Comments by DerekNalls

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'.

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.

Mirror West Chess
http://www.zillions-of-games.com/cgi-bin/zilligames/submissions.cgi/98798?do=show;id=1429

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.

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.

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.

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).

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.

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.

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.

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.

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'... 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

'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.