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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 2005-02-16 UTCExcellent ★★★★★
My, you are a barn-burner!
[Fast, too.]

You seem to clearly understand what you have undertaken and introduced. 
For the test purpose you have in mind, my preliminary assessment is that
your assortment of games are above average to excellent.

Are you hoping for a collective interest and effort which will get enough
of these games adequately playtested within a reasonable time to prove
and/or disprove one of our competing, mutually-exclusive hypotheses?

Perhaps, it will happen.
I hope so.

Best of luck and my compliments for your remarkable initiative!

By the way, you may have invented a great game today (which you will
someday be remembered for) even if doing so was merely incidental to your
main purpose.

Mark Thompson wrote on 2005-02-16 UTC
If you really want to go for the ultimate in symmetry, I would suggest we
need to do away with the notion of a square board. A square has only eight
symmetries: reflection NS or EW, 180 degree rotation, or any (or no)
combination of these. Indeed, the ultimate in symmetry would be to do away
with the board's edges: the board should be infinite, hence giving it
translational as well as reflectional symmetry. And we should do away with
the notion of cells within the board: the most symmetrical 2-dimensional
object being the entire Euclidean plane, in which any point is equivalent
to any other. Then we have complete rotational symmetry, about any point,
as well as translations and reflections.

But since we're pursuing symmetry as the ultimate goal here, we need to
embolden ourselves to take the next vital step as well. To do away with
the last vestiges of ugly asymmetry, we must also abolish the pieces: for
once pieces are introduced into our pristine continuum, they render the
game asymmetrical again, by causing some points and directions to have
more importance than others: in particular, the points pieces occupy, and
the directions they would need to move to attack other pieces, would have
special importance. Our ultimate, perfectly symmetrical chess must
therefore consist of an infinite plane with NO PIECES AT ALL.

It might be objected that without pieces it will be difficult to state
rules of movement, capture, initial setup, and object. But clearly, since
we desire a perfectly symmetrical game, we must abolish these notions as
well: because the perfectly symmetrical chess game must be symmetrical in
time as well as in space, and therefore it must have no beginning, no end,
and no change: the state of the game at any point must be the same as its
state at any other point. 

And so, at last, we have our perfectly symmetrical game: no cells, no
pieces, no goal, no players: is not its perfect, chaste serenity a thing
of beauty? Have we not achieved true theoretical perfection? And can we
not get back to discussing real chess games now?

Fergus Duniho wrote on 2005-02-16 UTC
My reflection on these games has led to the conclusion that Symposium
Chess, named for a story told in Plato's Symposium, is the variant that
most closely approximates Chess while having perfect bilateral symmetry.
Almost any Game of Chess can be played as a game of Symposium Chess. So
can almost any game of Sinister Queens Chess. A game of Symposium Chess
could also play out as the mathematically equivalent mirror image of
either Chess or Sinister Queens Chess. White's first move cannot
determine which of these the game will be played as. After White's first
move, all four possibilities remain. So each move White can make gives him
about four times as many possible games as the first move in Chess makes
possible. But half of these are mathematically equivalent to the other
half, and it turns out that half of White's moves lead to games
mathematically equivalant to what would follow from the other half. If we
consider only the moves available to White on one side of the board, say
the left side, each possible combination of King and Queen remains
distinct, so that each move leads to four times the possible games as a
move in Chess does. And if we consider the moves available on the other
side, the same will be true, but each game in one set will be paired with
a mathematically equivalent game in the other set. So White's first move
let's him choose from only about twice as many possible games as he has
to choose from in Chess. If White had 40 opening moves to choose from, he
would have more control over the course of the game on his opening move,
but with only ten mathematically distinct opening moves available,
White's first move exerts less control over the course of the game than a
first move in Chess does.

Besides taking away some of the control White has on his opening move,
Symposium Chess gives more control to Black. Both players have the power
to differentiate their Monarchs into King and Queen. This gives players
power not only over the course that the game will take from there but also
power over the significance of previous moves.

Now, although most games of Chess can be played as games of Symposium
Chess, an actual game of Symposium Chess would probably play out
differently than a game of Chess, because it does change the dynamics of
the opening game. Until a player differentiates his King and Queen, his
opponent doesn't have a clear target for his attack, and if he does pick
one Monarch as the focus of his attack, that just increases the odds that
this Monarch will be the Queen and not the King.

Overall, it would seem that Symposium Chess puts White and Black on a more
equal footing, so that White gains less of an advantage from moving first.
But questions remain to be asked. How great a difference is it? What
significance does it make? Will the difference be seen only by
statistically comparing game scores of top players? Does this difference
make Symposium Chess the better game? If so, how much better?

My inclination is that it makes only a slight difference, and that if it
is the better game, it is not better by that much. I would not presume
that Chess is junk for being asymmetical while Symposium Chess, which is
not that different from Chess, is so much greater for being symmetrical.

Doug Chatham wrote on 2005-02-16 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?

Peter Aronson wrote on 2005-02-16 UTCGood ★★★★
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>

Joe Joyce wrote on 2005-02-16 UTCGood ★★★★
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.

Doug Chatham wrote on 2005-02-16 UTC
I wonder how Bachelor Chess compares with <a href=''>Bachelor Chess</a>. :-)

Joe Joyce wrote on 2005-02-16 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.

Derek Nalls wrote on 2005-02-17 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.

Fergus Duniho wrote on 2005-02-17 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.

Fergus Duniho wrote on 2005-02-17 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.

Derek Nalls wrote on 2005-02-17 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?

Derek Nalls wrote on 2005-02-17 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.

Fergus Duniho wrote on 2005-02-17 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 2007-02-11 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.

Derek Nalls wrote on 2007-06-17 UTC
Mirror West Chess;id=1429

Derek Nalls wrote on 2007-06-25 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 2007-06-26 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.

Abdul-Rahman Sibahi wrote on 2007-06-26 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 2007-06-27 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.

Derek Nalls wrote on 2007-06-27 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.

Jeremy Good wrote on 2007-06-27 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.

Abdul-Rahman Sibahi wrote on 2007-06-27 UTC
In fact this setup has the same problem Derek complained from in Mormon Chess, all knights start on the same color.

Sam Trenholme wrote on 2007-06-27 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.

Derek Nalls wrote on 2007-06-28 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).

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