐B (the GA unicorn/rhinoceros) is omitted, presumably as being too similar to Anchorite (since it can be equivalently described as W‐then‐Ski‐Bishop, perhaps it's a ‘Ski‐anchorite’?).

Cazaux's suggested Dragon and Basilisk are, as HGM found, Betza's Reaper and Harvester (mentioned also in M&B13) — their compund the Combine probably also qualifies as ‘more than crazy’ :D

Piece 3 is, for Gilman, a Fimibrated Gryphon, while piece 4 (if not a typo for “(W-then-B) + (D-then-B)”, which would be a fimibrated anchorite) is M&B13's Ancress, except that the rook component is Ski‐; the ancress' counterpart, gryphon+bishop, is a Metropolitan.

Fwiw, M&B09 suggests Contra‐ versions as well, which make the sliding move before the leap

Not sure if any besides the Tripunch set have been used though…

Thanks a lot

I am pretty sure I have seen a variant here that used such 'triple-barrel' sliders. I think it was by Betza.

I found it! The variant was called Tripunch Chess. Betza calls Piece 1 (Gryphon + Rook) a Reaper, and Piece 2 (W-then-B + B) a Harvester.

I am pretty sure I have seen a variant here that used such 'triple-barrel' sliders. I think it was by Betza.

In the 'more-than-crazy' limit, such pieces become 'hook movers'. These are known from the large Shogi variants in the flavors that turn a 90-degree corner. (Orthogonal: Hook Mover; diagonal: Capricorn & Long-Nosed Goblin. The latter has an additional Wazir move to break the color-binding.) But this is not qualitatively different from turning a 45-degree corner in an arbitrary point along the trajectory. Like the Hook Mover the 45-degree benders cover the entire (empty) board, but they can only reach each square through a single path. While the Hook mover had two paths to most squares. OTOH, the path to a given square is shorter than the paths of the Hook Mover. So I would not know which piece is stronger. The compound of B-then-R and R-then-B (plus R plus B) would definitely be stronger than the Hook Mover.

Another piece I wonder if it ever was used is Nao

I was thinking of some very mighty pieces, probably playable only on very large board, 12x12 or more.

Those pieces could threaten wide bands of lines

Piece 1: compound of Gryphon/Eagle + Rook (I once suggested to Zied to call it a Dragon)

Piece 2: compound of (W-then-B) + Bishop (I once suggested to Zied to call it a Basilisk)

Piece 3: compound of Gryphon + (A-then-R)

Piece 4: compound of (W-then-B) + (D-then-R)

Why stopping there, one can have also compound of P1+P3 and of P2+P4, threatening even wider bands, probably more than crazy.

I was wondering if anyone had used them in CVs?

I was thinking a few days ago about pieces that HG would call R2 then bishop and B2 then rook, meaning a further weakening of the gryphon and aanca. They come natural to me but I'd like to hear other people thoughts.

I have made significant edits to this page to fix the inaccuracies while preserving all Betza was trying to say (including extraneous stuff.)  The edits, along with justificaiton and any extra information I had available, have all be documented in footnotes.

I spent more time on this than I had expected, given that I don't really like this page anyway.  A new page on bent riders befitting a piececlopedia would be beneficial, but in the meantime, this page should hopefully at least be accurate (the board game preferences of space aliens notwithstanding.)

Yes Fergus, this is the kind of analysis that we've done. But of course not only 1 passage must be checked, any "theory" has to be tested with other passages of the text. Basically, this is what Sonja has done in her PhD.

To go further on this particular passage, the authors used the verb "to do" instead of "to go". Let's do more litteral:

"corre mucho desque comienca & faze ante en salto en trauiesso como Cauallo."

>> runs a lot when it begins & does before a jump in oblique as a Horse

"& assi lo establecieron en este acedrex que anda el primer salto como Cauallo"

>> & so they established in this chess that walks (anda) the first jump as a Horse

& depues en sosquino como la Cocatriz fata do quisiere; o que tome.

>> & then in corner as the Cocatrice (mythical animal probably inspired by the crocodile. Consider that no crocodile was frequently seen in Castile in those days) does as it wants; or take.

(the punctation ; is given in the numeric Spanish text)

"E daquella casa o salta non puede tornar a tras si non yr siempre adelante."

>> And from that square where it jumps cannot turn back but goes (yr) always forward
 

Again, there are several points where Murray went wrong with this text. Murray was quite good at many languages, not sure he was with Spanish. Another possibility, I believe it, was the poor consideration that Murray had for those large chess variants. I can elaborate on this if you want.

All my best,

I don't know Spanish, but based on the English translation, I can see where Murray would get the idea that the Unicorn's Knight move is non-capturing. This part of the description makes a distinction between go and take: "then goes in corner like the Crocodile does when it wants to go or take." This suggests that "go" is intended for non-capturing moves, and "take" is reserved for capturing moves. In the first part of the sentence, he just uses "go" in reference to the Knight part of the move: "It goes the first jump like a Horse." To be consistent with the use of "go" in the later part of the sentence, that part could be understood as non-capturing. However, the sentence seems to use "go" inconsistently in the middle. When it says "goes in corner," this is followed by "like the Crocodile does when it wants to go or take." If we consistently used the word "go" to mean a non-capturing move, then the piece could not capture at all. But that seems unlikely. Whichever interpretation we go with though, "go" is still being used in two different senses in this sentence. I'm not sure if this is a problem with the translation or with the original text. Would a more literal translation avoid this equivocation?

Hello all. I'm reading the thread with some days late. I believe I can answer some questions. You have to know that Sonja Musser from the USA, has defended her PhD on the Libro de los Juegos, the Alfonso X's codex, few years ago. On that particular aspect of the Grant Acedrex, I worked with her analysing the Spanish text. Sonja and I speak Spanish. The language used here is a medieval Spanish but it is not a big problem to understand it because that medieval Spanish has more latin roots than the modern one. 
You can find the full text on the web and large extracts concerning our Grant Acedrex on my own website here (Spanish text AND Sonja's English translation) : http://history.chess.free.fr/acedrex.htm

The original text and a litteral translation are also given in A World Of Chess, my most recent book.

You will see that we had 2 possible interpretations for the Unicornio, which is clearly a Rhinoceros, nothing else, in the mind of the author of the 13th century. When writing A World Of Chess with my mate Rick Knowlton, we considered it again, and Rick finally convinced me that the most probable interpretation is the more natural N-then-B. I will try to update my website today.
I have studied Murray's a lot and owe a strong respect to his work. What he did is unsurpassed. No one can do something like this today. That being said, Murray's look on chess variants was not very deep. He did not have a lot of estimate for them, being more attracted by chess and its direct ancestors. He made several mistakes, especially on Grant Acedrex, but also on others like Ciccolini's chess. Having access to original sources we have corrected many small details like this in our book A World Of Chess.

To answer the last question from Fergus whether the Unicornio was capturing or not on its initial N's move: Murray affirms that cannot, but the text does not say that. The text says: 

"corre mucho desque comienca & faze ante en salto en trauiesso como Cauallo. & assi lo establecieron en este acedrex que anda el primer salto como Cauallo & depues en sosquino como la Cocatriz fata do quisiere; o que tome. E daquella casa o salta non puede tornar a tras si non yr siempre adelante." (in these times they used an u for a v)

Which means (literal translation)

it runs a lot when it begins and begins with a sideward jump like a horse, and so does it in this chess. It goes the first jump like a Horse and then goes in corner like the Crocodile does when it wants to go or take. And from that square where it jumps, it may not turn back, it shall always go forward.

In Grant Acedrex, the Crocodile moves as the MODERN Bishop. (Bishop at that time was an Alfil). 

Could the Rhino take when jumping as a Knight? Personally I believe yes, but nobody knows.

We have no more information. People from 21st century shall realise that those of the 13th century didn't have the Internet and a community of chessvariant enthusiasts to comment and discuss any tiny points of the rules :=) 

Hope this helps.

Note that there is no indication whatsoever that the first step of the Grant-Acedrex N-then-B would be non-capturing in the Alfonso codex. This just states (after describing the real-life animal as a Rhino):

First, like leaps like a knight. It may remain on
that square if it wishes or may also continue to any square on the diagonal(s) of that square,
maintaining its movement in a forward direction from that square

I don't know where Betza got the idea (which he then himself rejects) that the piece could have been divergent.

Given that the game had no Knights, leaving the piece vulnerable to Knight attacks would not have been important. But making its Knight move non-capturing would leave it vulnerable to all of the Gryphon's moves. It would also diminish its usefulness for defense, which would help make the game more decisive. Since the Gryphon is the most powerful piece in the game, there is less need to diminish its usefulness for defense. After all, it is the main piece that a player will use for offense if it is available. But if the Unicorn could capture with its Knight move, there would be more tempatation to use it defensively, and that could make the game more drawish. So, I think that Gryphon/Unicorn is a better choice for a game than the other two pieces used together.

Indeed. The W-then-R and F-then-B would have overlapping paths, which could be considered a design flaw.

All these pieces have a leap followed by sliding. Of course there also are the 'hook movers' of the large Shogi variants, which have both legs of their move a slide, which makes them immensely powerful.

In the same place was described a piece called the Unicorn, moving as Knight then Bishop. Supposedly the Unicorn couldn't make a capture using its Knight move, but I'll ignore that silly rule.

Not described there is a piece which makes a one step Rook move and then continues outwards as a Bishop. For lack of a name, I'll call it the Aanca (13th century Spanish for "Gryphon"). Although the Aanca is not described, one can suppose that the same mind who conceived the Gryphon and the Unicorn probably also considered the Aanca.

I don't know if Betza ever visualized movement diagrams for these pieces. Assuming non-overlapping paths of movement, the Unicorn covers most of the same spaces as what he calls an Aanca. One of the main differences between them is that the Unicorn cannot attack any of the same spaces as a Gryphon, whereas the Aanca and the Gryphon can both attack the same spaces as a Knight. This would have been an intelligent design choice, and not a silly rule, for the following reasons:

• It makes the Gryphon and the Unicorn complementary like the Rook and Bishop are.
• It gives the Unicorn greater mobility in tight spots, which could increase it's usefulness in the midgame.
• It leaves the piece vulnerable to the Knight and keeps it from forking pieces like a Knight.

So, it seems likely that the designer did consider the "Aanca" and for the reasons I gave, rejected it in favor of the Unicorn.

Likewise, the Gryphon and what might be called the Hippogriff cover nearly the same spaces under the assumption of no overlapping paths. So that paths don't overlap, its orthogonal move could continue only in the direction of the longer part of the Knight leap. Like the Unicorn, the Hippogriff would have more mobility in tight spots, and its short-range attacking power would be crippled. If it were allowed overlapping paths, it would be a monster piece that could force checkmate against a long King, because it could attack adjacent ranks or files.

To prevent confusion it is probably best to drop the name Aanca from English completely. We could have:

• F-then-R: Griffon
• N-then-R: Hippogriff
• W-then-B: Antigriff
• N-then-B: Monoceros

There are some other possibilities with 90-degree bends:

• W-then-R: Ultragriff, the logical extension of the series Hippogriff -> Griffon -> Ultragriff
• F-then-B: Chirogriff. (Entirely new move pattern, chimera of a Bat (Chiroptera) and a Lion, with claws at the tip of its wings.)

Logically the degenerate cases (which make a 0-degree bend) also belong in this class

• D-then-R: Ski-Rook
• A-then-B: Ski-Bishop

I think I have to revise the spelling in Apothecary Chess Modern then for both Griffin and Aanca!

So, Ancaa (or Anqa) is not really another word for Gryphon (or Eagle for that matter), but a mythological creature with no parallel to a mythological creature known to English speakers. This would make sense, given that mythological creatures are made up, and different cultures are unlikely to have the same ones. It's sort of like translating the Korean Gumiho (nine-tailed fox) as a werewolf or the Japanese Oni as a demon. In that case, I don't object to using each name for a different piece. It's just a bit awkward that Betza lifted the name from the Spanish name of a piece he was using the English name for with the description given for it.