Comments/Ratings for a Single Item

Vampire: turns other pieces into Vampires.

The leading themers have to be Ralph Betza, Charles Gilman, and Gary
Gifford.  Betza's Nemeroth is divided into two articles for closest to
Halloween theme in CVs, to kick off the holiday season. So, Betza would approve adding Mummy, Basilisk, Ghast, Leaf Pile, and Go Away, each in spot use differing from great Nemeroth.

I'm thinking of a piece called a Headless Horseman, which would move as a
Gryphon or Aanca, but cannot capture when moving 2 steps or more:

m . m . m . m .
. m . m m . m m
. . m . m . m .
m m m m x x x m
. . . . x H x .
m m m m x x x m
. . m . m . m .
. m . m m . m m

I would estimate it to be worth about 7 Pawns. Does anyone have other
value suggestions, with reasons or playtesting?

Werewolf: Moves like a Man except on moves 10,20,etc, during which they
move like some monstrously powerful piece, an Ubi-ubi, maybe?

The Virgin Maiden: the goal piece which is only able to flee.

John, there's some discussion on pieces similar to the Headless Horseman
here: http://chessvariants.wikidot.com/attack-fraction 

In the discussion following the chart, Graeme Neatham gives an estimated
value of pieces that move like a K but capture like a Q - 8.45, move like
a Q but capture like a K - 4.50, and a knight-wazir pair with a similar
difference in values. There's also a discussion about why this might be.
Basically, a piece that has a great capture range tends to be more
valuable than one that has a very limited capture range. As long as the
piece can move and position itself to capture, then it is able to fork
widely separated pieces and basically take potshots at pieces across the
board. A piece that can move almost anywhere, but telegraphs its attack by
having to move directly next to its victim, then wait 1 turn before the
capture, is far too susceptible to being killed before it captures. It's
a more limited piece.

Others may well have much better answers. But it seems to me that 7 is a
bit high for that value; yes it has great range, but... 7 would seem to be
a maximum value for the piece.

'A piece that can move almost anywhere, but telegraphs its attack by
having to move directly next to its victim, then wait 1 turn before the
capture . . .'

This sounds like a good movement for the Vampire.

I guess you're right, Joe. I just based my assumptions of capturing move
values on a theoretical piece that moves as a Shogi Pawn, but can only
capture, being more valuable than a piece that moves as a Shogi Pawn, but
can only not capture. I'll try to have the correct value up.

Hey, John, my guesses are just that, guesses. There are others - many, many
of them - who are far more qualified to give piece values. Most of what I
say was learned from them. It's a very controversial field, still pretty
open and unexplored, but I suspect the field is going totally from human
estimates into computer statistics right now. Here's the catch: very few
programmers work with CVs; FIDE chess is a gold standard of programming
skills, but I don't know of much more than maybe a double handful of
people who program variants. This doesn't count Zillions, of course, but
ZRFs are a little different than, say, ChessV, Joker, or SMIRF. So a
player who can make good piece value estimates can often have an advantage
over someone who can't.

It should be worth 6, I estimate, to apply the 12 (value of the Gryphon +
Aanca)/ 9 (value of the Queen) ratio to the Keen, which is worth 4.5 .

I have also come up with a new piece, the Unicorn, which moves as an Advancing Mao-rider. Does anyone know the value of an Advancer? I estimate it to be about 10 or 11, being more than a Queen because it takes 8 pieces to be able to fully defend a piece from it. A Mao is worth about 2.5, I think, so we can apply the 2.5 (Mao) / 3 (Knight) ratio to the Nightrider, which is worth about 5 or 6, to make 10 (a bit less than an Advancer, as it only attacks 4 squares) / 9 * 2.5 /3 * 5.5 = about 5, same as a Rook.

I have run some tests on Keen and Quing, in the context of the normal FIDE
opening array. I always forget which is which, so I like to refer to the
piece that moves like a pedestrian, but kills at a distance (mKcQ) a
'Trapper', and the one that moves far, and then tramples around in
destruction (mQcK) a 'Tourist'. (The Knight-like counterparts of those
could then be 'Hunter' for mNcQ and 'Pegasus' for mQcN.)

One Trapper lightly beats the Bishop pair, perhaps by as much as a quarter
Pawn. With the Kaufman values B=325 and B-pair bonus = 50, this would give
Traper = 725.

Two Tourists beat R+N by at least half a Pawn (perhaps 75cP). With the
Kaufman values R=500 and N=325, this would make Tourist = 450. So it is
indeed clear that the extra captures make the piece much stronger than
having these same moves as non-captures.

This should be compared with the Commoner (opening) value, which is
slightly below that of a Knight (so ~300). Note there are clear non-linear
effects: adding the distant non-capture moves to the Commoner ups the value
from 300 to 450 (+150cP), while adding the same moves to the Trapper ups
the value from 725 to 950-975 (the Kaufman Q value), i.e. +225 to +250.

I've been thinking about this variant for a while: Fool Chess (not to be
confused with Graeme Neatham's Fool's Chess) . It would incorporate all
kinds of Fool, Jester, or similarly named piece in Chess variants. For
example, it could have the Courier Chess Fool, which moves as a Wazir, the
FIDE Chess Fool, which moves as a Bishop, and even the Jester from Jester
Chess, which imitates the last moved enemy piece. Does anyone know of any
other Fools?

Actually, I might try to 'combine' these pieces into a sort of average,
or use all of them in one piece, like my Super Asian Chess Elephant.
Imagine a new kind of Falcon, which moves N spaces backwards as a Hunter
Falcon Falcon, then N spaces forwards as a Hunter Falcon Falcon, then
repeats either of those, and can move in any order of the moves I've
said, thus resembling a Sissa, but with a Falcon name also somewhat
resembling a Falcon Chess Falcon. I hope that George Duke is OK with me
using a multi-path piece named a Falcon in a variant without credit,
although it is not the same piece.

And another combination piece!: The Lion, which is a WFDAN +
Omnidirectional English Draughts King. It has the abilities of every piece
bar the Crocodile from Congo, and whose range is the same as the Chu Shogi
Lion!

I am not sure I understand the hybrid yet, but there are two examples
related. One Charles Daniels' Asylum Redux and Abdul-Rahman Sibahi's
Falcon Hexagonal Chess. Sibahi's has been much discussed in 2007, and
Daniels' is very interesting, almost a perfected idea in combination of
halfway Falcon with respectively Bishop and Rook. There were conflicts of
view between myself and Daniels, or I would have commented there by now. Please
explain this one more. Why ''...falcon falcon,'' two of them? // Oh I see now, like a Sissa, sure go for it and call it falcon, the name is only secondarily patented. I actually wasted one of 20 claims in 1996 with the name Falcon. Anyway, you know by now with many CVs, the 'credit'' just becomes a line in the text, not coauthorship when that would be different-enough piece, though becoming multi-path. Interesting.

In my variant, I could have the aforementioned falcon, a piece called a
fool which moves as a Wazir or Renniassance Chess Duke, and an elephant
which moves as a Wazir, then Alfil, or Alfil, then Wazir, or as a Waffle,
which makes altogether a bent-path bonanza!

How about this Falcon? : Moves as Hunter Falcon Falcon , but after
capturing moves at a 135 degree angle off of the piece. It is what Mats
Winther would call bifurcating, and mimics the hunting style of a real
falcon.

I have been considering a truncated planar piece. One that performs an
orthogonal planar move but only up to a 4x4 area.

For those that are unfamiliar with planar moves, this is basicly an area
leap with the condtion that there are no other occupied cells within that
particular area(excluding the piece which is moving and its potential
target cell).

A classic Knight leap is a 2x3 area leap without the restriction of
occupancy for its particular group of cells.

The planar move offers a piece which can by itself easily checkmate the
common King. So it might only be obtained through promotion, or in games
which utilize a stronger King(such as the Emperor).

Of course, this planar piece could be restricted to performing only area
leaps of 2x4 and 3x4. Thus allowing its use in games with weaker Kings.

This may be so similar to the 'piece that shall not be named', it may
trigger my aversion therapy causing extreme migraines and projectile
vomiting.

I don't know what to say, but that seems like a really weak piece,
according to Betza's magic number. The awkwardness explodes
exponentially, making it probably worth a maximum of 1/8 of a Pawn. Have you tested this piece? To quote David Paulowich, it strikes me as almost as bad an idea as the original Shatranj Elephant. Only worse. Much, much worse.

Yes, it is an extremely weak piece. Probably not even worth considering.
Thankfully, since I was having dry heaves just thinking about it.

John Smith finds  there are more possibilities for bifurcation pieces. Jeliss and 20th
Century problemists must have had nearly ten. Winther has added 40 or 50.
Like most piece-type categories, there are almost unlimited imaginative
possibilities. Only bland long-range leapers seem restricted by the board size.  That is definitely bifurcation, but it would be better with
three-path Falcon. Then sometimes player would have choice of direction of
continuation after the capture, depending on the pathway chosen to
indicate. The Falcon-Hunter version instead, as described by John Smith,  would overlap with some of Winther's already
conceived, differing only in the reverse direction.

Yeah, I guess my old Falcon is more creative. I've never seen any piece
other than a Sissa that is a multipath that can move an unlimited amount
of spaces. You seem to have misunderstood my piece, which can only capture
on the square it finishes its move on, but your version is great because
then it can swoop like a real Falcon. Well, that leaves at one more piece
for my next variant. I think it could be an Elephant (any ideas?) , and I
could rename the Falcon as the Hawk, so to fit in nicely with a Seirawan
chess set. ;) (And no, I'm not H. G. Muller.)