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Oops! I have made a programming error in the Guanaco. The black Guanaco can only make one two-square jump toward the white position. This makes it much weaker than the white Guanaco, of course. The reason why I missed this is because I only tested the game with the white side, and the white Guanaco moves correctly. (I had simply forgotten to insert the 2-jump directions into the symmetry statement.) The programs which contain the Guanaco are the following, which have been corrected.
http://hem.passagen.se/melki9/guanacochess.htm
http://hem.passagen.se/melki9/pilgrimchess.htm
http://hem.passagen.se/melki9/pioneerchess.htm
/Mats

Yes, it seems I have to go 'back to basics', and first make sure that the
program handles the pieces well. I was running the test where the Guanaco
did so poorly with programmed-in values that had the Guanaco worth slightly
less than a Knight (240 vs 259 in the peculiar micro-Max internal units
that have B=296). So the problem you mention could not have occurred.

I did not program the Guanaco as a piece that has to be centralized,
however. Fairy-Max knows two kind of pieces, those that are lightly) drawn
to the center (Kings, Knights and Bishops), and those that move neutrally
over the board (which works better for Rooks and Queens). I programmed the
Guanaco as belonging to the latter group, because I figurered that its rider
moves woud make it behave like a Rook, while the Llama was obviously short
range and not very valuable, so the center was the obvious place for that.
But perhaps the Guanaco has to be centralized to perform well. This can
matter a lot: for the Lion (FWADN) I initially figured that it was too
valuable to centralize it (it would only be chased), but giving the program
a drive to centralize upped its value by nearly half a Pawn.

So the first thing I will do now (last night's tests were spoiled by
auto-updates...) is to test a symmetric position with Guanaco-for-Knight
substitution, between two differently configured versions of Fairy-Max, one
that centralizes the Guanaco, the other that doesn't. (And perhaps repeat
it with Guanaco-for-Bishop substtutions, or GG for BN.) This should tell me
if a Guanaco gets you more when it is centralized.

After that I will do a a Guanaco vs Llama test, between idenical engines
that handle the Guanaco in the way that proved best. In this test I will
configure the Guanaco only very slightly above the Llama in value. We know
the Guanaco must be better. This should result in an initial empirical
Guanaco-Llama difference. The test should then be repeated with this value
programmed in, for confirmation.

One question: would the end-game you show not be equally won when black
had a Llama rather than a Guanaco? That it is won might be due more to
thefact that black has an extra Pawn, while white has two very awkward
Pawns (one backward, one isolated) than to the Guanaco being so powerful.

It is obvious that the Guanaco is very strong in endgames with pawns, so
the results are strange. In a replacement test it's necessary to tweak the
value of the knight to be the same as the value of the Guanaco. Otherwise
the knights become dominant while they can chase away the Guanacos. The
Alpaca and the Llama have this advantage against the knight, too.
/Mats

Hmm, I am starting to doubt that the Guanaco is anywhere near a Bishop in
value. In the match of two Guanacos vs two Knights the Knights lead by 80%.
Strange thing is that two Llamas vs one Knight seems to go towards a very
clear victory for the Llamas (64%, which suggests a difference of the order
of a Pawn). All this after a mere 100-150 games, so with a sizable error
bars. But these results would put a Guanaco quite close to a Llama, which
is a bit strange, as it is clearly upward compatible with it.

Perhaps I should start with a test of two Guanacos against two Llamas, (say
as Knight replacements), to get a direct measure of how much the difference
between the two really is. It might be that the distant non-captures are
pretty useless. Thee are only few squares from which you can actually make
them on 8x8, and perhaps the Llama is already fast enough.

One thing I can confirm straight away, though: Both two Llamas and two
Alpacas make a generally won end-game. (Maximum distance to mate 43 or
51 moves, respectively.)

Thanks for this. One factor which is very important in the Guanaco and the
Alpaca is that they become quite strong in endgames with pawns. They can
rather easily attack a pawn chain while they can move to an adjacent square
of a different colour, and hop over pawns. To attack an enemy pawn chain
could be impossible for a bishop of the wrong colour, and be somewhat
difficult for a knight, while it has to maneuvre many moves. I found that
Zillions has difficulties handling the Guanaco in the beginning while it
demands planning. You must maeuvre it in order to use it, so it's not the
ideal piece for computers. Therefore one cannot expect that the replacement
test will work very well. The Guanaco is very strong in the endgame, and
two Guanacos plus king seem able to checkmate an enemy king (needs to be
verified). If this is true then two Alpacas would also be able, together
with the king, to give mate. The Llama has fewer capture squares than the
Alpaca. Only on the inner 6x6 square it has four capture squares. So I
suppose it's worth somewhat less. On the other hand it can threaten at a
two square distance. Notice also that the Guanaco *slides* on the squares
on which it stands. In a sense, it is an orthogonal bishop.
/Mats

OK, I started some tests of the Lama pieces. As they are regular Chess
pieces that fit in the Betza classification scheme, Fairy-Max can handle
them without modification. Both Lama and Alpaca are handicapped versions of
the Woody Rook (Betza WD). I tested this Woody Rook in the context of Great
Shatranj, and IIRC it tested as slightly less than a Knight. From my
current understanding of short-range leaper values, WD should have been one
of the weakest of all 8-target leapers, due to the small number of forward
moves. And forward moves seem to contribute about twice as much to the
overall value as backward or sideway moves. But I guess the global property
of having mating potenial is worth some extra bonus.

The Lama and Alpaca should be practicaly equal in value; moves of 1 step
seem to contribute to the value of a piece about as much as moves of 2
steps in the same direction. If I would have to do a prediction, I woud use
the formula Value = (30+5/8*N)*N, which would put 8-target SR leapers at
280 (centi-Pawn). I would count non-capture moves in the second factor N
only for 1/3, though, so that we would get 35*16/3 = 187 cP.

For rider-like pieces like the Guanaco I have no theory yet.

I started tests by replacing the Knights of one side by Lamas, to see how
badly they are beaten. I will then probably switch to replacing two Knights
by 3 Lamas.

On the other core of my C2D I am playing a substitution of 2 Bishops by 2
Guanacos. I will keep you posted.

(I cannot promise I will be able to complete all necessary tests shortly,
As I might need the computer to test my Xiangqi engine HaQiKi D, which I
entered in the World Championship in Pamplona, taking place early May. And
I still have a lot to improve on that before I will have any chance on
winning there...)

Joe, these pieces can also make a non-capturing move to capture square. The Alpaca is interesting because it can sometimes invade the enemy position by jumping, and drive away enemy pieces while they have a higher value. However, it is a common theme that a light piece is exchanged for Alpaca + pawn. Pieces valued 2 are interesting, as long as they are short-range, it seems. I have now also implemented the Vicuña, which captures only on the second square, and jumps continuously. A peculiarity is that the Guanaco can continue jumping although it has a capture possibility on the first square. This is wholly logical. I decided to call this category Lama pieces, after genus 'Lama'. I don't know how good they are, but they can be tested in my programs. They are described here:
http://hem.passagen.se/melki9/llamapieces.htm
/Mats

Nice-looking set of short-range pieces there. I do have a question, though.
Do the Llama and Alpaca have a non-capturing move to their capturing
squares? I don't find the definition precise enough to tell, although
based on the description of the third piece, it appears they do. You did
not intend to have the pieces move only one way and capture only the other,
I don't think, or did you? Still, either way, they make nice pieces. With
the different movement and capture modes, they are very reminiscent of the
excellent game Separate Realms, by Peter Aronson and Mike Nelson.