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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 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.

Derek Nalls wrote on Sat, Jun 30, 2007 04:38 AM UTC:
The Games Of 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 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.]


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 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).

Sam Trenholme wrote on Wed, Jun 27, 2007 11:54 PM UTC:
Guys, please be aware that the Mormon church outlawed polygamy and bigamy a long time ago. Yes, they had polygamy in the 1800s, but that is a long time ago, and the church only allows one wife per man today.

On the topic, V.R. Parton (the guy who invented Alice Chess) invented a games called Double King Chess. This is a symmetrical opening: RNBKQQKBNR; checkmating either king (or attacking both kings at one with a piece that can not be taken) wins the game.

Abdul-Rahman Sibahi wrote on Wed, Jun 27, 2007 10:49 AM UTC:
In fact this setup has the same problem Derek complained from in Mormon Chess, all knights start on the same color.

Jeremy Good wrote on Wed, Jun 27, 2007 08:29 AM UTC:
N-R-N-B-B-Q-K-Q-B-B-N-R-N -- trivial contribution, I know, but this would allow all pawns to be defended.

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 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:


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.

Abdul-Rahman Sibahi wrote on Tue, Jun 26, 2007 05:31 PM UTC:
Mulling over things, how about this setup :

10 r n b q k q b n r
9  r n b q q q b n r
8  p p p p p p p p p
7  - - - - - - - - -
6  - - - - - - - - -
5  - - - - - - - - -
4  - - - - - - - - -
3  P P P P P P P P P
2  R N B Q Q Q B N R
1  R N B Q K Q B N R
   a b c d e f g h i

or this :

10 r b b q k q b b r
9  r n n q q q n n r
8  p p p p p p p p p
7  - - - - - - - - -
6  - - - - - - - - -
5  - - - - - - - - -
4  - - - - - - - - -
3  P P P P P P P P P
2  R N N Q Q Q N N R
1  R B B Q K Q B B R
   a b c d e f g h i


If you don't like the five Queens, files d and f could be just removed.

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 Mon, Jun 25, 2007 04:05 PM UTC:
Mormon Chess

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 Sun, Jun 17, 2007 03:27 PM UTC:
Mirror West Chess;id=1429

Derek Nalls wrote on Sun, Feb 11, 2007 01:31 AM UTC:
Large Variants

Mirror West Chess

This game extends the board to 10 files by 8 ranks, giving each player 1
extra queen and 1 extra king.  White's first rank is RNBQKKQBNR and
black's is symmetric to it.  Hence, the name as the western 5 files from
Chess are mirrored and duplicated.  Each player gets 10 pawns.

The 2 kings should be royal on an extinction basis with the loss of the
first king [whichever one] not stopping the game but loss of the second
king causing the loss of the game.  For the purposes of comparison to
Chess, I am displeased with this alteration to the game-ending condition
but I see no way to avoid it while preserving all of the original pieces
with their original opening setup and original numbers as much as
possible.  Notwithstanding, Mormon Chess is arguably a better game for
the purposes of comparison because the game-ending condition is not altered.

Essentially, 'long-side' castlings to both sides would be accommodated,
each involving a different king and rook.

This game could be implemented using the Zillions Of Games program but
not using SMIRF or ChessV due to their intolerance for more than 1 king.

🕸💡📝Fergus Duniho wrote on Thu, Feb 17, 2005 04:56 AM UTC:
<BLOCKQUOTE> I settle upon 'Mormon Chess' as my favorite (although I find its strange name unsettling). </BLOCKQUOTE> <P>Yes, I think that is one of the most promising ones. The first name I thought of was something like Episcopal Bigamous Chess, and then I immediately thought of the Mormons, a religious group well-known for bigamy. I didn't check beforehand if Mormons have bishops, but I just did now, and they do.</P>

Derek Nalls wrote on Thu, Feb 17, 2005 04:25 AM UTC:
'The idea is to change only one factor, asymmetry to symmetry, and
see whether this is an improvement.'

Upon reflection, I agree.  Yes, it is imperative to isolate one variable
to stay on-track with your test objective.  I got distracted by Aronson's
ideas for better games (which have a worthy place elsewhere).

I settle upon 'Mormon Chess' as my favorite
(although I find its strange name unsettling).

I wish its number of board spaces and pieces were closer to the game it
is being tested against, though.

Derek Nalls wrote on Thu, Feb 17, 2005 04:03 AM UTC:
'Although they gain left/right symmetry, for whatever that is worth,
I think it is more important to have one's Bishops on opposite colors.'

Your assessment is correct.

Having both bishops trapped in the same spacing (light or dark) is a
serious imbalance (asymmetry) and design flaw.

This is not a correct way to gain left-right (E-W) symmetry.  Fortunately,
it is not unduly difficult to devise a correct way to gain left-right (E-W)

If you gain a treasure chest but its weight sinks your ship, what have
gained ultimately?

🕸💡📝Fergus Duniho wrote on Thu, Feb 17, 2005 03:47 AM UTC:
Peter, I did have Potential Chess in mind, since I was still living in
Rochester when David created it, and he told me about it. But I don't
remember if we ever actually played it. I'm meaning to elaborate on the
rules of Symposium Chess to fill in the details. Regarding check, here's
what I have in mind. 

When both of a player's Monarchs are checked simultaneously, he must move
to eliminate one or both checks. If he cannot eliminate either check, it is
checkmate. If he eliminates only one check, the one no longer in check then
becomes the King, and the one left in check becomes the Queen. If this is
done by moving one of the Monarchs, it must move as a King, since this is
the Monarch that will become a King. If he can eliminate both checks, such
as by capturing a piece forking the two Monarchs, and this does not involve
moving one Monarch as a Queen, then the two Monarchs remain Monarchs.

If a single Monarch is checked, and it is left in check, then it becomes a
Queen, and the other Monarch becomes King.

If a Monarch is deliberately moved into check, it becomes the Queen, and
the other Monarch becomes King.

It is illegal to make a move that puts both of one's Monarchs into

The general rules are that you cannot do anything with two Monarchs that
you cannot do with a King and Queen, no move may treat a Monarch as though
it were both a King and a Queen, and when any move is legal only under the
assumption that one Monarch is specifically a King or specifically a
Queen, then the two Monarchs immediately differentiate into King and

If Sinister Queens Chess increases White's advantage, then that supports
the importance of bilateral symmetry over diagonal symmetry.

While a leaperless combination of Episcopal Chess and Bigamous Chess might
be closer to Derek's ideal, that was never the goal of this project, which
is merely to create symmetric variants that are as close as possible to
Chess. The idea is to change only one factor, asymmetry to symmetry, and
see whether this is an improvement. Removing the Knights would spoil the
results of any comparison.

🕸💡📝Fergus Duniho wrote on Thu, Feb 17, 2005 03:17 AM UTC:
Doug, a bug is something to debug and get rid of, whereas a feature is something planned. Having the Bishops on the same color is neither a bug nor a feature. It is a necessary evil, a consequence of this method of trying to create a symmetric game that is otherwise as close to Chess as possible. If only because the Bishops do start on the same color, I think it is safe to conclude that Bachelor Chess, Spinster Chess, and Narcissus Chess are all inferior to Chess. Although they gain left/right symmetry, for whatever that is worth, I think it is more important to have one's Bishops on opposite colors.

Derek Nalls wrote on Thu, Feb 17, 2005 01:37 AM UTC:
'A leaperless combination of Bigamous Chess and Episcopal Chess with
RBBQKQBBR would probably be closer to Derek's ideal, I would think, and
avoid the 'all Bishops on one color' problem of Bigamous Chess.'

Just my opinion-

On an 8H x 9W board, this is the best possible test game of all I have
seen proposed if you are willing to admit one more large variant.

All credit is rightfully Aronson's.

Joe Joyce wrote on Wed, Feb 16, 2005 11:19 PM UTC:
Doug, after looking your version over, I think I can safely say that Bachelor Chess is probably better than Bachelor Chess. :-) I played over the Zillions vs Zillions illustrative game. Loved the humor although it hurt my head so much it took me two tries to play through the game. It made me feel much better about the two Joe vs Joe openings. I did push the pieces around some afterwards - is there any decent opening other than 1) e3 c4 ? On a serious note, I think the geometry conspires against the pieces here, and again I suspect white has the best of it. I'd need to find someone other than me as an opponent, though.

Doug Chatham wrote on Wed, Feb 16, 2005 09:43 PM UTC:
I wonder how Bachelor Chess compares with <a href=''>Bachelor Chess</a>. :-)

Joe Joyce wrote on Wed, Feb 16, 2005 06:50 PM UTC:Good ★★★★
Fergus; some thoughts on Bachelor Chess.
	I  went to bed swearing I would not get involved in this, but I woke up
thinking about geometry and Bachelor Chess. I believe the geometry of the
board is a key factor in any game, the first factor to make or break a
game. So, I set up and played your first variant a bit. First, I assumed
the board is a checkerboard, with a white square on the white player's
right corner, so I covered the original 'A' file and set the pieces up.
Both white bishops are on white squares, both black bishops on black; an
interesting asymmetry. The white king starts on a black square; and the
black, on a white, as are their castling squares. Here are two openings I
1)	d4		d5
2)	f1-e3		e6 rather than c6, allowing check
3)	e1-b4		f1-d2 white attempts trade of B for N, black   
declines, but N placement blocks Bs
4)	b3		b7
5)	c4		c5
6)	Pxc5		Pxc5
7)	b4-a5 check	e7-b6 if 7) ... d8-e7, 8) PxP PxP 9) NxP check
8)	BxN check	PxB
9)	PxP		PxP
10)	NxP		a8-a6
white may continue by castling or by c1-g5 check, with much the better
The way this played out, I felt black should not directly contest the
center of the board with 1) ... d5
The second opening:
1)	d4		e3 
2)	c1-f4		b8-c6
3)	c3		d5
4)	b1-d2		b6
5)	e4		c8-b7
6)	PxP		PxP
7)	f1-e3		c6-e7
8)	BxP check	KxB probably a serious blunder on white's part
9)	c3-c4		a8-d8
10)	PxP		NxP possibly better if ... BxP
11)	NxN check	BxN
12)	O-O check	e8-c6 white has a passed pawn that is going nowhere fast for
a lost bishop

As I am not the best of players, and cannot play chess against myself,
these openings are not of the highest quality - the B sacrifice, in
particular, was poor, as it could not be followed up. White may actually
have an edge in this variant, but I am certainly not good enough to 
tell, only to suspect this is the case.
However, I do get some clearer impressions of this variant. I think the geometry
is important, as I feel these games are not as subtle as FIDE chess. Two
of six non-royal pieces can never directly interact*, yet they attack the
two most likely squares the opponent's king will occupy. Checks appear to
be easier in the opening. I always had the urge to trade one of my bishops
for the 'opponent's' knight, believing this is advantageous. I think
the openings and patterns of threats are considerably reduced, and less
subtle, because of the geometry. The game gives me more the feel of a
bludgeon than a rapier. This could be because of my style of play,
however. I do believe the knight is worth more than the bishop, and I'd
definitely prefer to have 2 knights and 1 bishop against 2 bishops and 1
knight. I would also think this admittedly very preliminary analysis has some
relevance for your other 7x8 variants and the 58 square variants, 
as the geometry is basically similar. I would suggest a variant of this
game on a 7x9 board, but I wonder if the draw potential goes up. For what
my opinion is worth, I think this is an interesting variant, but FIDE
chess is better, and better because of its' geometry. The 8x8 board
allows better pawn moves in the opening and balances the bishops.
*This would seem to increase the subtlety on the surface, but that's not
the impression I got moving pieces.
I see Peter Aronson** and Doug Chatham anticipated a couple of my observations. 
To Doug, I believe the answer to your question is: 'yes'.
To Peter, I'm real new at this, could you direct me to your sources? Thanks. 
**My error on confusing Spinster queens and Sinister queens - 
apparently Mr. Aronson does not confirm my suspicion that white has 
the advantage in the 7x8 variants, as Sinister Queens is 8x8.

Peter Aronson wrote on Wed, Feb 16, 2005 04:39 PM UTC:Good ★★★★
Assorted comments: <ul><p><li> Symposium Chess looks a bit like a more restrained version of <a href='/play/erf/Identifi.html'>Identific Chess</a> or <a href='../other.dir/potential.html'>Potential Chess</a>, with the ambiguity restricted to the King and Queen pair. I'm wondering if the Potential Chess rule that a piece left in check becomes known not to be a King would make sense in this game. <p><li> The setup for Sinister Queens Chess is found in a number of historical variants. Curiously, I seem to recall that several commentators felt this setup <em>increased</em> White's advantage. Certainly it has been universally abandoned for the current setup. <p><li> A leaperless combination of Bigamous Chess and Episcopal Chess with RBBQKQBBR would probably be closer to Derek's ideal, I would think, and avoid the 'all Bishops on one color' problem of Bigamous Chess. <p><li> You have a missing /DL tag at the end of the 7x8 section. </ul>

Doug Chatham wrote on Wed, Feb 16, 2005 04:24 PM UTC:
In your version of Bachelor Chess, the Bishops can only reach half the squares --- they both start on the same color. Is this a bug or a feature?

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