Comments by MichaelNelson

What are the general characteristics of a pawn-like piece? I'd nominate
these characteristics:

1. Most numerous piece type in the game.
2. Weakest piece type in the game.
3. Short range.
4. Non-retreating.
5. Promotes to something decisive (can force mate).

For illustration, consider how several variants stack up:

FIDE Chess: pawn satisfies each criterion perfectly.

Shatranj: Perfect for 1-4, deficient in criterion 5, as K + Ferz that a
pawn promotes to can't force mate (less of a problem with the Shatranj
ruleset as stalemate and bare King are wins).

my own Pocket Mutation Chess: 1-3 is perfect, 4 is not so much so, as a
pawn can retreat via a pocket move, 5 partially not a fit, while the pawn
has a promotion path to a decisive piece, it can only only promote directly
to a Knight or Bishop, which can't force mate.

Betza's For The Birds Chess: 1, 2, 4 and 5 OK but the pawn-like piece has
a long range move.

my own Wizards' War: nothing remotely resembling a pawn in this game (by
design--one of my design objectives was a playable, pawn-less, strong piece
game).

I submit that all the games are playable Chess Variants (broadly defined)
but the better a variant conforms to these criteria, the more
'Chess-like' it is.

Try analyzing some other variants with these criteria and let me know what
you think of this hypothesis, offering alternative/additional criteria if
you wish.

Add my favorable vote to the others. I find the articles interesting and
enjoyable--and I say this as someone who has has disagreements in the past
with Mr. Duke.  If anyone doesn't like them they are easy to skip--no need
for the CVP to spoil it by removing interesting articles.

Thanks to everyone for welcoming me back!
I have updated my profile with my new  email.

I presume that capturing the opponent's King on the eighth rank with your last Pawn also wins. This is clear from the logic of the loss conditions, but you might want to state this explicitly.

Also, stalemating by promoting your last pawn should win.


You may wish to consider triple repetition as a loss--this is fairly common where stalemate is a loss.


I intend these suggestions as minor clarifications for a very fine game.

I'm working on a couple of additional piece sets for PM. One is part of the Short Range Project and the other eliminates Nightriders and provides additional enhancements. In both cases I expect a more strategic, less explosive game.

I am in no way dissatisfied with the classic piece set, I just think providing some alternatives will be interesting for players who like the game concept but would prefer a different feel.

When I have them worked up I will amend the game page and submit a new ZRF.

David is surely correct. Black's Queen is not in check so how can moving
it along the shared line of movement with the Lion put it in check? For
the Lion to capture the Queen, there must be a third piece between them to
act as a screen: Qh1, Qi1, or Qj1 being interpreted as check means that
Black's Queen is being used as its own screen.

A fine start to what I hope will be a lengthy and very informative series.
The various games already generated by this project are first rate and I
expect many more as the work continues. 

I might point out that the shorter range of pieces opens some
possibilities that may be more practical than in games with long range
pieces. Relay Chess leaps to mind, as well as various forms of
Progressive.

While I love the Shatranj Pawns in the variants, I think that a shortrange
piece game with stronger Pawns might be most interesting as well.

An excellent concept game and I think it will be quite playable. Joe's
whole series of Shatranj variants are fascinating. The varying power
levels of short and medium range pieces with few or no long range pieces
make for something quite different. 

This particular variant with its direction changing moves reminds me of
Jetan.

The Mammoth is a strong piece. Betza's Atomic Theory suggests a 4-atom
value, equal to a Cardinal. Its lack of range is compensated by
unblockability and excellent coverage of nearby sqaures.

Let me try restating the rule and Charles can either affirm I am correct,
or he might think of yet another way to express the rule if I am wrong.

1. For the purpose of applying the recruitment rules, we pretend that a
neutral piece can capture a non-neutral piece.
2. After moving a piece, the player who just moved may recruit any piece
which is attacking a piece owned by either White or Black. 
3. If rule two applies to multiple pieces, they can all be recruited.
4. Recruitment is applied recursively, so if a neutral piece which is not
attacking a White or Black piece is doing so after a recruitment, that
piece can be recruited also.

Charles, is recruitment mandatory or is it legal for a player not to make
a recruitment he is entitled to, either by intent or oversight?

By the way, I think this is a fine game concept that deserves more
exploration--I expect there are many ways to apply it in different game
settings.

I am most honored that Pocket Mutation Chess was selected as the newest
Recognized Chess Variant and the voted Recognized Variant of the Month the
first time out.

Clearly PM is my finest creation but I never imagined it would join such
august company in under three years.

Roberto, thank you for your comment. I'm putting the finishing touches
on a ZRF and it will be up later this weekend.

Andy, the restriction was added to prevent check on the opening move,
followed by continuing attacks resulting in a White win in 10 moves or so
in most cases. The current rule for the Pao/Vao moves strengthens the
defense as well as weakening the attack.

The idea of Josh getting a hold of rifle cature is pretty scary (though
fascinating).

I have made some small changes to get a playable game--I explaind my
reasoning to Josh and he seemed to get it--saying 'OK, Daddy, I think
that's a good idea.'

Originally Josh allowed the cannon moves without restriction: the piece
leaped over could belong to either side and the move could be capturing or
non capturing. This in combination with the hook move is much too powerful--White's Queen jumps
over its pawn line and checks, then plays King hunt until mate.

But limiting he line pieces to leaping over a friendly piece only make the
game playable. Also, a piece cannot both leap and hook in the same move.

So here is a description of Joshua's Chess as it now stands, pending a
full web page.

Joshua's Chess is played on a 12x12 board with the usual pieces: the
armies are on the back ranks and centered.

The Pawn moves and captures one or two squres straight forward, diagonally
forward, or sideways. These are strong little guys and protect each other
well. A pawn reaching the twelfth rank may optionally promote to any piece
its owner has lost. If the option is not taken, the Pawn may be later
promoted after moving one or two squres sideways on the twelfth rank. No
e.p.

The Knight has its usual move and in addition can leap 3 squares
orthogonally or move a single square orthogonally. This is precisely the
move Joshua invented: he understands the Knight's move to be a L shape,
two squares othogonally then one at right angles: he generalized this by
allowing the one squre move to continue in the original direction or go
back the direction it came.

The Bishop may move and capture normally. It may also move and capture
after leaping diagonally over one friendly piece. A Bishop which did not
leap and finished on an empty sqare may optionally move one squre at right
angles to its original path--a one square hook move.

The Rook is the Bishop's orthogonal counterpart, with the same leaping
and hook move options.

The Queen has the combined Bishop and Rook moves. This is one scary
piece. Though not a powerful as the Queen piece in Betza's Tripunch
Chess, it can use the leap move to develop faster.

The King can has its usual move, can move as a FIDE Knight, or leap to the
second square orthogonally or diagonally. Leaping over check is legal. No
castling.

The Pawns and Knights allow fairly good defense in the opening and
middlegame. In the endgame, K Q vs K and K R vs K are easy: a Rook can
mate unassisted on an empty board. King and any two minor pieces should be
a win. K P vs K should win in most cases--the Pawn can't be blocked.

He knows about Chess variants in a very vague way--that it is possible to play Chess with alternate pieces/rules, but he has never played a variant.

Yesterday Josh and I were playing Chess and he got taken by the Muse (or temporary insanity) and started inventing a variant! He reinvented the Chinese Cannon and its diagonal counterpart as well as the hook move, and used these moves to strenghten the Rooks, Bishops, and the Queen. He also created an augemted Knight and some very powerful pawns.

He also made some design decisions without prompting from Daddy. He decided an unlimited hook move was too strong, so it will be limited to a single square. He also decided that strengthening the other pieces required a stonger King and came up with the idea the the King could move KNAD and could leap over check. He also suggested that stronger pieces might make a better game if placed on a larger board.

It was most fascinating to observe Josh's though processes.

The game seems playable. While I don't expect it to have the acclaim of Demian Freeling's Congo, Joshua is nearly two years younger that Demian was.

I will be creating the ZRF and webpage over the next few days.

David,

The SR Murray Lions seems to be a capital addition to the SR army and
would make for a nice variant. I don't care for pushing the pawn line
forward. I invented it solely, Peter didn't collaborate on this--and I
despise this variant: it ruins the peculiar flavor of Separate Realms.
I'd prefer to  try it on an 8x10 board, or position the Lions as you
suggest and only move the Pawns on the Lion's squares forward.

Clearly K L vs K is a win in most cases in separate realms: K vs K is
decisive if the Kings are on the same color--the King able to gain the
oppositon can force statemate. 

So if the Kings are on the same color, the Lion stays out of it if you
have the oppositon and wastes a move if the enemy has the opposition, thus
giving the oppositon back to you.

If the Kings are on opposite colors and the Lion is on the same color as
the enemy King, forcing a win should be no trouble. If the Lion is on the
same color as the friendly King, it should be quite possible to set up a
position where the Lion is moved adjacent to the enemy King which is
forced to make a losing realm-switching capture.

It would take extensive analysis to demonstrate a forced win in all cases,
but the win percentage is certain to be very high. The only non-trivial K X
vs King ending with the standard SR pieces which is draw is K B vs K with
the K B on the opposite color from the enemy King.

The apparent ambiguity in the Roccoco rules for the Long Leaper were
carried over into the rules for Fugue.

Since the Fugue Long Leaper cannot make multiple captures, there is no
need for the phrase 'jump over adjacent pieces' and I hereby remove it
from the rules. (Could an editor make this change as soon as convenient?)

In Fugue, a capture such as 

+--+--+--+--+--+
|LL|  |p |p | x|
+--+--+--+--+--+

is illegal as a multiple capture in any case, regardless of the ambiguous
'adjacent pieces', while

+--+--+--+--+--+
|LL|p |  |  | x|
+--+--+--+--+--+

is legal as in ultima and Rococco.

For a drawless chess, amend FIDE rules as follows:

1. Stalemate is a loss for the stalemated player.
2. Triple repetion is a loss for the repeating player.
3. If fifty moves by both sides have elapsed since the last capture or
Pawn move, the player who made the last capture or Pawn move may claim a
win.

The problem is in a scoring system the rates two draws as good as a win and possibly the tiebreaker method. The conditions of the contest create incentives to play for draws.

Other games have done worse--I can cite examples in bridge, football, and hockey where the conditions of contest created incentives to lose certain matches.

But then this can happen in Chess in any kind of elimination event. Say I'm assured of qualifying for the next round and in my final game of this round I'm playing A who is 1/2 point ahead of B for the last spot. Now let's say that based on past experience, I just can't beat B. It is to my advantage to dump my game to A to make sure B does not qualify.

A fine design. The strong Pawns and the random variablity of the Knights
will produced a a slashing, highly tactical game. Piece values will be
skewed--it will virtually always pay to trade Bishop for Knight, not
infrequently Rook for Knight will work.

A variant worth looking at would be to treat a 5 as 0--this eliminates
some of the longest leapers and brings the Wazir and Dababbah-type leapers
into the game.

A note on dice probabilites: The chance of rolling exactly one 6 on a pair
of dice is 10/36 or 5/18, not the 1/18 chance cited on the page.

The system works quite well. I was able to recreate a page for Decima with
my revisions in about 45 minutes.

When it is approved, would it be possible for an editor to append the
original Decima comments to it and then remove the original Decima page?

I really like this game concept: randomness at a managable level. The
Bermuda Triangle imagery is rather enjoyable as well.

Some rules clarifications: 

1. If a Knight leaps another piece on c3 and c3 is the BCAF, then both the
Knight and the piece leaped over disappear?

2. If a piece captures another piece on d5 and d5 is the BCAF, the catured
piece does not reappear?

The rules as a whole seem to me to indicate that the answer is 'yes' to
both questions--I'd like to hear the designer's intent.

Larry is on the right track, but the moves to attack a piece measure will
give false results in some games. 

In Decima, for example, White's usual opening move attacks a Black piece,
yet the game is less sensitive than FIDE chess. 

It may be that number of moves to attack a goal piece is not always
accurate, though no examples spring to mind. Clearly more resarch is
needed to decide the best measure.

Here is the 'Excellent' I thought I would be giving this fine game.
Having seen it in action while coding the ZRF, I am quite convinced of the
game's quality. 

The piece set is quite interesting and works well together. The Pawns are
unusual but easy to learn to use. The Pawns are quite strong: I'd guess
about halfway between a Ferz and a Knight (slightly closer to Ferz). 

The Forest Ox is the big gun of the board on both offense and defense. 

The Valkyrie is not quite as strong as the Forest Ox, but is much more
powerful than a Queen: the swap move allows if easier developement (can
swap with a Pawn in the opening setup) and more ways of escaping trouble,
while still having all of a Queen's move and capture power. 

Rook and Bishop are minor pieces, with the Rook the stronger but with less
gap between them than in FIDE Chess, since a Valkyrie swap can get the
Bishop to the opposite color.

The idea of the King's movement depending on the friendly pieces adjacent
to it works quite well here and I'd love to see it used in other
variants.

Overall, a highly playable and enjoyable game.

I have resubmitted my final revisions for the Decima webpage and the ZRF. I
have been haivng email problems and I am uncertain if my previous
submissions after the original have been received. 

Could one of the esteemed editors let me know if this morning's
submissions have been received?

Mason,

I have not found Decima to be overly drawish, especially in the latest
version I descibed in my previous comment. In my test games (Zillions of
Games vs. itself at the most intelligent setting), the outcomes in order
or frequency:

1. Win by getting two pieces to the tenth rank.
2. Win by getting a King to the tenth rank.
3. Win by annihilation of the enemy army (including forced suicide
capture).
4. Draw.
5. Win by Pawn promotion.
6. Win by getting more than two pieces to the tenth rank.


The Pawn promotion seldom wins outright by often leads to a win by another
means by forcing a suicide capture by a key defensive piece. 

Some very small endings are decisive  for example Pawn vs. Pawn is a win
by annihilation or promotion in all cases except where the Pawns are in
front of each other on the same file. King vs. X is only a draw if X is a
Rook or if X is a King in certain positions. King vs. Queen, Marshall, or
Seneschal is loss by annihilation. King vs. Palladin, Pope, Duke, Bishop,
or Knight is a win by reahcing th etenth rank. King vs Pawn will depend on
the positioon, but will only draw if the King catches the Pawn on the
promotion square--all other King vs. Pawn endings are decisive.

Greg,

Excellent work in doing all the calculations. 

Your figures confirm my designer's intuition that the value classes
(desinged based on Betza's atomic theory of piece values, with no
detailed math) are well-defined and playable. The worst case scenario is a
discrepancy of 1.47 mobility between Nightrider and SuperBishop in class 3.
This is vitually identical to the smallest difference between two pieces of
differnt classes: 1.48 betweenS SuperCardinal (class 5) and ChancellorRider
(class 6). 

However, some hard to quantify but very real values tend to narrow the
former gap and widen the latter: 

The Nightrider is particularly strong in the opening and as a drop
piece--this brings it closer to the SuperBishop which is not particularly
outstanding in either respect (though hardly poor). 

The ChancellorRider has a Rook move, so it has King Interdiction power
(the ability to prevent a King from crossing a rank or file covered by a
Rook move, thus confining it to a restricted area of the board). As the
SuperCardinal does not have King Interdiction power, this gap widens.

I've been doing some extensive playtesting of my creation and find that it
plays well--the win condition works very well. Some serious endgame testing
with Zillions has lead me to change the last piece conditions. Now a the
full win/loss/draw conditions are:

1. Having pieces worth 10 or more points on your tenth rank at the
beginning of your turn wins.
2. Capturing your opponent's last piece wins.
3. Losing your own last piece via suicide capture loses.
4. Doing 2 & 3 on the same move (leavng an empty board) wins.
5. Stalemate, triple repetition, and the 50-move rule are draws.

Charles is of course correct--one will never promote to Rook, Bishop, or
King in this game, as their moves are subsets of the Queen's move. this
can never be desirable when stalemate is not an issue.

Underpromoting to a Knight can be correct as its move is distinct from the
Queen's

An excellent tournament--well run and well played. Congratulation to
Antoine for his near perfecto: 10.5/11 is very impressive in any
tournament. Congratulations to Roberto for a very solid second with a
score that might well have won had Antoine been less dominating.

I loved playing this tournament in spite of finishing last (of those who
completed the tournament) and in spite of gaining only 1 point over the
board. I did at least chalk up a fairly impressive win at my own Pocket
Mutation Chess.

I hope that the preparation for Mutivariant 2005 will be underway
soon--definetly count me in.

Define two directions with links:

(links cw (e5 e6) (e6 e7) (e7 e8) (e8 e9) (e9 e10) (e10 e11) (e11 f11)
(f11 g11) (g11 h11) (h11 i11) (i11 j11) (j11 k11) (k11 k10) (k10 k9)
(k9 k8) (k8 k7) (k7 k6) (k6 k5) (k5 j5) (j5 i5) (i5 h5) (h5 g5)
(g5 f5) (f5 e5) )

(links ccw (e5 f5) (f5 g5) (g5 h5) (h5 i5) (i5 j5) (j5 k5) (k5 k6)
(k6 k7) (k7 k8) (k8 k9) (k9 k10) (k10 k11) (k11 j11) (j11 i11)
(i11 h11) (h11 g11) (g11 f11) (f11 e11) (e11 e10) (e10 e9) (e9 e8) (e8
e7)
(e7 e6) (e6 e5) )

Use these directions in the serpent's move.

I think the real issue is to alert the players to the fact that a drawn
game has in fact been achieved so the game can be concluded and the final
round started.

It is evident that both players were suffering from the same misperception
of the PMC draw rules. Carlos had earlier posted an inquiry to the PM page
about a perpetual check draw. I answered him that the rule was the same as
in FIDE--perpetual check is not a draw per se, but always leads to triple
repetion or the fifty-move rule (virtaully always the former).

It is self evident that Carlos intended to achieve a draw--Antoine has a
won game absent the perpetual check--therefor he must have been unaware
that he has done so.

The correct value depends on what magic number (square emptiness
probability) is chosen. I go with Ralph's uppen end estimate of .7 With
his lower end estimate of 2/3 then the value of the SS Rhino would be 
2 + 2 *(2/3) = 3 1/3

The Gnomon is a different matter: its lame H move must be multiplied by
.49 or .44 as there are two interventing squres.

I have an idea for Pocket Mutation Demotion Chessgi. It will use the same
pieces and value classes as PM. 

The rules for using the pocket are expanded:

When you capture an enemy pawn, it is removed from the game. If you
capture any other enemy piece, it is demoted to the next lower value
class, mutated to a friendly piece of your choice in that class, and put
in your pocket. This is mandatory even if your pocket is not empty and
will cause the removal of any piece in your pocket from the game. 

Notice how you can't put a strong piece in the pocket and wait around for
a good drop--in effect you can only capture pawns as long a s that strong
piece is there.

Imagine having a Queen in your Pocket and the opponent checks with a
Knight and the only counter is to capture the Knight. At the cost of a
Knight, the enemy has changed your Queen into a pawn!

Tim,

The Rhino can move one step in any direction and stop on that square (same
as a non-royal king) as well as turning 45 degrees in the appropriate
direction and moving a second square.  The non-royal King move alone is
worth 2 atoms. If the  second move comonent if it were a leap would also
be 2 atoms. To allow for lameness, mutiply by .7, so add 1.4 atoms for
this component for a total of 3.4 atoms. The piece is substantially
stronger than a Rook.

You may be confused by some incarnations of the Rhino requiring the first
step to be orthogonal -- such a piece is indeed worth only 1.7 atoms, less
than a Knight.

I think the fifth category for historically significant variants is a good
idea. Los Alamos Chess definitely belongs here because of its seminal
importance in the history of computer chess. Star Trek 3D does't belong.

The 'excellent' is for Fergus and his fine ideas for improving the
Recognized Variants list.

Carlos, 

Yes and No.

FIDE Chess rules apply to Pocket Mutation Chessexcept where otherwise
stated.

Under current FIDE rules, perpetual check is not a draw in and of itself
(it once was), but if you are able to give perpetual check, you can always
force triple repetition or the 50-move rule, both of which are draws. 

Note that Pocket Mutation's 50-move rule is different from FIDE:
promotions and captures reset the move count, but Pawn moves do not.

Ralph Betza's work suggests doing mobility conditions based on about 60%
of initial piece density. This is 30% for FIDE Chess and 26.4% for Unicorn
Chess. 

If Ralph is correct and this is the best value for overall mobility
ratings, the Unicorn is measurablly stronger than the Queen with respect
to mobility, as break even occurs at 22% piece density.

One overlooked Queen advantage that tends to even out the non-mobility
evaluation factors:  The Queen has the King Interdiction ability and the
Unicorn lacks it. King Interdiction refers to the ability of a Rook (or
any piece having a Rook's move) to confine the enemy King to a certain
section of the board by attacking the entire length of a rank or file so
that the King cannot cross it.

The only advantage in sticking to orthochess rules as much as possible is
to simplfy describing/learning the game. But this doesn't really apply to
complications such as e.p and castling.

It is reasonable to use e.p. if the Pawn has a double step--but it isn't
a given that the Pawn should have a double step. (It works badly on a 7x7
board, for example). 

E.P. isn't the only reasonable alternative, either. I rather like the
Nova Chess rule that prohibits a pawn from moving thru a square where it
could have been captured by another pawn if it had stopped there--this
works especially well when there are several pawn type pieces in the
game.

Similarly, if you have castling, it is good if it is similar to
orthochess, but whether to have castling is a design decision based on the
overall character of the pieces and the game. 

But again, ortho castling isn't best for every game--free castling suits
some games better.

I like this game concept. I thinks that the two Kings will be playable and
it isn't necesary to change the win conditon--a player threatend with the
capture of one of his Kings has a move option not present in FIDE
Chess--the counter-check. You check one of my Kings and I defend by
checking back. You capture my King I capture yours. 

I would suggest a small rules change--whenever a player captures an enemy
King, he must drop it on his next turn. This keeps all four kings in paly
and allows the player with a single King some nice chances of
equalizing--he has three royal targets vs. his opponents one.

Not quite. Chaturanga allows a pawn to promote to the piece whose starting
square it reaches--a pawn prmoting on a8 becomes a Rook, on b8 a Knight.
It doesn't matter which pawn it is, only which square it promotes on.

In Tamerlane's, the Rook's pawn always promotes to Rook no matter where
on the back rank it promotes, the Knight's pawn promotes to Knight, etc.
Here what square the pawn promotes on doesn't matter and which pawn it is
does--pretty much the exact opposite of Chaturanga.

A most fascinating game concept. A world of interesting variants can be
developed from this idea. A large board variant with powerful but
short-range pieces comes to mind. Perhaps an 11x11 board with some empty
ships in the center.

Ryan, 

This is not the proper forum for the discussion of ozone depletion,
Walmart, Bush vs Kerry, Iraq, The Passion of the Christ, etc., etc., etc.

If you are not discussing Chess variants or very closely related topics,
please post to an appropiate forum for those topics and not here.

An elegant rule solving this problem:

If the player is in check when it is not his turn due to a rule change,
the effect of that rule change is delayed until it is his turn--the old
rules will apply to his opponent's turn.

Charles,

I checked the Zillions implementation for the answers, as the page is
somewhat unclear on some of them.

(1) Yes, you can capture an uncombinable piece.

(2) Yes, the captured piece is removed form the game.

(3) You must alway capture with the compound piece, as splitting may only
be done by moving to an empty square.

Split and capture would make an interesting variant. In that variant, my
answer to (3) would be:

Yes. If for you need to vacate the starting square (for example to give
discovered check).

George,

I understand that you have devoted a great deal of time and effort to
perfecting Falcon Chess and that you passionately love your creation--as a
CV designer I can relate to that. But your are letting your passion blind
you when you go to the extreme of accusing Peter Aronson of theft--he
invents a game using your Falcon piece using a perfectly obvious name for
the game and your scream bloody murder. His game calls favorable attention
to the piece, the helping your game and not harming it, and your response
is to engage in character assassination.

I note that you collaborated with Peter on (or at least approved of)
Complete Permutation Chess. But a variant he invents without your
participation is theft? Do you honestly think that you own the rights to
any and every CV that uses the Falcon piece, the word 'falcon' or the
name 'Horus'? If anyone ever finds a reason to challenge your patent
(not that anyone will--no one makes money on CV's), a good patent
attorney will rip your claims to shreds.

For:

1. The inventor's mistaken belief that this is the best chess variant ever invented.

2. Patenting a game whose distinguishing difference from Chess is a lame Bison with an improved movement--an innovation, to be sure, but a small one.

3. His desire to prevent anyone else from using the Falcon in any game (no matter how unlike Falcon Chess).

I'm playtesting a revised ZRF for Fugue where I'm tweaking the piece
values in hope of getting Z to play better.

The values I'm using (normalized to Pawn=1)

Pawn   1
Swapper  3
Archer  4
Long leaper 4
Queen  5
Pushme-Pullyu 5
Immobilizer 6
Shield 6


I'm fairly certain the the ordering is at least mostly correct, but have
doubts about the magnitudes of these numbers. I've already noticed
Zillions making better use of the Swapper and trying harder to capture the
enemy Immobilzer and Shield.

Comments about these suggested piece values?

I wonder if Piece Type Density needs to be considered in conjunction with
Move Type Density. FIDE Chess has six piece types in 64 sqaures and also
has 7.5 move types (King, Rook, Bishop, Knight, normal pawn move, normal
pawn capture counted at full value; Castling, Pawn double step, and e. p.
counted at half value.) No move type for the Queen as it combines the Rook
and Bishop.

Capablanca's Chess has 8 piece types on 80 squares, but has type same 7.5
move types. Does this mean that Capa's game is clearer than the 8/80
ratio and its Power Denisty would indicate?

Perhaps PTD and MTD need to be averaged in some way?

My own Pocket Mutation Chess scores poorly on clarity by its PTD of 12/64
(the six starting piece types counted at full value and the 12
promotion/mutation types counted at half value). But its MTD is only 8.5
(FIDE moves plus Nightrider). My own playing experience is that Pocket
Mutation isn't as clear as FIDE, but that the disparity seems less than
PTD would indicate.

George, 

Men and women are about than 2% genetically different--but it's a really
important 2%! Similarly, some people love apples and hate oranges and vice
versa.

I believe that you are making a real contribution to the 'Science of
Chess Variant Design' while denigrating the 'Art of Chess Variant
Design'.

I think we need both. 

Preferences and not the be all and end all of design, but neither are they
irrelevant--what is the point of designing a 'mathematically perfect' CV
that no one wants to play? And aren't clarity/depth and
drama/decisiveness important precisely because they speak to game
players' preferences?

It's also possible that some of these numbers have non-linear
relationships. For example Hectacomb with Amazons instead of Queens might
not be that much different in playablity in spite of the high PD
difference (aout 40%)--the PD is huge in either case.

Simiarly, assuming an 8x8 board, a game with 100 piece types might be
scarely less clear than a game with 50 (clarity approaching zero in both
cases), while 10 piece types vs. 5 makes an easily perceptible
difference.

It is also very possible that numerical criteria are best at comparing
games of somewhat similar types, and become more and more 'apples and
oranges' as the game types diverge.

The latter is why I objected to George comparing PTD in Fugue to PTD in
Chess. Compare it to Ultima and Rococo and it doesn't look so bad by
this criteria. It is by this measure less clear than Ultima or Roccoco 
but the difference in not as extreme as the the difference with Chess.

Apology accepted--I will feel toward you exactly af if this thread had
never been posted.

George,

The Archer as it appears in Fugue is my creation and was not part of a
collaboration. The Rococo variant thread discessed the merits or range 1
vs range 1 or 2 vs range 2 only Archers and whether special considerations
should apply to attacking the King. No one before me said a word about an
Archer that needed a spotter for long shots. I got the idea from artillery
rules from some of Avalon Hill's war games, where certain units need a
spotter to hit a target at beyong half range or in certain defensive
positions. To my knowledge this concept has not been used in a
Chess/Ultima variant before--I am open to correction if I err in this
assertion.

George,

I have yet to see a game of Fugue where 'one move is as good as
another', excluding lost positions of course.

Fergus, 

I'm not sure if you received my email.  My preference is simple: I'd
like to play a game of Pocket Mutation, as I invented it. Apart from that,
all are good games and I would be happy to be assigned however works out
the best for the tournament.