Comments/Ratings for a Single Item

On the naming of combined leapers: I developed a family of combined leapers
for Beastmaster Chess.  Positing the Horse's move as three squares
including a turn (another way of describing a 1,2 leap), I used pieces
with four, five, and six square moves including a turn.

The colorbound Roc is (1,3) + (2,2), Camel+Elephant.
The colorchanging Pegasus is (1,4) + (2,3), Giraffe+Zebra.
The colorbound Wyvern is (1,5)+(2,4)+(3,3).

None of these names is in =common= use elsewhere.  Pegasus found its way
into ximeracak. as well.

I've been trying out the Gnu as a chess piece and really enjoy playing
with it.  One variant it does well in replaces knights with Gnus and
bishops with FADs and is otherwise orthodox.  A pretty simple change but a
very different game than FIDE Chess.  The Gnu seems to be a pretty strong
piece, with 16 squares it can move to from the middle of the board.  I
wonder if somebody with some experience estimating piece values could say
what they think it would be worth, relative to the orthodox pieces.  If a
pawn is worth one point, how many points is a Gnu worth?

I have that same question concerning the other oblique leaper compounds. 
In particular:

* The Bison (Camel+Zebra)
* The Gazelle (Knight+Zebra)

(Incidentally, I've noticed that the latter piece isn't in the
Piececlopedia, and I wonder if 'Gazelle' is even an agreed-upon standard
name for it or where it comes from, etc.)

I suspect the Gnu is the strongest of those 3 pieces, and I don't know
whether Bison or Gazelle would be next-strongest.  The Gazelle has to
change color every time it moves, which is not the case for the other two
pieces, which might put it at a disadvantage.  But then again, both of the
Bison's attacks are longer than the knight move, which makes me think it
might be a weaker piece.  Has anyone considered these questions?

Thanks from a new fairy chess amateur.

The Gazelle is a pretty standard name for the knight/zebra compound.
There are many pieces not mentioned in Piececlopedia.
If you have Zillions of Games, download my game 'Piece Promotion Games 2', it has the Gnu, Bison and Gazelle in it's variants. Zillions rates these pieces as follows ..
Gnu 16,338
Gazelle 15,245
Bison 14,316.
Also you can see the Buffalo (knight/camel/zebra) and Squirrel (knight/dabbaba/alfil) in this game.
Another place to look at different fairy pieces is
http://www.mayhematics.com/v/gm.htm

Christine, thanks for responding so quickly.  I do not currently have
Zillions, but I may check out your game recommendation if/when I get it. 
From Zillions, you give the ratings: Gnu 16,338; Gazelle 15,245; Bison
14,316.

Is this in terms of 'pawn value = 1'?  In that case, I would assume your
commas are decimal points and that we're talking about a Gnu being worth a
little over 16 pawns, a Gazelle around 15 and a Bison around 14.  That
seems much stronger than I was expecting!

But I wonder if I misunderstand how Zillions rates pieces.  Is there some
other unit in use here?

Thanks in advance for the clarification.

I dont really understand what you mean when you say '.. the Gazelle would be weaker, and that that was why it was not popular enough to merit a Piececlopedia page.'
I don't think a piece not mentioned in piececlopedia means something negative about it. 
I think Fergus is in charge of this page, but anyone can write about a piece and put it up for being added to the page. There are many fairy pieces in existence and if one person is in charge of the page, i can easily see why it doesn't have every different piece under the sun added, too big a job if you have a life hehe. 
The ratings i gave is what 'zillion's' gives the piece, i am not saying that this is correct either, it just give's you an idea, i'm sure there are people who probably can give more 'correct' answers to the strength of these pieces.

Bison > Gnu > Gazelle should be right order of three very close bi-compounds on board greater than about 72. They should each rate nearest 6.0 than any other whole number? Then too I still say Falcon(reducing to 5.0 after so many moves) > Rook(5.0) very slightly on 72-100, and Muller has temporarily ''proved'' that wrong; so Zillions too may have some different rationale hard immediately to dispute. Besides colourswitching handicap of Gazelle, Gilman would say correctly that longer-range weaker value does not kick in yet at Bison (1,3 + 2,3) distance. Low piece-value Antelope(3,4) is under 'A' at Piececlopedia, so Gilman knows that one remark of his not up to his usual excellence, and that clever subtle weakening, combined with binding pairwise, in fact makes the best p-ts for Piececlopedia or Short-Range projects, not the implied other way around.

What makes you think that a color-switching piece would be weaker than a non-color-switching one?

It is easy to understand that color-boundness is disadvantageous because it means there are squares you cannot reach even with an unlimited number of moves, but color-switching implies no similar disadvantage that I can see.  A knight can famously tour the entire board.

If I were to guess, I would say the Bison is likely weakest of the three, because I conjecture it is more useful to have both a shorter and a longer move than to have two long moves.  The long move gives you speed, but the shorter gives you more maneuverability.  But this is only a guess.

As George said, they are all very close. I do like Jeremy's comment too, 
'The long move gives you speed, but the shorter gives you more
maneuverability.'

Right, they are three very close. Orthodox chessists do not dwell on relatively trifling 0.05, 0.10, 0.20 differences say in FRC line-ups between Knight and Bishop or minor rules changes affecting stalemate or whatever, do they? Good moves are more important the players, and for designers good piece-types and rules that jibe and reinforce, not exact valuation. (For instance, Winther's dozens of bi-furcators he reports as ''about 3.0'' or ''estimated at 4.0,'' close enough for initial purpose.) Yet specifically here, the disadvantage of forced colourswitching is in view of other pieces' like Bishops being colourbound. Gazelle cannot capitalize on positional advantage against such colourbounders generally speaking. Bison and Gnu can elect to switch or not, and Gazelle cannot.  It takes play of Bison to internalize the power of long-range forks both Gnu and Gazelle have not the same ability. 'Bison > Gnu > Gazelle' is pretty clear on our intermediate boards, meaning over 72, notwithstanding Zillions' formula. Only three steps of Bison, either Camel or Zebra, lose nothing in versatility.  More so striking would be Bison over the others on greater than 100 squares. Anyone playing Omega Chess on 100(104) for example knows how lost get both Wizard, whose reach is 3 only half the arrival squares, and Champion to the line pieces. However, the over-100-squares set should result in Gazelle eventually overtaking Gnu for that very range-advantage of Zebra ''farther out'' than Camel. Over-all, we are talking most board sizes/piece mixes within best common sense, 80-120 squares, of values like 6.2/6.1/6.0 the three bi-compounds near equal. [On a Jupiter 16x16 or even possibly a Typhoon 12x12 start about Bison 7, Gazelle 6, Gnu 5 and see what happens.]

AndR, i have no idea how zillions comes up with these numbers, it gives a pawn in this game the rating of 2,752.
It is free to become a member of this site, and your comments will be posted straight away instead of the wait, you should consider this :)

Unless I am mistaken, the Bison cannot triangulate either.

Attacking the same square after a move is an advantage, but attacking a different square after a move is also an advantage.  I'm not currently persuaded that the former is better.  You mention forking power, but attacking a new square seems likely to be better for that--if one of the pieces you 'fork' was already threatened and your opponent chose to leave it in place (and you chose not to capture it), then the fork isn't likely to distress him overmuch, is it?

It is interesting to compare the Bison to the Centaur (WFN, knight+king).  Both have 16 moves, but the Centaur's power is concentrated, while the Bison's is dispersed.  If you drop them on a random location on a crowded chessboard, the Centaur reaches more squares on average (because its moves are less likely to be limited by the edge of the board), but the Bison has more squares it can reach within 2 moves.

I've played with both in For the Crown, and found the Centaur effective for defense and (with support) for forcing a checkmate, but the Bison appears to have far more forking power and makes an excellent harassing piece (though part of this advantage seems to come from 'stealth', having more moves that are not shared by enemy pieces).  Though perhaps players with greater skill would draw different conclusions.

I would probably agree that forking isn't increased with triangulation; I hadn't though about it long.  On the other hand, if the guarded square is friendly, triangulating means attacking some new squares while still guarding the old one.  I don't think in general that attacking a new square or attacking an old square is more advantageous, but having _both_ options is certainly nice.

Anyway, I hadn't really looked at which pieces were being discussed below yet.  You're correct that the bison doesn't triangulate (despite not being colorswitching), so my argument doesn't help in that discussion.  I wanted in my previous post just to present one reason why colorswitching may be detrimental.  (As a side note, the interaction of colorswitching with colorbound pieces is interesting.)

I agree about the bison vs. centaur.  The bison is an annoyance at range, and the centaur is strong locally.  In For the Crown, I have found the bison to be particularly nice in the early to midgame, especially since the attack cannot be blocked by dropping a piece adjacent to the King (in particular with the Guard's order).

I just found a comment that I had meant to post sooner:
	I never meant that being weak was per se a reason why a piece might be neglected, I was thinking more in terms of weakness combined with complexity. The Antelope is indeed in the Piececlopedia but the Fiveleaper, an Antelope compound with another colourswitching piece, is not - making it slightly puzzling that the Fiveleaper's colourbound dual the Root-50 leaper is.