Comments/Ratings for a Single Item

The snappiest way to describe the different crooked Nightriders wouild be
by the angle they turn through, to the nearest half a degree. These are:
37° (narrow diagonal); 53° (narrow orthogonal); 90 (Quintessence) 127°
(wide orthogonal); 143° (wide diagonal). Thus this game's end ranks
would
run 127° crooked Nightrider, Rose (curved Nightrider, alternating between
37° and 53° turns), 37° crooked Nightrider, straight Nightrider, King,
143° crooked Nightrider, 90° crooked Nightrider, 53° crooked Nightrider.
	For crooked Camelriders the angles are the same but with orthogonal and
diagonal swapped over. Crooked Zebra-, Giraf- &c. riders would have
completely different angles.

After a comment on one of my piece articles I have come up with some ideas
for easily-extrapolated angle-specific Crooked-piece names, using prefixes
and suffixes. In each case _____ represents the name of the straight
linepiece minus -rider (e.g. Night).
	Long_____flyer: 53° Night-, 37° Camel-, 67° Zebra-, 28° Giraf-
	Short_____flyer: 127° Night-, 143° Camel-, 113° Zebra-, 152° Giraf-
	Long_____sidler: 37° Night-, 53° Camel-, 23° Zebra-, 62° Giraf-
	Short_____sidler: 143° Night-, 127° Camel-, 157° Zebra-, 118° Giraf-
	Long_____flyer+Short_____flyer=_____flyer
	Long_____flyer+Long_____sidler=Long_____lady
	Short_____flyer+Short_____sidler=Short_____lady
	Long_____sidler+Short_____sidler=_____sidler
	_____flyer+_____sidler=_____lady

Quite .. er .. nutty ..

Just a thought, what if the King was replaced by a Royal Knight ? And the
pawns by Fergus's Cavaliers ?

Answering George Duke's question: Yes, the quintessence is two-path like
the other crooked pieces, e. g., the boyscout.

--JKn

The latter list features the Spiralspringer very well. Note the difference between german terminology and the terminology used here; what in german is called eng is called wide here, and what in german is called weit is called narrow here.

Note also, that Ralph Betza's Crooked Nightrider (combined narrow straight and diagonal crooked nightrider) is called Boa by problemists with the following reference given: R. Bedoni, Phé­nix (45) X 1996 S. 3344

Carlos Cetina proposed an even more elegant solution to this minor problem:

'My suggestion is to place the armies under the reversed symmetry principle. That is the true simplest and elegant solution. Then both the king and the rose would protect the [before] undefended piece.'

I agree completely and shall accordingly implement his idea for my preset.

The Quintessence lacks the can-mate property on regular rectangular boards. The necessary piece of analysis goes as follows:

There is only one mating position with King and Quintessence vs. King, namely Black: King a1, White: King a3, Quintessence d2. Note that the position with a white King on b3 is a stalemate because the white King now blocks the check against the black King.

To force the the black King to a1, the position prior to the mate must look like Black King b1; White King a3, Quintessence controls squares c1 and c2. This can be done with Quintessence on b4 or d4. However, there is no quintessential move from b4 or d4 to d2. Therefore no mate can be forced.

The compound of Quintessence and Rook is namend Leeloo in Quintessential Chess after the Fifth Element in Luc Bresson's film.

The compound of Quintessence and Queen is namen Pentere (with synonym Quinquereme) in Quinqereme Chess

The missing compound of Quintessence and Bishop I name Sai after Fujiwara no Sai, the ghost in the Go board in the manga Hikaru no go. Go is in japanese homophonous to the number 5. The ghosty connection is suggested by the analogous pieces Banshee (Nightrider-Bishop compound) and Dullahan (Knight-Ferz compound). Speckmann also reports that the Janus/Paladin (Knight-Bishop compound) was called "die reinste Geisterwaffe" (a pure ghost-weapon) by a problem solver.

The Sai is even stronger than the Banshee (having more directions and attacking more fields on the same board), but seems to be less tactical on 8 times 8. Because of its strength I wasn't yet able to design a CwDA army for the Sai. A simple modification of the Fearful Fairies is not possible.

Jörg, I very much enjoy the game and exploring these pieces. You are a very good variant designer and thinker about chess variant fairy pieces.

I also like Quinquereme and I'm very excited one day to try experimenting with your CwDA army, Sai Squad (as well as your other CwDA armies). 

I am trying to get an idea for an estimate of the strength of these Nachtmahr pieces - I believe the Rose is strongest, maybe followed (in order of strength) by straight wide crooked nightrider, quintessence, regular nightrider, diagonal wide crooked nightrider and diagonal narrow crooked nightrider. Any thoughts? Maybe after more experience, I will have a better theory - these are just vague guesses.

How might the Nachtmahr army fare against FIDE? It's commonly thought that a normal nightrider is worth as much as a rook on an 8 x 8 board. I suppose the Nachtmahr army would handily defeat the FIDE army...

/play/pbm/play.php?game%3DNachtmahr+vs.+FIDE%26settings%3Djudgmentality

If you please, what are the names for pieces other than rose, nightrider (qua nightrider) and quintessence? In your notes, you mention a French and German name but you don't say which piece specifically these names apply to...

Also, Carlos and I are having a bit of discussion about the Quinquereme - he created a nice diagram which you can see here: 

http://www.chessvariants.org/index/listkibbitz.php

I have ideas about some other nightriders one might develop for fun and a sort of game design for a Nachtmahr 2 (which I might call something more akin to "a dream") introducing some of these other nightriders.


Please email me if you're interested in discussing or as a courtesy, I shall email you when I've come up with an actual variant. It too will be a "study game" but maybe playable as well...certainly I am having fun playing Nachtmahr right now and it's, at the very least, helping me to become more familiar with how these pieces move.

An excellent to Carlos Cetina for the really nice diagram.

All Knight moves in the first step are "equal" (in the sense of symmetry), but the continuations fall in two classes that Jelliss terms "3D" (crossing the diagonal, the pure trajectories in Carlos' diagram) and "3L" (crossing the lateral, the "impure" trajectories in Carlos' diagram). Here's a reference on the terminology:

http://www.mayhematics.com/t/2b.htm#%282%29

Splitting the Quintessence into a diagonal and lateral piece is surely feasible and the pieces should both be very playable.

--

The German and French term (Spiralspringer and Cavalier spirale) are generic (like crooked Nightrider), for further precision they are qualified (German: enger Diagonalspiralspringer = wide [sic!] diagonal crooked Nightrider etc.)

--

Yes, the Nachtmahr army put a lot more of strength on the board than the FIDEs: Just exchange whatever Nightrider against Queen, the Rooks, and one Bishop and you are left with a stronger rest of the army. And because of the huge forking power of the Nahctmahrs, I don't see a chance for the FIDEs to avoid this.

--

On relative piece strength: The here termed "wide" pieces are clearly the strongest: They have an enormous "capturing density" and the can-mate property. The classical Nightrider is the weakest, the others are in-between.

--

I'd like to see your design of Nachtmahr II (allthough I cannot promise to have time for discussion)

We can get a first approach to the relative strength of these nightriders by placing them on the central square (g7) of a 13x13 board and counting the number of squares affected/checked from there.

Doing it, we would find these results:

Hence, the following equivalences should be near to be true:

NN11 = NN00 + NN33 = NN00 + NN21 = NN31 + NN04 = NN02 + NN04

There are reams more nightriders mostly unutilized than the ordinary hack one developed by Dawson a century ago. So far they remain in problems and thought experiments.  Classic essay here proposes Straight Wide Crooked, Diagonal Narrow Crooked, Diagonal Wide Crooked, and Straight Narrow Crooked.  Best of all, the essential nightrider Quintessence.  Each one makes better more interesting play than Betzan-tagged 'NN'.  Play of that ordinary Dawson nightrider is inferior because it just duplicates successive Knight moves same direction.  It is no more interesting than "limited" pieces like an up-to-three-step Bishop or Chess Different Armies Short Rook.

Quintessence itself gets play in odd-shaped 84-square Quintessential Chess, adding also  Leeloo compound R + Quintessence.  

Quinquereme takes it up to 12x12 with the same Quintessence.  Each of the various nightriders in combinations, one and two of each together with some of the other 6 or 8 piece-types in the set, on different board sizes can create thousands, well millions easily, of individualized CVs.  Worth exploring in the abstract are the standard boards 9x9, 9x10, 10x10, 10x12, 12x12, 10x16.  All the large sizes should have a variant nightrider species for improved implementations. Even rudimentary Dawson NN of such wide appearance is superior to also-overused Carreran BN and RN, four hundred years beat to death.

wouldn't a 8th nightrider be possible which goes left-right for both vertical and horizontal moves?

There is no SVG image for the Rose, so I used a butterfly. SVG images for nighriderwazir and nightriderferz do exist, but there are no PNG renderings of those.

There is no SVG image for the Rose, so I used a butterfly. SVG images for nighriderwazir and nightriderferz do exist, but there are no PNG renderings of those.

I will take care of these this weekend.