Comments/Ratings for a Single Item

Fairy-Max is a derivative of the normal Chess engine micro-Max. This is
listed with a computer rating of slightly over 2000 at CCRL. It is not
really known how this corresponds to human ratings. The top engines on that
list are rated nearly 3300. At 10x8 Chess Fairy-Max is about 400 elo weaker
than my dedicated engine for this variant, Joker80. This is again derived
from my normal-Chess engine Joker, which is indeed rated around 2400 at
CCRL.

All I can say is that Fairy-Max should be beatable by a good club player at
normal Chess. But like playing any computer, you should play very secure,
and avoid tactical complications, as computers are very resourceful in
tactics.

To dumb it down a bit, you can give it shorter time. Either just set it for
a few seconds for 40 moves, and ignore your own clock, or specify the time
the human is supposed to obey, and define a large time-odds factor for
fairy-max (= engine #1). Like 40 moves per hour, and then a time odds of
120, so that Fairy-Max should do the 40 moves in 30 sec.

Of course even strong Chess players are likely to be a lot weaker at Spartan Chess then orthodox Chess, as humans rely a lot on memory and experience. While Fairy-Max could not care less whether it plays Spartan or FIDE, as it has no specific knowledge for either.

Just how strong a game does Fairy-Max play? 

I have had some friends download and use it and we are all impressed with how strong it seems.

> I have been asked a time or two about Spartan Chess sets;
> is there a plan to make one? At this time the answer is no.

For those that can handle a saw it is not that difficult to get
good-quality 3-d pieces: just buy two identical chess sets. One you leave
untouched, to play FIDE Chess. To play Spartan, you turn the Rooks
upside-down to make the Captains, reminding you they are Rook-like, but
slightly different. The Bishops of the second set can act as lieutenants;
to distinguish them from ordinary Bishops you make a second cut in the head
to remove a V-shaped chunk out of the top. The King of the second set
completes the Spartan King pair. So now you only need General and Warlord.
As the General is also Rook-like, you can make it by putting a Rook of the
second set onto a pedestal. Sometimes Knights have detachable bases, (or
you could cut the head off with a saw), and you could put one Rook on top
of that. Or you could glue it on top of one or two draughts chips. You
could glue the head of the Knight on top of the other Rook to make the
Warlord. (Or cut off the head of a Queen and replace it by the upper part
of the Knight. But it is always handy to have a spare Queen, so maybe you
don't want to demolish it.)

So the only work is really:
1) Complete the V-shaped cut in the Bishop heads.
2) Cut a Knight in two.
3) Combine the two Knight halves with the two Rooks (glue).

And you only have to do that for black!

Very interesting. I have not gotten to doing end-game tests yet. I tried
some more opening values:

A+H >~ Q
R+B ~ A

I have noticed that in tests like this Rooks tend to be under-estimated a
bit. Probably the opening value of the Rook in orthodox Chess is really
lower than the classical value 5, because it gets into play only late in
the game. But as it is difficult to trade with other material before it
gets into play, neglecting this effect and always using the value 5 (which
probably includes positional contributions like open-file bonus)is a
workable simplifiction.

For humans the best rule of thumb would be to keep simple integers as much
as possible, and the following system is pretty close to the truth:

Q=9
W=8
G=7
R=5 (5- before developed on (half-)open file)
K=5-
L=3+
B=3+
N=C=3
P=H=1

Bishops require some extra explanation anyway, which orthoChess players are
well aware off: alone it is equal to Knight (i.e. 3), but in a pair it is
worth significantly more. I could be said that because of the color-change
move the Lieutenant makes up its own pair, and thus equals the paired
Bishop in value even when it is alone.

So the easy-to-remember implication is that all light pieces are nearly
equal, but if possible, protect your Bishop pair or Lieutenant. The second
rule is that you don't have to be impressed too much by Rook attacks on
your spare King, as long as the latter is protected, and your other King is
in a safe location.

The thing that still puzzles me is that when you add everything up, it
seems the Spartans have a significant advantage. (Of course the Spartans
need some advantage to compensate the fact that they do not hve first move,
but that should be only 1/6 of a Pawn, and they seem to have more.) This
could be compensated by assuming the Hoplite is worth slightly less than a
Pawn. Your tests of K+8P vs K+8H suggest that, but there is more to it, as
in a more open position the Hoplites seem to regain the advantage. Of
course it shoud not come as a surprise that evaluation of Hoplite
structures involves much more than simply adding piece values, as it is
well known that for FIDE Pawns this is certainly the case. Hoplites turn
into passers much more easily than Pawns.

Anyway, currently I am running a match to calibrate the scale of the other
tests, by deleting a single Hoplite, (and after that I want to delete a
single Pawn) to be able to translate all measured score advantages into a
number of Pawns. My plans are to make a slight refinement of Fairy-Max
after that, so that it really implements the Bishop pair, by making the
last piece of a color-bound type worth 12.5% less than the programmed piece
value, and then run some tests of Bishops against Lieutenants.

Thanks, George. I like your version better, but didn't remember where I'd
seen it. The quote I grabbed from wikipedia was remarkably bland.

This is not to say there is anything wrong with Spartan Chess. I agree
wholeheartedly with Ji that this entire online conversation/balancing of a
very novel Chess with Different Armies force was totally fascinating. HG,
Steven, thanks to both of you. 

ps: Steven - see, you're actually safer when I'm on vacation... ask
George! :-D

And updated to realities ten years ago Archilochus' same lines introduce
''CMIX,Sacrifice'':
http://www.chessvariants.org/fiction.dir/poems/falconpoem10.html. The translation Joyce has misses the defiance in the Greek from several tries. Only armchair orthodox academics would come up with ''Life somehow seemed more precious'' and lose the meaning of Archilochus' clenched fist, whilst the captor waves his very shield triumphantly safely across the valley at him. To this insulting silent body language, he horrifically thunders back, importuning Ares or Athena, ''Some barbarian is waving my shield, a peerless piece of equipment I left behind under a bush. But I got away alive, so what does it matter? Let the shield go! Plague take it! I will find me another one hereafter -- and just as good to me!.'' HIS Shield of course can never be replaced...

Some barbarian is waving my shield,
    since I was obliged to
    leave that perfectly good piece of equipment behind
    under a bush.
    But I got away, so what does it matter?
    Life seemed somehow more precious.
    Let the shield go; I can buy another one equally good. 

Archilochus of Thasos

Self-described mercenary and poet, Archilochus was revered by the Greeks
as a lyric poet of the first order, credited with inventing iambic meter. He
wrote a/the victor's song for the Olympics, but was reputedly thrown out
of Sparta for cowardice and licentious poetry. So much for the man the
Greeks considered the equal of Homer, and whose birthplace of Paros
instituted a hero cult for him that lasted 8 centuries. ;-)

Yes, I see your point regarding the hoplite. 
I am making the change now.

Unnecessary and certainly not used in sample game.

Some remarks about the page you prepared:

I am not sure if this is a typo, but in the notation part you use
lower-case 'h' for Hoplite. In general this is a bad idea as it leads to
ambiguities with the file indicators, and WinBoard would not understand the
moves. In the sample game you don't seem to use it at all, but treat the
Hoplites like they are Pawns (which is probably a good idea, but would only
work in WinBoard if the Hoplites were indeed represented by a Pawn type, in
stead of Lance.

As to the two Kings: there actually is a variant that can be played on
Internet Chess Servers such as FICS and ICC which is called TwoKings. The
f-Bishop is replaced by an extra King in the FIDE setup. Despite the equal
armies, the game is not symmetric: tke King that at any time is closest to
a1 (in a raster-scan sense) is royal, the other not.

Well, no more test results from this side in the forseeable future, I am
afraid. It seems the hard disk of my Chess PC crashed, and I can no longer
boot from it.

The second set of 200 games, with white Spartans, ended in a 53% victory
for them. That might just be due to some remainder of the white advantage.

WinBoard has two graphics modes: built-in bitmaps, and font-based piece
rendering. Each piece type has a fixed built-in bitmap, but with font-based
rendering you can assign an arbitrary glyph to it (by assigning the
corresponding font character in with the /pieceToFontCharTable option).
WinBoard has a fixed idea how its various piece types move. 

But since this game for the time being has to be played with legality
testing in WinBoard switched off, you can basically represent the Spartan
pieces by any of the 22 WB piece types you like. The engine is in charge of
determining the move legality, and WB will dutifully move the pieces as
instructed by user or engine, in this mode. There is a downside to this,
though: to store the game in Short Algebraic Notation, WB has to know how
pieces move. If it doesn't, it cannot decide correctly if the otation is
ambiguous. So a move that WB thinks is illegal for the piece will always be
written in long algebraic notation. And if the move is legal, WB has to
figure out if there is another piece of the same type that could also
legally move there, in order to add disambiguation to the SAN. So it could
either add unnecessary, or omit necessary disambiguation. That is,
(un)necessary for the Human reader; WB will always be able to read the file
back unambiguously, exctly because it adds the dismbiguation according to
its own idea of the possible moves. But the bottom line is that you get
much nicer SAN output if the moves the piece can do more or less correspond
to what WB thinks, even if legality testing is off.

For this reason I chose the Elephant for the Lieutenant: WB thinks this
moves as F+A in variant fairy (in some more specific variants known to WB,
such as Shatranj, it is restricted to A). Then only the sideway moves will
be illegal, and be written as long algebraic. Similarly, the piece
represenitng the Captain is thought by WB to move as R+D, and thus very
suitable for Rook-like pieces. The crossed swords is the WB standard
representation of the B+N, which was exactly what we needed, and the
6-pointed star of the R+N (which is close, and was an exact match before
the rule change). The Lances are a wild-card piece, and their moves will
always be written in long algebraic (and any move will be allowed even with
legality testing on). Unfortunately WB has no piece types for Berolina
Pawns: it implements Berolina Chess by redefining the motion of the normal
Pawn type in that variant (I wanted Pawns to look like Pawns even in
Berolina Chess). But you could not play Spartan Chess as Berolina with
legality testing off, because then also the white Pawns would be thought to
move as Berolinas. First I tried using normal black Pawns to represent the
Hoplites, but WB assumes they are FIDE Pawns and capture en passant, so
when they move diagonally to an empty square, white Pawns were disappearing
as a side effect! Thus I had to use something else. Now the Pawn symbol is
significantly less 'fat' than most other pieces, so usising, for
instance, the Ferz (which would at least get most non-captures as legal
moves) looked really ugly. The Lance was the only slim built-in symbol. But
for Hoplites it is of course very applicable, so I took the poor notation
of their moves for granted.

You can change the piece types used by WB in the /pieceToCharTable option
in the Spartan.ini file. If you put, say, the h in another place (replacing
one of the periods) it will use another piece for Hoplites, etc. To see
which symbols are available, you can switch to Mode->Edit Position, and
right-click a King to call up the context menu, and then promote it. When
you do this repeatedy, you will cycle through various pieces. The same when
you demote a Queen.

When you render pieces through a true-type (Chess) font, you can make them
look like anything. But you would have to supply the font.

I decided to swap colors for the second 200 games, to immediately average out any color bias or first-move advantage. (I am not sure there would be much of a first-move advantage in these tests, as Fairy-Max randomize its first three moves, so the chances that it will play a pretty useless first move are appreciable.) After 116 games they were exactly equal. I see a similar draw rate as you.

So it seems the following tentative conclusion is justified:
The setup with G=R+K and W=B+N is very well balanced, with 20% draw rate.

I have been watching the games for some time, and they are very
interesting. All pieces participate actively, their values are such that
there is plenty of opportunity for nearly equal trading or light
sacrificing. Most games get into an end-game, and because of the unequal
material, the end-games are always fascinating. It is half familiar because
of the Persian army, half exotic, (but not weird). All pieces are highly
symmetric, normal Chess pieces.

I really think this is a wonderful design, and to my taste it is immensely
aestethically pleasing. SO TO ALL READERS: I can highly recommend it!

I will continue to run tests for more exact piece-value determination, to
better tune Fairy-Max.

I ran 100 games overnight with:
G = R + K
W = B + N

Result was (W/B/d):
39/40/21

With W=B+K and G=R+N the Persians finally won with 54.6%. I have now
started a run where black moves first, to see how much the white advantage
is. As I have never done this kind of testing in asymmetric variants
before, I should be careful: there is the theoretical possibility that
Fairy-Max plays better with one color than with the other. This is because
of the order it generates moves: it scans the board looking for own pieces,
and for white it typically encounters Pawns first, while for black it
encounters Pieces first. And when two moves have equal score, it plays the
first one. So there could be a bias towards Pawn moves for white, and
against them for black. A style difference which could affect playing
strength. Normally I average out such a difference by not playing from a
single position, but from a pair with inverted colors. E.g. give white the
Spartan army on even games, annd black on odd games, and then play a match
with alternating colors, so that the same player always has the same army,
and the score kept by WinBoard is useful. Except that here I cannot do
that, because the Pawns are not identically, so I would either end up with
a Persian army with Hoplites, or with FIDE Pawns that move backwards, when
I set it up on the other side of the board. So I would really have to
change the directionality of the Pawn defintions in the fmax.ini file. If
there turns out to be a significant effect, I would have to conduct all
future tests as 200 games with black Spartans plus 200 games with white
Spartans and the reflected game definition, rather than just playing 400
games.

I guess it would be good to make a version of Fairy-Max that would
automatically reflect the move direction of all the black pieces, so that,
for instance, in orthodox Chess you would only have to define the Pawn one
time. That should not be too difficult. Then all pieces you define can be
automatically used for white and black, in stead of asymmetric pieces
having to be defined twice.

Btw, after 200 games the test with W=B+N and G=R+K was still practically
equal (50.5% in favor of the Spartans).

I never tested R+A or B+D. It seems concentration of targets is good for
piece value, though. On Knight vs Commoner this effect is overshadowed by
the slowness of the Commoner. But I would expect R+K (R+F really) to be
better than R+A, as the speed there is set by the Rook component. But only
slightly better.

For B+D I am pretty sure it must be worse than B+K (B+W). Not only because
of the smaller target concentration, but also because B+D is color bound.
Now color bounding is not a big deal if you have the pair. But it will mean
there is a large pair bonus, probably larger than the 50 centiPawn pair
bonus for orthodox Bishops. So I expect a pair of B+D to be marginally
weaker than a pair of B+K. But in the former case, 70-100 cP will come from
the pair bonus. And in Spartan Chess you have only one, meaning that it
will be some 50-65cP weaker then a single B+W.

I once tested B+K and R+K by crowning the Rooks of one side, and the
Bishops of the other, in an therwise standard FIDE array. IIRC the Crowned
Rooks had a slight edge there, but less than half a pawn in total. Standard
orthodox values (from Larry Kaufman) are B = 325, B-pair = 700 and R = 500.
The B+K pair tested 50 cP stronger than two Rooks, so 1050, a 350 cP
increase by crowning. Two B+K gained a bit more, so ~1380, so 690 a piece.
On that scale R+N = 900 and B+N = 875.

Relative Strength
I meant to pose this question in my last post but it slipped my mind. What
do you have to say about the relative strength of these two sets of
pieces?
1. Crowned Rook: R + K vs. R + Afil (jumps 2 squares diagonally)
2. Crowned Bishop: B + K vs. B + Dababa (just 2 squares orthogonally)

At first blush I though the jumping piece in each pair would be stronger
but now I am not so sure.

Setup
With the set up of the back rank not mattering so much I am standardizing
on using the setup in the rules: l g k c c k w l

Download Fiery-Max
I just downloaded Fiery-Max and it has the Warlord as uncrowned B+N and the
General the same way, that is R+N. I will change the General to a crowned
general by changing fmax.ini and start running games.

Weakening General and Warlord
My weakening both the the General to a (R + Afil) and the Warlord to a (B +
Dababa) is certainly too much a shift in favor of the Persian.

Knife Edge
It does not take much to change the balance a lot, just has to be the
change.

Well, after about 200 games the score has crept up to 57% for the Persians.
(Note that the download still uses the rules of your website!)
I am playing 40 moves/min, which makes the average game take 3 min. So I
can do 20 games/hour, 480 per day. But I am playing with ponder off, so it
takes only a singe core to play a game, and I have a dual. So I am running
two matches in parallel. :-)

On the other core I started the test with promotion to Colonel. It hardly
seems to matter. After 60 games, the Spartans are still leading by 70%. So
I guess we can scratch this idea, and I probably won't finish the run.

As the Persians are now winning, weakening the Warlord to a Crowned Bishop
was too much. When  look at the games, it is also awkward: the Spartans
have very much trouble in the standard setup to develop it. Fairy-Max is
reluctant to move away the f-Pawn (Hoplite) because it is shielding a King
and also reluctant to play Hg7h6, because it puts a Hoplite on the edge.
And after Hg7f6 it still blocks the Warlord after Wg7. So apart from the
fact that the intrinsic difference between B+N and B+K is much larger than
that between R+N and R+K, it also does not make good use of the B+K.

So the next thing I will try (on the other core) is to keep Warlord as B+N,
and make the General R+K. This should work much more smoothly: moving the
b-Hoplite immediately opens a file for it, so there should be no problem
developing. Promotion can then be to B+N Warlord, which, based on the test
with Colonel-promotion, should cause no weakening at all. An alternative would be to equip the B+K piece with some extra moves that help in development, e.g. a (2,2)-jump, or when that is too strong, only as a non-capture. But that makes it a bit of a weird piece, so I would prefer the clean R+K if it does the job.

When I have a setup that is fairly balanced, I will start running tests
with some pieces deleted from the opening array, (preferably in pairs, to
increase sensitivity), like Colonels on one side and Knights on the other,
to see how this changes the score (i.e. to whom such a trade would be
favorable). This to verify if the values I programmed into Fairy-Max are
close enough to reality. If not, it would be wise to repeat the tests with
corrected piece values in a second iteration. My experience is that
slightly wrong values hardly affect the score, as long as both sides share
the same misconception. (E.g. it does not matter if you program the value
of the Bishop higher or lower than that of the Knight: two Bishops will
beat two Knights by ~58% in both cases.)

54% winning advantage for white sounds great. 

If I understand correctly
General = R+N
Warlord = B+K

I will download your new version and find out.

Also, it seems you have a faster computer than I do :)

I posted the updated WinBoard/Fairy-Max package at
http://hgm.nubati.net/Spartan.zip . 
I also included the WinBoard help file, this time. (But don't look there for info on Fairy-Max; WinBoard is an independent project, and Fairy-Max is just one of the many hundreds of engines that can run under its control.)

This version of Spartan Chess is configured for having black promote to
R+N, and white to Q. (I had to fix a lot of bugs in WB to get that working:
it was not prepared for white and black playing with different piece sets
at all.) The explanation on the encoding in fmax.ini is fully updated. (And
with this version of Fairy-Max, the order of the piece defintions is more
important than it was before, but also this is explained.)

In the mean time, the test with the B+N replaced by B+K has reached 100
games, and white was leading by 54%. Now this is close to the normal white
advantage (which is 53-54%). So after this test is done (i.e. 400 games), 
I will try it with a start position where black has the first move.

To get back to Spartan Chess:

I doubt if shuffling the initial setup can create enough difference. I
agree that the proposed array seems the best, but as all pieces can jump
over the Pawns it is not terribly critical where you put them. The rule of
thumb is that 3 tempi is a Pawn, and we need to bridge more than a Pawn.
Even if you would make the Lieutenants and Colonels obstruct each other by
having them jump to the same square, that would only take 2 moves to
correct. (And a second move with the same piece to evacuate the square for the other might even be partly useful.)

Similarly, the sideway Lieutenant move is not worth very much. I tested the value of such moves on Bishops once, and there was almost no benefit compared to a plain Bishop, (about 0.25), as long as these came in pairs. The double Hoplite push will be worth something, but as the Spartans are not really dependent on Pawn moves for their development, I doubt it will be much. (It would be interesting to test it, though.)

Having artificial rules like the pinning of Hoplites is something I
generally dislike. Let me suggest two more options for trimming the Spartan
strength:

1) reduce the value of the General or Warlord, by using the corresponding
crowned slider rather than the knighted one. I am currently running games
whwer I replaced B+N by B+K, which should be worth R+0.25. The Persians are
leading there 24-18 (so not yet significant, but quite a change from what
it was). If this is too much, the R+N could be replaced by R+K, which
should be around 7.

I think the main problem is that the Hoplites are better in the end-game
than FIDE Pawns, so that the Persians need stronger piece material to hold
them back. Normally, trying to balance a significant Pawn advantage with
pieces unbalances a game, because in the middle-game the Pawns are
irrelevant, and the stronger pieces lead to quick checkmates. You can
always balance the over-all result to 50%, but you will get a game where
one side must inflict a quick middle-game checkmate, or he will be doomed
with certainty in the end-game. This is usually not very interesting. In
Spartan Chess, however, a quick middle-game mate is not easy because of the
dual King. So we can afford much larger strength differences in piece
material than usual without running into this problem.

This brings me to the second proposal:

2) If the problem is that Hoplites promote much easier than FIDE Pawns in
the end-game, it might be possible to offset this by strongly reducing the
value of the piece they promote to. So much, that a single promotion is no
longer decisive, but you need two. (Assuming that it is about as difficult
to promote two Hoplites as it is to promote a single FIDE Pawn.) So perhaps
it would work if the Hoplites are forbidden to promote to G or W. The
preferred choice than probably would be C (which has mating potential).
This would also provide more incentive to promote to K, which might be
stronger than C, but is so much weaker than G or W that the possibility to
promote to K in Spartan Chess in the current rules is of as much practical
relevance as promotion to B in orthodox Chess (namely none...).

Here is what I think I have deduced so far…

For second part of vector:
3 = Any distance slide to move or capture
5 = capture only
6 = move only
7 = Jump to move or capture
64 = first move only, movement no capture
E4 = first move only, jump, no capture

Now I just have to figure the first part, the destination square.

A friend of mine gave me some insight into the movement vectors. For
movement the first number is a direction and the second number a movement
type. 

For the Colonel therefore:
1,7: 1 = 1 square forward and 7=jump movement type
2,7: 2 = 2 squares forward and 7=jump movement type

I will see if I can figure the rest of it out in the morning.