Comments by DerekNalls

C-R-N-B-Q-K-B-N-R-C  mirror I
C-R-N-B-K-Q-B-N-R-C  mirror II

The problem with opening setups where both chancellors are placed upon outer files is that, compared to those where both chancellors are placed upon inner files, king safety is deficient.

Powerful, composite pieces such as the chancellor can contribute markedly to king safety [which is vitally important!] and yield higher, measured values for king safety than typical in standard Chess (by comparison) but only IF they are close enough to the king to help protect its 3 adjacent pawns.

In your proposed opening setup (mirror I), the diagonally adjacent pawn to the NE of white's king (for reference) has only 1 backup.  With 18-22 pawn backups available (depending upon the particular opening setup) to be distributed for 10 pawns, an average of appr. 2.0 backups per pawn exists.  Consequently, I consider a figure of appr. 1/2 of average to be unacceptable- too low for any pawn diagonally adjacent to the king in this class of games.

For an opening setup, its rapid transition to a solid development phase and smooth play characteristics are of secondary importance to its stability.

'I only think color balance for pieces matter if the pieces are colorbound. It doesn't matter to me what colors non-colorbound pieces end up on since those pieces can change color at will.'

The color-bound pieces imbalance (e.g., queen and archbishop both on dark or light spaces) is measurably a much more efficacious fault than the color-changing pieces imbalance (e.g., chancellor and archbishop both of dark or light spaces) although I classified both as 'minor faults' in the overall scheme consisting of only 4 distinct faults.

As measured by the movement capabilities for each power piece taken one-at-a-time on an otherwise empty board at its opening position [an ideal, potential maximum evaluation to reveal space-based imbalances rather than an actual, obstructed condition existing upon the very first move of the game by white], a color-bound pieces imbalance often results in a number for one color that is appr. twice as high as the other color in CRC. For example, 39 dark spaces can be occupied while only 20 light spaces can be occupied on the first move. So, it is NOT merely a trivial fault (instead of a minor fault).

A color-changing pieces imbalance typically only throws the numbers (from a total of appr. 55-59) out of balance by 2-4 more than they would otherwise be since a perfect balance never exists anyway with any CRC positions. Still, when you have a vast number of positions to choose from (12,000+ according to Reinhard Scharnagl), why tolerate this imbalance, either. Logically, I cannot tolerate the former fault. So, I will not tolerate the latter fault of a similar nature, either. Thereby, I maintain consistent standards for the model.

_______________________________________________________

'... I no longer think it's essential that each and every pawn in the opening setup is defended. I think it's a good idea for white to be unable to threaten mate on his first move, since otherwise Black can be prevented from making natural developing moves in the opening; having all pawns defended stops these kinds of threats.'

Yes but ...

An undefended pawn can, with perfect play by white (the player with the first-move-of-the-game advantage) over a number of moves irrefutably result in a stolen pawn despite perfect play by black. [{proven to us by someone}* using a powerful, multi-CPU computer with one proposed CRC opening setup.] Ultimately, this material disadvantage is probable to lead to the eventual defeat of black. This is too unfair to black. The potential amplification of the pre-existing and marginally, unacceptably-high advantage for white is the reason that an undefended pawn is unconditionally classified as a fatal fault for any CRC position under my system.

__________

'I am not sure every pawn around the king has to be defended two times or more. FIDE chess has had, for over 500 years, the King Bishop's pawn defended by only the king, and this has not stopped FIDE chess from becoming the most popular Chess variant that we will ever have.'

Yes but ...

Standard Chess is the most stable FRC position available.

[You can quickly verify this fact by creating a select FRC scheme in a likewise manner as you created a select CRC scheme.]

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'However, I can see why one may not want these weakly defended pawns in a Capa setup, since there is 18 pawns more power (2 more pawns, the archbishop, and the marshall/chancellor) on the board than in FIDE Chess.'

Exactly.

My analysis of fault-free and faulty positions exists entirely within the relative context of what resources are available with a given piece set and class of games. Consequently, I demand higher standards of the CRC piece set on the 10x8 board defensively than of the FRC piece set on the 8x8 board.

Since I have only developed one tool to date, the select CRC analysis tool, I realize this fact was unexplained and undemonstrated.

_____________________________________________________________

Whatever piece set and gameboard with 100's-1000's of possible opening setups is presented, my goal is to customize a method to it by:

1. Focusing upon a highly-selective set of positions based upon your well-defined, easily-used criteria as potentially most favorable, interesting, least asymmetrical and worthwhile to investigate in detail- existing in a number manageable for one person in terms of the time and work required.

2. Applying an extremely-selective filter so that only one to a maximum of a few of the very strongest positions available survive with a rating of fault-free.

The very best possible game(s) out of the vast number within a class should exist there. This is due to the fact that the number of pawn backups (in chess variants related to standard Chess) impose mathematical limitations upon what is possible, despite the vast number of tactical, offensive multi-move options available, to effectively imbalance the game to the further advantage of white (the player with the first move of the game).

*Edited - JG

'I hope the posting I made did not, in any way, show disrespect towards
your opinion, research, nor criteria for choosing the opening setup you
did.'

No.  Definitely not.  My stoic, argumentative, hardened, informational
writing style has unintentionally and unnecessarily created some
cyber-enemies for me over the years that I never wanted at all and never
personally disliked.

Actually, I am somewhat relieved that you were not personally offended and
publicly hostile over the implication within my work (select CRC analysis
tool) that Schoolbook Chess is not fault-free due to its exclusion from
the select 48 games I analyzed in detail (along with all other king &
archbishop centered positions).

It is very significant that I did not see my way clear to devising
anything like the select CRC analysis tool until you first devised a
couple of simple rules for paring-down candidate CRC positions to a
manageable number.
__________________

''Colorbound', for me, has a very specific meaning. I use Betza's
meaning for colorbound: A piece that, for the entire game, always has to
be on the same color. A bishop. for example, that starts on the white
squares will always be on the white squares for the entire game, since it
can not make a move going from the white squares to the black squares.
Neither the queen nor archbishop are colorbound; both pieces can reach any
square on a blank board in two or three moves.'

Yes, my usage of color-bound in association with the queen and archbishop
was too vague and deserves clarification.  To be sure, I agree that the
queen and archbishop are NOT color-bound pieces.  Still, they will
contribute to the 'color-bound pieces imbalance' if both of them start
the game upon the same dark or light spaces.  This is due to the fact that
both composite pieces contain, in part, color-bound bishops.  That nuance
was absent in my explanation.  It is difficult to be concise without
losing vital completeness and accuracy.
_______________________________________

It is debatable that the rating system used with the select CRC analysis
tool is too strict.  Admittedly, it was designed to detect faults of
various importance within the vast majority of CRC positions presented to
it thereby eliminating all except one to a few.

'Hex Chess SS' stands for Hex Chess (square-spaced).
The overall board is approximately hex shaped.
The board spaces are square.

I apologize for poor naming.
I am not a poet.

Please make the minimal effort to find-out what you are talking about
before raising Hell?

Hex Chess (square-spaced)- Bishops & Rooks
http://www.symmetryperfect.com/shots/hex-br.html

Hex Chess (square-spaced)- ZZ Pieces I
http://www.symmetryperfect.com/shots/hex-zz-i.html

Hex Chess (square-spaced)- ZZ Pieces II
http://www.symmetryperfect.com/shots/hex-zz-ii.html

The proof Nalls' 50-page program is comparatively inadequate is that he
will not likewise use it for such estimatations on command.  Since his
system is only good for three sets now (FRC,CRC and the one of his own),
it apparently does not even achieve hit-or-miss or willynilly import.
_____________________________________________________________________

You are too gracious.  In fact, I only know my model to be reliable for
two sets now- FRC & CRC.  It could be way off track for one set- Hex Chess SS.

To be sure, I appreciate your efforts on behalf of Joe Joyce. 
Unfortunately, despite your very good intentions, I also regard your
efforts warily as borderline irresponsible.

Contrary to naive intuition, with relative piece values, guesses can be
worse than using no values at all.

If you have no relative piece values to play by, then you will naturally
use caution in forcing exchanges that are not obviously advantageous (or
allowing your opponent to force exchanges upon you).

If you have relative piece values that you hope are instructive yet are,
in reality, too inaccurate, then you will feel justified in forcing
exchanges that are allegedly advantageous (or allowing your opponent to force exchanges upon you).

This doomed course of action will cause you to lose repeatedly.  The
material nature of the loss will not be immediately clear since you will
assume this could not possibly be the problem.  Instead, you will
incorrectly attribute the loss to a positional shortcoming or poor move at a critical junction and for instance, analyze every move in the opening
game in detail.  Of course, all of these efforts will fail to solve the
problem and you will still continue to lose.

The moral of the story is that if you know nothing, admit it since other
courses of action can be disastrous.  Be honest, realistic and
responsible to the greatest extent possible.

In the total absence of feedback, you have no means of obtaining any
vitally needed experimental knowledge regardless of how high your
intelligence may be.  You are like a man target shooting blindfolded or a
man hunting gold with a metal detector wearing earplugs.

Please remember that reliable relative piece values have only been
established, to date, for FRC & CRC.  These are the only two testbeds
available for ANY model.  Forays into other games, if you must make them,
should at least carry a strong 'use-at-your-own-risk warning'.

It is contradictory and arrogant on your part to hold no confidence in my
model yet hold irrationally too much confidence in your model.  As far as
your model goes, you are as confident as you are reckless.  Good luck!

It is useful to classify inaccuracies and try to define how much inaccuracy
is too much with relative piece values.

The first, most dangerous inaccuracy is what I classify as a 'direct
inversion'.  A direct inversion is where two pieces with significantly
different values have their order of value reversed from its true
existence.

I am referring to more than a trivial case of, for example, mistakenly
defining the knight (30.00- DN model) as more valuable than the bishop
(32.42- DN model) upon an 8 x 8 board IF the reverse is actually true
since the values of these two pieces are truly very close.

Instead, I am referring to a non-trivial case of, for example, defining
the rook (59.43- DN model) to be more valuable than the archbishop (70.61-
DN model) upon a 10 x 8 board where the reverse is actually true.  Under
such a mistaken belief, a player willfully enters disadvantageous, simple
1-to-1 piece exchanges involving his/her archbishop for the opponent's
rook.  If any game is won where this exchange has occurred, it is against
the odds.  Incidentally, such simple exchanges are realistically likely to
occur in typical games.

I think most of us would agree this is too much inaccuracy.

The second, potentially-dangerous inaccuracy is what I classify as an
'indirect inversion'.  An indirect inversion is where, despite the
hierarchy of values for the lineup of pieces being correct, the numerical
erraticities within it are great enough to cause incorrect conclusions in
evaluating complex exchanges involving more than one piece per player.

Derek Nalls
relevant FRC pieces upon the 8 x 8 board
material values

knight-  3.000
bishop-  3.242
rook-    5.088
queen-   9.371
_____________

Reinhard Scharnagl
relevant FRC pieces upon the 8 x 8 board
material values

knight-   3.0000
bishop-   3.4488
rook-     5.3030
queen-    9.0001
______________

Note that under the RS model, 1 queen + 1 knight (2 pieces) is valued at a
total of 12.0001 and 2 bishops + 1 rook (3 pieces) is valued at a total of
12.2006.  It values the 3 pieces 0.2005 higher than the 2 pieces- a
marginal amount.  In practice, it would probably be indifferent to this
exchange.

Note that under the DN model, 1 queen + 1 knight (2 pieces) is valued at a
total of 12.371 and 2 bishops + 1 rook (3 pieces) is valued at a total of
11.572.  It values the 2 pieces 0.799 higher than the 3 pieces- a
significant amount.  In practice, it would probably aggressively pursue
this exchange.

Due to their contrasting evaluations of this complex 2-to-3 pieces
exchange, both players (RS & DN) would willfully enter opposite sides of
this exchange as being advantageous.  Unless both models are inaccurate so
that, in fact, this exchange is absolutely neutral to the interests of both
players, one player who willfully enters this exchange will get harmed by
it and probably, eventually lose the game.

Predictably, it is my contention that a player who trades 1 queen + 1
knight for 2 bishops + 1 rook will probably, eventually lose the game for
a reason, albeit indirect and less effectual, based upon the fact that a
player who trades 1 queen for 1 bishop + 1 rook will probably, eventually
lose the game.  However, such complex exchanges occur rarely in typical
games.  In fact, the example exchange never occurred between 2 versions of
SMIRF that Reinhard Scharnagl compiled for playtesting- 1 using his piece
values, 1 using my piece values.  So, I was never had the opportunity to
see my point proven.

Still, I am discontent with this type of subtle inaccuracy.  How do the
rest of you regard it?

We all agree that the relative piece values for FRC and CRC (to a lesser
extent) are reasonably well-established.  I think we should reaffirm WHY
(even if it seems too obvious to some of us) in order to pinpoint what
important steps need to be taken to bring other desirable chess variants
into our realm of understanding.

Thru much human effort, relative piece values for Chess (FRC) were
understood with only a little less accuracy than today long before chess
computers and programs attained impressive playing strength.
Notwithstanding, powerful computers and AI programs are now available and
affordable even to individuals in the modern era.  Accordingly, I think
this great resource should never be neglected and furthermore, should be
regarded as indispensible to our future endeavors.

Even in the absence of any predictive theory, a powerful program,
custom-written to play a single chess variant as well as possible, can
determine the correct relative piece values for an entire lineup of
pieces.  The greater the depth (in plies), time or number of positions
searched per move throughout a playtested game, the more narrowly it can
define the range of correct values for each unique piece (although a
tantalizingly-large, range of values remains with any game playtested at
survivable times using today's state-of-the-art technology).

Since FRC & CRC are fairly, closely related, it seems probable that no
predictive, universal model for relative piece values will mature until
additional reliable, experimental testbeds involving less-related chess
variants have been created to test results against.

Forget about the Zillions Of Games program.  It only plays chess variants
that are closely related to Chess reasonably well- NOT great!- when given
a lot of time per move.  The less related a given chess variant is to
Chess, the worse the ZOG program plays to the point of taking an enormous
amount of time to make poor moves.

The recent development of achieving within-range relative piece values for
CRC is a useful roadmap.  How did it happen?  Out of appr. 8 billion people
worldwide, an adequate number of individuals took an interest in learning
to play one of a few popular Capablanca Chess variants very well.  A
minority of these chess variant players succeeded at their goal.  For
whatever reasons, three programs were written and made available for free
for the worldwide popular IBM-compatible, MS Windows configuration that
the best human players confirmed to be strong.  In the course of making
each of these three programs as strong as possible at playing one another
and some of the best human players, the relative piece values for CRC were
refined to the point that improvements in playing strength no longer came
easily and quickly with adjustments.

How many efforts of this magnitude is the worldwide chess variant
community capable of?  In any case, we need at least a few more.

'If Archbishop and Chancellor have equal value, it DOES NOT IMPLY ANYTHING
for the value difference of Rook vs Bishop. They are all different pieces,
and have nothing to do with each other.'

YES it does according to my model and every quality, holistic model built upon a proper foundation I have ever seen.  Contrary to your statement, I think it obvious to any logical person that the component pieces have at least SOMETHING to do with their composite pieces.

Some computer chess programmers are notorious for achieving useful relative
piece values that are within decent range of their optimums based purely upon AI playing strength without creating any coherent, fully-developed theory that is logically explained, justified and consistent.  Unfortunately, such people contribute little to the understanding of
relative piece values for themselves or other interested parties.

I have appr. two years of experience working with Reinhard Scharnagl's 
excellent SMIRF program, my fast dual-CPU server and choice Capablanca chess variants.

Reinhard Scharnagl would compiled two, otherwise-identical versions of his 
program using his and my favorite sets of relative piece values (at that time) which would played against one another using a great amount of time per move.  Eventually, we carefully completed many games this way.  We would both analyze the game results and discuss conclusions.  Sometimes we would agree.  Sometimes we would disagree.  Subsequent tests would settle disagreements ... sometimes.  In this manner, we both improved our models over time until we reached a point where any further minor improvements became prohibitively difficult to achieve within a survivable time frame.

'In real life the value of a piece is not the sum of the value of each of its individual moves ...'

YES it is although not exactly.  The moves of component pieces of a composite piece have far more effect upon determining its relative piece value than ALL other factors added together.

'... but also depends critically on properties like mating potential,
color-boundedness, forwardness, speed, manoeuvrability, concentration,
sensitivity to blocking.'

I have also read ALL of the pioneering works of Betza on the subject.
Essentially, my model mathematicized a subject (to the extent possible
present day) he had only speculatively verbalized.  Rest assured, my model 
makes quantitative adjustments for all non-trivial, effecacious factors to relative piece values that I know of with certainty.

You need to read and thoroughly understand my 58-page paper on the subject.

universal calculation of piece values
http://www.symmetryperfect.com/shots/calc.pdf

'Theoretical considerations like you refer to are just nonsense, with no
connection to real life.'

The connection of my model to 'real life' is very strong.  My theory was
adjusted and refined numerous times to comply with game results over
different piece sets and game boards.  Experience dictated the details
of the theory in accordance with the scientific method.

'What would you rather have (if you can choose to make a trade or
not), a piece that is more 'valuable' according to some contrived
reasoning, or a piece that gives you a larger probability to win the game?'

Both.

Under a proper model, they should not be mutually exclusive at all.
In fact, they should be in agreement ... until a point in the endgame
where checkmate becomes possible.  Be mindful that significant
differences in relative piece values between the opening game, 
mid-game and endgame (to the limited extent that they are applicable)
are accommodated under sophisticated models.
____________________________________________

See the published values of Ed Trice and Reinhard Scharnagl for
CRC pieces upon the 10 x 8 board.

http://www.gothicchess.com/piece_values.html

In addition to the published values of Hans Aberg and Derek Nalls, this verifies that it is beyond dispute that your published values for the archbishop and chancellor are radical.  Your radical contention that an archbishop and a chancellor have appr. equal relative piece values requires an especially sound theoretical framework to be convincing.  Instead, all I am receiving from you is piecemeal descriptions of endgame scenarios where material values are likely to disappear and become meaningless compared to positional values (i.e., checkmate achievable regardless of material sacrifices) and consequently, conclusions drawn are likely to be faulty.