Check out Janggi (Korean Chess), our featured variant for December, 2024.


[ Help | Earliest Comments | Latest Comments ]
[ List All Subjects of Discussion | Create New Subject of Discussion ]
[ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]

Comments by DerekNalls

EarliestEarlier Reverse Order LaterLatest
Kings. A modest variant with more than one king. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]
Derek Nalls wrote on Fri, Jun 15, 2007 02:52 PM UTC:Good ★★★★
experiments in symmetry
Mirror West Chess
8H x 10W
http://www.chessvariants.org/index/listcomments.php?itemid=ExpSym

Just a few months ago, I independently proposed 1 of the 3 'kings' games
Abdul-Rahman Sibahi created.  Note that I did nothing with it.  No ZOG
implementation or Game Courier preset (if possible).  I hope ARS shows
more initiative than I.

'Is not the 10 x 8 version with two kings more symmetrical than
symmetrical variants with just one king?  Because a solo king stands out
as an asymmetry to the rest of the pieces on the board.'

Yes, it is impossible to symmetrically place one king upon an 8H x 10W
board because there is no defined, single center file.  Since there are
two center files, two kings are required.

Derek Nalls wrote on Fri, Jun 15, 2007 05:44 PM UTC:

All of the games on the 'experiments in symmetry' page (including Symposium Chess) were invented by Fergus Duniho. To the best of my knowledge, he never considered any of them worthy of development.

In the comments section under that page, I proposed only one game- 'Mirror West Chess'.


Derek Nalls wrote on Sat, Jun 16, 2007 06:16 AM UTC:
I think Sam Trenholme's concern about drawishness is well-founded.  So, I have abolished castling (a special move designed to enhance the protection of a single king) from all variants of Mirror West Chess.  Furthermore, there are variants included where the 2 royal pieces have the movement of a wazir or ferz instead of a man (i.e., king).

The submission I just sent to Zillions Of Games consists of 48 variants total.

Derek Nalls wrote on Sat, Jun 16, 2007 01:28 PM UTC:
Mirror West Chess
http://www.zillions-of-games.com/cgi-bin/zilligames/submissions.cgi/98798?do=show;id=1429

Experiments in Symmetry. Several experimental games to test whether perfect symmetry makes a game better.[All Comments] [Add Comment or Rating]
Derek Nalls wrote on Sun, Jun 17, 2007 03:27 PM UTC:
Mirror West Chess
http://www.zillions-of-games.com/cgi-bin/zilligames/submissions.cgi/98798?do=show;id=1429

[Subject Thread] [Add Response]
Derek Nalls wrote on Wed, Jun 20, 2007 08:52 PM UTC:
Message #2255 in the 'Chess Variants' Yahoo group described 'a game with
no name' by Derek Nalls that was, in retrospect, merely a flawed precursor
of the game that became Optimized Chess by OmegaMan [my pen name for games
I invent but do not recommend playing].  So, thank you but I doubt it is
worthy of mention.

symmetry[Subject Thread] [Add Response]
Derek Nalls wrote on Thu, Jun 21, 2007 10:41 PM UTC:
I think you are on the right track putting an emphasis on symmetry to solve
problems involving fairness (and balance) for chess variants.  Obviously,
there are several factors that determine the complex functioning of a game
which affect fairness- more than just geometric symmetry of the pieces (and
board) ... as Thompson correctly points-out.  From my own positive
experiences in refining Hex Chess SS, I am confident that if your efforts
are thoroughgoing and if you are willing to break with tradition to a
sufficient extent with your game designs, you will achieve a level of
fairness that satisfies your high standards.

Some problems impacting fairness are traceable to using the traditional
white-black turn-order in chess variants.  The first-move-of-the-game
advantage (for white) is too high in relatively-small games such as
standard Chess.  Of course, this problem can be reduced by the use of more
pieces per player, more limited-range pieces instead of unlimited-range
pieces, a larger board, etc ... but never solved and eliminated as a game
becomes ridiculously large overall and unplayable for people.

The white-black-black-white turn-order has passed every test I have thrown
at it.  The predestined unfairness generally characteristic to turn-based
chess variants [With theoretically 'perfect play' by both players, one
player is certain to win despite the unsurpassable gameplan of the other
player in Hex Chess SS.] is so very small, I am unable to pinpoint whether
it actually favors white or black (although I hold the opinion that it
probably favors white).  So, I have abolished draws as an admissible
game-ending condition while maintaining a higher level of fairness than
exists for the vast majority of chess variants.

In case you are wondering, conclusive endgames are always achievable in
chess variants having the appropriate pieces starting the game and the
appropriate board geometry.  This so-called 'pendulum turn-order' is
symmetrical and fair to black in ways that the white-black turn-order
provably fails to be.

These two statements have complicated explanations available here:

Description
Symmetrical Chess Collection
http://www.symmetryperfect.com/shots/descript.pdf

I recommend reading the entire 52-page essay to better understand the
following sections.

See section 14 (pages 20-23).
'minimizing the first-move-of-the-game advantage'

See section 20 (pages 36-41).
'game-ending conditions'

Living proof exists in all 3 variants of the working game Hex Chess SS
which requires the Zillions Of Games program to play:

Symmetrical Chess Collection
http://www.symmetryperfect.com/shots

Experiments in Symmetry. Several experimental games to test whether perfect symmetry makes a game better.[All Comments] [Add Comment or Rating]
Derek Nalls wrote on Mon, Jun 25, 2007 04:05 PM UTC:
Mormon Chess
http://www.symmetryperfect.com/shots/Mormon

Push the 'Download Now' button.

Out of curiosity, I implemented this invention by Fergus Duniho for the Zillions Of Games program.  This game and Mirror West Chess are the two best symmetrical alternatives for comparison to standard Chess (in my opinion).

Since this game is not mine, I do not feel at liberty to submit it to the ZOG web site or The Chess Variant Pages for publication, though.  I leave that decision to Fergus Duniho if/when he rejoins us.  Just consider this a demo available only to CV Pages activists (who follow the new comments).

Derek Nalls wrote on Tue, Jun 26, 2007 03:51 PM UTC:
I removed Mormon Chess due to a minor design flaw.

After ZOG implementation, I noticed that both color-changing pieces (i.e., knights) start the game upon spaces of the same color (i.e., light or dark).  Ideally, they should be upon opposite colors for balance.

Although this flaw is not anywhere near as severe as, for example, having both color-bound pieces (i.e., bishops) start the game upon spaces of the same color, it creates a slight imbalance with respect to the ability of both players to threaten or occupy spaces based upon color at the start of the game.

Thanks to Fergus Duniho, notwithstanding.

Derek Nalls wrote on Wed, Jun 27, 2007 04:51 AM UTC:
In hopes of solving the knights imbalance for Mormon Chess, I experimented with a Zillions Of Games implementation of a wider, 8H X 13W version having the following opening setup:

R-N-N-B-B-Q-K-Q-B-B-N-N-R

the first rank of white
(black is symmetrical to it)

Unfortunately, it leaves 2 undefended pawns, on the b-file & the l-file.  Moreover, they can both be exposed to attack simultaneously in one move by an opponent advancing the pawn on the center g-file by 1 or 2 spaces.  Incidentally, this is also a sound move toward development.  Obviously, if white does so on the very first move of the game, black cannot prevent this and can only react to defend one of the two threatened pawns.  The other, undefended pawn can be stolen.  This is hardly a fair way to start the game.

I give-up on this game idea.

Derek Nalls wrote on Wed, Jun 27, 2007 05:17 AM UTC:
In my opinion, both of your game proposals look like recipes for better games than standard Chess that are symmetrical.  However, I think opening setups that are 2 ranks deep with power pieces deviate too greatly from that of standard Chess to be directly comparable in accordance with the intent of Fergus Duniho's 'experiments in symmetry'.

His idea was to minimize the differences, to the greatest extent possible, between 2 games otherwise identical except for their respective symmetry and asymmetry.  In this manner, the tested variable could be isolated in theory.  In practice, this has been difficult.  To my present thinking, the only somewhat-satisfactory symmetrical game in existence to test against (asymmetrical) standard Chess is Mirror West Chess.  Unfortunately, this game has no single royal king per player.  Instead, it has 2 royal pieces (royal wazirs OR royal ferzes in different variants) per player.  So, its value for comparison is dubious.

Derek Nalls wrote on Thu, Jun 28, 2007 12:46 AM UTC:
Thank you for directing me to Double King Chess by Parton!

This is just what the 'experiments in symmetry' need as a second somewhat-suitable game for comparison.  However, I would not use the game exactly as invented.  In fact, I would reinvent it substantially and give it a different name appropriately.

Essentially, I think of this opening setup as 'Mirror East Chess' (compared to 'Mirror West Chess') where the 5 eastern files from standard Chess are duplicated onto the west thereby creating a symmetrical opening setup of 8H x 10W.

With 2 royal pieces, 2 royal wazirs or 2 royal ferzes would be used instead of 2 kings (royal men) to prevent the game from being too drawish.  Moreover, the game-winning condition would be extinction of BOTH royal pieces to increase game stability and decrease the first-move-of-the-game advantage (for white).

Derek Nalls wrote on Thu, Jun 28, 2007 06:17 AM UTC:
The variants of Mirror East Chess with royal wazirs just bit the dust due to undefended pawns on the c-file & h-file.  This leaves only variants of Mirror East Chess with royal ferzes being stable.  

[Mirror West Chess has no such limitations.]

R-N-B-F-Q-Q-F-B-N-R

the first rank of white
(black is symmetrical to it)

Note:  F = ferz (royal)

I will submit Mirror East Chess to the ZOG web site soon.

Derek Nalls wrote on Sat, Jun 30, 2007 04:38 AM UTC:
The Games Of OmegaMan
http://www.symmetryperfect.com/shots/omegaman

Push the 'Download Now' button.

11 Games

Optimized Chess 8H X 10W
Embassy Chess 8H X 10W
Sym Chancellor Chess 8H X 12W
Sym Archbishop Chess 8H X 12W
Chancellor Chess 8H X 10W
Archbishop Chess 8H X 10W
Non-Standard Chess 8H X 8W
Mirror West Chess 8H X 10W
Mirror East Chess 8H X 10W
Sym Chess 8H X 10W
Bishop Pairs Chess 8H X 12W

The latest-version ZOG implementations of all of these games will always be available here.

Derek Nalls wrote on Sat, Jun 30, 2007 05:34 AM UTC:
After over 2 years, I think the 'experiments' are ready to begin.  Who knows if conclusive, objective (rather than opinionated, subjective) results will ever be obtained.

Please do not get confused by all of the variants I have stacked-on in an attempt to improve the basic games?  The default, first-loaded variants are all that are needed.  Specifically, out of the 8 game rules files (*.zrf) by OmegaMan, you need to use only 3:

Non-Standard Chess | No Self-Captures  (non-no.zrf)
Mirror West Chess | No Self-Captures  (mirror-w-no.zrf)
Mirror East Chess | No Self-Captures  (mirror-e-no.zrf)

If you are one of the few chess variant hobbyists who has not already played standard Chess to the point of exhaustion, first try-out the
'Non-Standard Chess | No Self-Captures | Mirror I | 2-Step Pawns | WB' variant.  Essentially, it is very similar to but not identical to standard Chess.  The differences will not harm you.  Still, you may use a bonafide standard Chess program available elsewhere if you prefer.  This is the singular asymmetrical game for comparison.

There are two symmetrical games available for comparison.  Play either or preferably both
'Mirror West Chess | No Self-Captures | 2-Step Pawns | WB' variant and
'Mirror East Chess | No Self-Captures | 2-Step Pawns | WB' variant.

Please let everyone know whether you preferred the experience of playing the asymmetrical game or the symmetrical game(s)?  [Yes, you will become famous.]

Admittedly, this rings more like an 'experiment in democracy' (which scares me) than a 'scientific experiment' but your ideas and observations interest me.

[Subject Thread] [Add Response]
Derek Nalls wrote on Fri, Jul 6, 2007 02:56 AM UTC:
When I searched-out Opti Chess, I expediently focused-in upon a select set
of only 24 CRC variants where the king & queen occupied the center files.

1.  Indisputably, the queen is the most valuable piece in the game (after
the king).

2.  I consider the queen the most capable piece at protecting the king
since the chancellor and archbishop can be threatened without reciprocity
from a large distance by sliders that move differently.  Specifically, the
chancellor can be threatened by the bishop and the archbishop can be
threatened by the rook.

Nonetheless, I was intrigued by your assertion that the 2 other composite
pieces (chancellor and archbishop) are worthy escorts for the king.  So, I
have been examining your select set of 72 CRC variants for a few days now.

Using more stringent criteria, I determined all 24 CRC variants centered
by the king & archbishop to have a minor fault due to the impossibility of
placing BOTH the queen and the chancellor on opposite-colored spaces than
the archbishop for balance.  So, I felt no need to examine them in further
detail.

The reasons?

1.  Composite pieces containing color-bound bishops (i.e., the queen &
archbishop) should be on opposite (light-dark) spaces for balance.

2.  Composite pieces containing color-changing knights (i.e., the
chancellor & archbishop) should be on opposite (light-dark) spaces for
balance.

This left me with a select set of only 48 CRC variants (24 king & queen
centered and 24 king & chancellor centered) that needed to be explored in
detail- half of which I had examined long ago.  Accordingly, I created a
*.zrf to chart my results visually and when finished, conveniently share
with others:

Select CRC Analysis Tool
http://www.symmetryperfect.com/shots/crc

I hope you find it interesting.

Archbishop Chess. Replace one of the marshalls from birds chess with a cardinal and you have Dominique Leste's Archbishop Chess.[All Comments] [Add Comment or Rating]
Derek Nalls wrote on Thu, Jul 12, 2007 02:48 AM UTC:Good ★★★★
Upon noticing that Janus Chess, the best known entry within this class of games, had a flawed design with 2 undefended pawns, I did a complete study of all select opening setups with minimized asymmetry upon the 8H X 10W board using the 'Janus Chess piece set'. I discovered that yours is the single, most stable opening setup possible. Well done!

Chancellor Chess. On a 9 by 9 or 9 by 8 board with a piece with combined rook and knight moves. (9x9, Cells: 81) [All Comments] [Add Comment or Rating]
Derek Nalls wrote on Thu, Jul 12, 2007 06:02 AM UTC:
I did a complete study of all select opening setups with minimized asymmetry upon the 8H X 10W board using the 'Chancellor Chess piece set'.  I am referring to games designed with an architecture analogous to how Janus Chess and Archbishop Chess are based upon 2 archbishops but with 2 chancellors instead.

I discovered this to be the single, most stable opening setup possible:

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

I will name it 'Chancellor Chess 8H x 10W' and post it to the ZOG web site soon.

Derek Nalls wrote on Thu, Jul 12, 2007 03:27 PM UTC:
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.

[Subject Thread] [Add Response]
Derek Nalls wrote on Fri, Jul 20, 2007 01:09 AM UTC:
Select CRC Analysis Tool
http://www.symmetryperfect.com/shots/crc

The documentation has been expanded and revised so that the Zillions Of
Games program is no longer needed to view all of this information in
detail.

Description
http://www.symmetryperfect.com/shots/crc/descript.pdf

Faults
http://www.symmetryperfect.com/shots/crc/faults.pdf

Ratings
http://www.symmetryperfect.com/shots/crc/ratings.pdf

Report
http://www.symmetryperfect.com/shots/crc/report.pdf

Summary- 48 Games
http://www.symmetryperfect.com/shots/crc/summary.pdf

Presentation- 48 Games
http://www.symmetryperfect.com/shots/crc/48-games.pdf

Derek Nalls wrote on Sat, Jul 21, 2007 04:18 AM UTC:

'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.]

______________________________________________________

'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


Derek Nalls wrote on Sat, Jul 21, 2007 06:53 PM UTC:
'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.

SMIRFBROKEN LINK!. Program that plays various 8x10 chess variants.[All Comments] [Add Comment or Rating]
Derek Nalls wrote on Wed, Jul 25, 2007 05:22 PM UTC:
The link to SMIRF is dead.  A transition is underway that will take a long time from SMIRF for IBM-compatible computers running MS Windows to Octopus for Mac computers and OS.

SMIRF > Octopus
(in German)
http://web.mac.com/rescharn/iWeb/Octopus/Blog/Blog.html

The last version of SMIRF released was BC-168a.  If you want it but missed your chance to download it, please send me an E-mail privately.  I can send you the file.  Please remember it is donationware- donations to its developer, Reinhard Scharnagl, are encouraged!

[Subject Thread] [Add Response]
Derek Nalls wrote on Wed, Jul 25, 2007 08:57 PM UTC:
I don't know exactly what is going on at BrainKing but I would refrain
from using their limited stats without reservation to draw firm
conclusions.  The first-move-of-the-game advantage for white in Chess by a
few percent is well-documented via various, numerous reputable sources.

I suspect that a minority of individuals there are experimenting-
attempting, mostly without success, to devise radical yet effective
opening theory gambits when playing white.  Such people are unconcerned
about winning the game compared to 'discovering something great' that
works against all-most other Chess players.  This could skew the stats by
a few percent.

I doubt that there is a chess genius amongst them of the caliber of Bobby
Fischer.  I doubt that large, radical shifts in opening theory remain to
be discovered today.

The win-draw-loss stats for CRC and related games seem to make sense,
though.  They can be used to draw tentative conclusions (with a sizeable
plus-or-minus margin for error).

[Subject Thread] [Add Response]
Derek Nalls wrote on Thu, Jul 26, 2007 12:39 AM UTC:
You might notice that currently I am only publishing the relative piece
values for 3 games:  FRC, CRC and Hex Chess SS.

I only consider the established relative piece values reliable for FRC
(primarily) & CRC (secondarily).  So, there is essentially no feedback to test a model against with any other chess variants.  Therefore, I suspect that the time and effort invested in calculating piece values for other games could be wasted if my model is flawed with other classes of games.

[Note-  Hex Chess SS is my personal, favorite invented game.  I was just
too curious to find-out its relative piece values even though they are
tentative.]

I understand that Joe Joyce may be just as curious as I about some of his
favorite games.  I respect that.  Still ... If he wants to know badly
enough, then he needs to calculate the piece values for these games
himself.

There are a few models that can be used.

My model is the most accurate one that can presently be read on the
internet (although it is well-tested only for games closely related to FRC & CRC).  My model is supposed to be virtually universal- adaptable to many different types of chess variants other than standard Chess- but this stated objective cannot be tested.  My model is the most complex to use (58 pages, currently).

Although Reinhard Scharnagl's model is easier to use and equally accurate
(according to 1 year of intensive computerized playtesting against mine),
it is not presently published anywhere that I know of.

25 comments displayed

EarliestEarlier Reverse Order LaterLatest

Permalink to the exact comments currently displayed.