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Quintessential has only the one other comment idle over 7 years. Natural Quintessence is two-path to the first Camel square, but not to the first Knight square since it's a leap. How about all its other arrival squares? Pawn Bockspringen speeds up 10-deep.
Over 4 years incredibly since excellent Quintessential(2002) is even Commented, where the best Nightrider appears from Knappen's 'Nachtmahr' article earlier in 2002. The previous Comment is Game Design Analysis, of which I charted up to 100 for different CVs, requiring piece values and using formulaic evaluation.
Quintessential Chess design analysis
#squares: 84
#piece types: 7
Piece-type density: 8.3%
Est. piece values: P1, K2, D5, Q6, J7, C7, L9 [Janus and Centurion are
close in value; on board any smaller C>J]
Initial piece density: 48%
Long diagonal: c1-j8
Power density: 1.64
Exchange gradient: 0.502; (1-G) = 0.498
Ave. game length projected: M = 3.5*Z*T/P*(1-G) =
3.5(84)(0.083)/(1.64)(0.498)= 30 Moves
Features: Diagonal-moving pieces predominate, yet values separate
enough that a typical Gradient appears.
Comments: To estimate these piece values takes more than usual sliding
of values up and down til they become appropriate
Charles Gilman wrote on Fri, Jan 9, 2004 10:08 AM UTC:Sorry for filling up the 'most recent comments' section, but I have just discovered that the -essence names are unnecessary. After looking at the Crooked Bishop and Crooked Queen I discover that what I termed Primessence and secondessence are in fact the Crooked Rook and Crooked Bishop. By extrapolation the Quintessence itself is a Crooked Nightrider. It also means that the Nonessence can be broken down into its orthogonal and 3d oblique components.
Correction to my previous comment: the 5th-generation move of the Quintessence has of course a SOLL of 65, which manifests itself as either 7:4 or 8:1. It is easy to get confused after a number like 40.
The reason why all the third-generation Quintessence moves have a length of 5 can be seen by comparing with a similar piece built up from the Wazir move rather than a Knight move. Such a piece might be called a Primessence. Successive-generation moves would have squares of leap length (SOLL) of 1 (Wazir), 2 (Ferz), 5 (Knight), 8 (Alfil), 13 (Zebra), 18... As the Quintessence starts with a Knight move, SOLL 5, all its moves get correspondingly mutiplied so that its moves have SOLL 5, 10 (Camel), 25 (5 squared), 40 (Caravan), 52 (Zerriage)... You could also have a Secondessence built up from the Ferz move, a Quartessence from the Dabbaba move, a Decimessence from the Camel move, and many others. In 3d Chess a Nonessence could be built up from 3:0:0 and from 2:2:1 moves (though not from a mixture), but there could not be a Sextessence as no 2:1:1 moves are at right angles.
I rated Quintessential Chess as excellent in my group's voting toward finalists in 84-space contest. Jorg Knappen's previous article 'Nachtmahr' establishes Quintessence as probably the best of nightrider species. (The camel square being also next logical one after rook-knight-bishop coverage) Bishop-like pieces (Janus, Dragon Horse) are correct complements to challenging Quintessence maneuvers; only Leeloo can move rookwise. Seven piece types make long-term strategy manageable not whimsical. Pawn's bockspringen likely being new idea, Squirrel/Centurion completes the mix so as to cover all pawns initially. Great game.
Anonymous wrote on Thu, Nov 7, 2002 07:56 AM UTC:Peter Aronson asked: > I assume that leap-riders can pass over missing squares as long as > they don't need to land on any of them? Yes, this is exactly what I wanted to say. > If I understand correctly, the Quintessence has 16-paths; that is, > two versions each of all 8 Camel-rider paths. Do I have that right? Yes, this is right. The 16-fold path does not really materialise before the fifth generation of the quintessence move: In the first generation there are 8 directions, in the second 8 directions with two ways to reach the target, in the third generation there are 12 directions, 8 with one way and 4 with two ways, in the forth generation there are again 8 directions with two ways. The third generation move of the quintessence is a lame 5-leaper move, both the (0,5) and the (3,4) moves are there. --JKn
A couple of questions:
<p>
<ul>
<li>'<i>Leapers may jump over the missing fields in the corners,
but riders can't ride thru.</i>' I assume that leap-riders can pass
over missing squares as long as they don't need to land on any of
them?</li>
<p>
<li>
If I understand correctly, the Quintessence has 16-paths; that is,
two versions each of all 8 Camel-rider paths. Do I have that right?
</ul>
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The Quintessence is the best species of KnightRider, along with regular Betzan NN the latter not in this CV -- double letter is always rider able to stop at any distance. Knappen removes corner squares from ten by ten to get 84 squares for an 84-square contest. The Quintessence makes successive right angle changes of direction.
Pawns are fast-moving with always having two-step option, and additonally have what is called bockspringen. Leeloo is Rook plus Quintessence. Centurion is tri-compound Alfil plus Dabbabah plus Knight. Dragon Horse is Wazir plus Bishop. It would be interesting to find point value of these pieces, accompanied as they are by only one "conventional" CV piece, the Janus, who is commonplace 400-year old Centaur as B+N. To get the piece values for Quintessence, Leeloo and Squirrel/Centurion, the three really novel p-ts, there would have to be discount for having to face off against the strong and unusual Pawns/Bauern.