Comments/Ratings for a Single Item

I just compared this game with Carrera's Chess at
http://www.chessvariants.com/historic.dir/carrera.html and found that this
game does not exactly match the starting position of Carrera's Chess. It
is in fact the mirror image of Carrera's Chess. The difference is that
the two new pieces have reversed positions in this game.

Since I'm working on updating my Chess,_Large.zrf file today, I was paying
more attention to the various games in it, and I started tripping up over
Aberg's variation. In this ZRF, which I originally wrote in 1998, I
implemented both Aberg's variation, or what I thought was his variation,
and a Capablanca variation of my own. When I originally wrote the ZRF,
this page did not exist, and I based my ZRF on the description which is
now at 

http://www.chessvariants.org/misc.dir/chessmods.html

I've just noticed that this old description has a contradiction in it.
The text description places the Chancellor on the Queen's side and the
Archbishop on the King's side, but the diagram reverses this. I based the
ZRF on the diagram, and my own Capablanca variation just reversed the
positions of Chancellor and Archbishop. Since this page agrees with the
old text and not with the old diagram, I take it that my variation was
actually Aberg's variation.

Furthermore, Pritchard's description of Carrera's Chess contradicts the
description on this website. Pritchard points out that Murray reversed the
names of the Champion and Centaur, and our page on Carrera's Chess was
based on John Gollon, who probably got his information from Murray. I
trust Pritchard more than Gollon or Murray, and so I take his description
of the game as more authoritative.

Therefore, it appears that Carrera's Chess, Aberg's Capablanca
variation, and my Capablanca variation all have the same setup. It looks
like my least original variant ever is even less original than I thought
it was. :)

All three variations keep the relative order between the old chess pieces,
keeping the positions of the rooks at the sides, and the queen and the
king at the center, with the white queen to the left. The board colors
are
such that the white queen ends up on a white square. All three variations
agree that the weaker of the two new pieces, the Archbishop, moving as a
Bishop or a Knight, should be at the Queen side, and that the stronger
piece, the Chancellor, moving as a Rook or Knight, should be at the King
side. This seems natural, as the Queen side is already stronger in
Orthodox Chess, thus balancing up the King side somewhat.

Bird put the new pieces next to the King, Capa between the Knights and
Bishops, and I suggested that they should be put next to the Rooks. I
think the preferred positioning may depend on playing style: The more
'rough' it is, the more one might want to have the new pieces to the
center. I like the Fianchetto where the Bishops point towards the center
four squares, and I want the light pieces early into the game, as is
customary playing in Orthodox Chess, therefore, I want the new, heavier
pieces out of the way in the earliest stages of the opening game.

In addition, widening the board I think will cause that too much moves
are
spent on castling preparations. Therefore I suggested an Enhanced
Castling
rule. The other variations do not have that, but those variations can be
played with or without it.

Note that the piece values given on this page are not empirical values at
all, but theoretical values: they are derived from the way the piece
moves, and comparison with known values for another game (8x8 Chess) for
pieces that move likewise. Empirical values are values that are derived
from win probabilities (as derived by statistical analysis of games) from
positions with material imbalance.

I have played and analyzed many thousands of such games, using my engine
Joker80 (currently the best free WinBoard-compatible 10x8 engine) in self
play, and I can vouch for the fact that the piece values given here are no
good. The true values are:

P=85, N=300, B=350 (pairBonus=40), R=475, A=875, C=900, Q=950.

Note in particular that there is no significant difference in value
between A and C, and that A+P on the average lightly beats Q. The P=85 is
for a Pawn in the initial position; a healthy Pawn in the center, or a
passer, are of course worth much more, a backward or edge Pawn much less.

CRC
practical attack values
http://www.symmetryperfect.com/shots/values-capa.pdf

Although Aberg's method of estimating the relative piece values for CRC pieces upon the 10 x 8 board was just an expedient extrapolation from established relative pieces values for FRC pieces upon the 8 x 8 board, his values are actually more accurate than yours.

One major flaw in your system is approximately equating the values of the archbishop and the chancellor.  This is a radical contention which implies that the values of the rook and bishop are equal (since the archbishop equals a knight plus a bishop and the chancellor equals a knight plus a rook).  This is inconsistent with your own system internally whereby the rook is (correctly) ascribed a higher value than the bishop.

Values given for P N B R Q K are just the empirical values used before the
days of computer programs, with an adjustment of the traditional B = 3,
mostly used as a point of departure, and how to figure out how material in
the long run would balance out. They also depend on position and the skill
of the player, for example, knights weaken in closed positions, and weaker
player might over-value them. I just put them up as a starting point so
your analysis is welcome. The surprising closeness of the A and C values
you get perhaps depends on the fact that A, unlike B, can move on squares
of both colors.

Pawns (just as knight) ought to weaken on large boards. So another pawn
rule might be that it is allowed to move two steps if it has not reached
the two middle rows (i.e., a pawn that has moved one square can still make
a two-square move).

Also, you might try to figure out the strength of a piece that can move as
a queen and a knight. Call this piece say 'General' or G. One might use
an 12x8 board. One setup might be (white pieces)
  R C N B A Q K G B N C R
It is derived by imposing the condition that all pawns are protected by a
quality piece in the start position.

To Derek:

If Archbishop and Chancellor have equal value, it DOES NOT IMPLY ANYTHING
for the value difference of Rook vs Bishop. They are all different pieces,
and have nothing to do with each other. In real life the value of a piece
is not the sum of the value of each of its individual moves, but also
depends critically on properties like mating potential, color-boundedness,
forwardness, speed, manoeuvrability, concentration, sensitivity to
blocking. See the considerations of Ralph Betza.

In particular, as to the R-B vs C-A difference:
A Rook has mating potential, a Bishop not. But:
A Chancellor has mating potential, and so does an Archbishop.
A Rook can stray on all colors, a Bishop can only access half the board.
But:
A Chancellor can stray on all colors, and so can an Archbishop.

Theoretical considerations like you refer to are just nonsense, with no
connection to real life. Elaborate nonsense, admittedly, but nonsense
nevertheless. No amount of _talk_ will increase the value of a Chancellor
versus an Archbishop. Only what happens on the board counts. And on the
board A+P beats C (in the presence of other material, between equal
players) by a sizable margin (like 60-40). Just like B+P is no match for a
Rook, in the presence of enough other material.

If you consider that 'flawed', because the fact that R is more valuable
than B+P 'implies' that C is more valuable than A+P, to be
'consistent', then I wonder what your concept of piece value really
means. What would you rather have (if you can choose to make a trade or
not), a piece that is more 'valuable' accoording to some contrived
reasoning, or a piece that gives you a larger probability to win the game?
If it is the latter, you should use the piece values I give, and not the
'more correct' ones of Aberg.

In real life A performs nearly as well as C in almost any combination of
material, and B gets crushed by R in almost any combination of material
except the sterile KRKB ending.

Theoretical considerations are not nonsense but must tempered by empirical experimentation. Below is my theoretical analysis of C vs A situation.

First let's take the following values:

R: 4.5
B: 3
N: 3

Now the bishop is a slider so should have greater value then knight, but it is color bound so it gets a penalty by decreasing its value by a third, which reduce it to that of the knight. 

When Bishop is combined with Knight, the piece is no longer color bound so the bishop component gets back to its full strength (4.5), which is rookish. As a result Archbishop and Chancellor become similar in value.

First I want to stress that the B-N value difference is dependent on board
size: on 8x8 they are roughly equal, while on 10x8 the difference is half
a Pawn. (In addition there is half a Pawn bonus for having a pair of
oppositely colored Bishops. So in these Capablanca-type variants, giving
N+P to break the opponent's B-pair is an equal trade.) This increased B-N
difference is not due to the Knight being weaker, but to the Bishop being
stronger! B+N+N vs Q, (in an otherwise full 10x8 opening setup) is about
equal, and the three minors beat the Queen by about half the Pawn-odds
score if the Bishop is part of a pair. B(paired)+P vs R in the opening
turns out to be an equal trade.

My guess is that the wider board makes the Bishop relatively more
valuable: its forward moves now attack the opponent usually in two places,
while on 8x8 one move usually ends on the side edge of the board. I noticed
this in an even more extreme way in Cylinder Chess, where the board is
effectively infinitely wide. A Cylinder Bishop (B*) amongst normal Chess
pieces is aworth a full Pawn more than a normal Bishop. R*-R is only about
a quarter Pawn. The lateral over-the-edge attacks are comparatively
worthless. Q*-Q, otoh, is about 2 Pawns.

Strangely enough, the explanation that the Knight move of Archbishop
breaks color-boundedness does not seem to fully explain the large synergy
between B and N moves. I tried a piece that moved as B+P (so one extra
forward non-capture step), which broke color-boundedness, but it hardly
gave any advantage over a normal B (about 1/6 Pawn) A Dragon horse (B+K),
however, is slightly stronger than R+P. But of course adding the K moves
(or Wazir moves, really) both as capttures and non-captures also endows it
with mating potential.

My current guess is that breaking of color-boundedness and mating
potential help a little to bridge the narrowed gap between R and B on a
10x8 board, but that the major contribution comes from the enhanced
close-range manouvrability and concentration of attack power: an
Archbishop covers several 2x2 blocks. Such contiguous attacked areas seem
to be very valuable, and is likely to be also an important factor
determining the value of the Bishop pair (because Bishops on bordering
diagonals also covering a lot of contiguous squares).

'If Archbishop and Chancellor have equal value, it DOES NOT IMPLY ANYTHING
for the value difference of Rook vs Bishop. They are all different pieces,
and have nothing to do with each other.'

YES it does according to my model and every quality, holistic model built upon a proper foundation I have ever seen.  Contrary to your statement, I think it obvious to any logical person that the component pieces have at least SOMETHING to do with their composite pieces.

Some computer chess programmers are notorious for achieving useful relative
piece values that are within decent range of their optimums based purely upon AI playing strength without creating any coherent, fully-developed theory that is logically explained, justified and consistent.  Unfortunately, such people contribute little to the understanding of
relative piece values for themselves or other interested parties.

I have appr. two years of experience working with Reinhard Scharnagl's 
excellent SMIRF program, my fast dual-CPU server and choice Capablanca chess variants.

Reinhard Scharnagl would compiled two, otherwise-identical versions of his 
program using his and my favorite sets of relative piece values (at that time) which would played against one another using a great amount of time per move.  Eventually, we carefully completed many games this way.  We would both analyze the game results and discuss conclusions.  Sometimes we would agree.  Sometimes we would disagree.  Subsequent tests would settle disagreements ... sometimes.  In this manner, we both improved our models over time until we reached a point where any further minor improvements became prohibitively difficult to achieve within a survivable time frame.

'In real life the value of a piece is not the sum of the value of each of its individual moves ...'

YES it is although not exactly.  The moves of component pieces of a composite piece have far more effect upon determining its relative piece value than ALL other factors added together.

'... but also depends critically on properties like mating potential,
color-boundedness, forwardness, speed, manoeuvrability, concentration,
sensitivity to blocking.'

I have also read ALL of the pioneering works of Betza on the subject.
Essentially, my model mathematicized a subject (to the extent possible
present day) he had only speculatively verbalized.  Rest assured, my model 
makes quantitative adjustments for all non-trivial, effecacious factors to relative piece values that I know of with certainty.

You need to read and thoroughly understand my 58-page paper on the subject.

universal calculation of piece values
http://www.symmetryperfect.com/shots/calc.pdf

'Theoretical considerations like you refer to are just nonsense, with no
connection to real life.'

The connection of my model to 'real life' is very strong.  My theory was
adjusted and refined numerous times to comply with game results over
different piece sets and game boards.  Experience dictated the details
of the theory in accordance with the scientific method.

'What would you rather have (if you can choose to make a trade or
not), a piece that is more 'valuable' according to some contrived
reasoning, or a piece that gives you a larger probability to win the game?'

Both.

Under a proper model, they should not be mutually exclusive at all.
In fact, they should be in agreement ... until a point in the endgame
where checkmate becomes possible.  Be mindful that significant
differences in relative piece values between the opening game, 
mid-game and endgame (to the limited extent that they are applicable)
are accommodated under sophisticated models.
____________________________________________

See the published values of Ed Trice and Reinhard Scharnagl for
CRC pieces upon the 10 x 8 board.

http://www.gothicchess.com/piece_values.html

In addition to the published values of Hans Aberg and Derek Nalls, this verifies that it is beyond dispute that your published values for the archbishop and chancellor are radical.  Your radical contention that an archbishop and a chancellor have appr. equal relative piece values requires an especially sound theoretical framework to be convincing.  Instead, all I am receiving from you is piecemeal descriptions of endgame scenarios where material values are likely to disappear and become meaningless compared to positional values (i.e., checkmate achievable regardless of material sacrifices) and consequently, conclusions drawn are likely to be faulty.

FYI: Smirf falls way behind Joker80 in any real-life tournament played so far. See, for instance, the Battle of the Goths Championship 2008, which is currently playing at http://80.100.28.169/gothic/battle.html . And the main reason it does so is because it loses many points against engines in the lower part of the ranking. If you would look at the games (they can be downloaded from the mentioned page) you see the same pattern over and over again: Smirf voluntarily engages in losing trades, thinking it is +4 or +5 ahead, and subsequently is slaughtered by the weaker opponent because its piece material simply cannot keep up with the opponents overwhelming force, even if wielded by a less competent player. So I would say using Smirf in connection with piece values is a particularly bad example.

As for your scientific method, you seem to forget that science is about explaining observed FACTS. So if your 'coherent, logical, consistent' theory predicts that A is of nearly equal value as B+N, while in practice the B+N have a losing disadvantage, I would say the World would was better off without it. A theory not explaining the facts can at most contribute to MISunderstanding of relative piece values... The ones who determine the facts through accurate measurement thus contribute in an absolutely essential way to our understanding, as without such facts the theoreticians cannot even start their work.

Your 'understanding' of piece values is such that you consider piece values that do have C-A different from R-B 'flawed'. I.e., to be flawless in your eyes, a theory would have to predict that two pieces which perform equally (C and A) have to be assigned values that differ by several Pawns, or pieces that differ by several Pawns in strength (R and B) to be assigned a value that is equal. Why would I read a 58-page monologue from someone adhering to such flawed logic? It can only be a waste of time. And the FACT that C offers no significant advantage over A in Capablanca Chess games won't go away by it...

'Also, you might try to figure out the strength of a piece that can move
as
a queen and a knight. Call this piece say 'General' or G. One might use
an 12x8 board. One setup might be (white pieces)
  R C N B A Q K G B N C R
It is derived by imposing the condition that all pawns are protected by a
quality piece in the start position.'

I prefer to call this piece 'Amazon': the name 'General' is already
taken by several Shogi pieces, where the various brands of Generals are
all more or less handicapped Kings. Furthermore, Ferz means 'General',
and indeed can be described as a handicapped King. Although in English one
uses the Persian name for this piece (like for the Rook), most other
languages don't, and overloading the name 'General' would cause
problems in translation.

That being said: I ran a preliminary test for determining the Amazon value
(on a slow laptop, as my main PC is tied up in running the 'Battle of the
Goths' Championship), by playing games where one side had an Amazon in
stead of Q+N. I did this on 10x8 from the Capablanca setup (removing the
Queen's Knight and replacing Queen by Amazon), because there the piece
values are accurately known. I did not want to use 12x8, because I have no
piece values there for the pieces against which I would compare the
Amazon.

After 116 games, the Amazon is leading by 51.3% (52+ 49- 15=). The
statistical error over 116 games is 4.3%, though, so this difference with
equality if far below significance. At these settings (40/2' on a 1.3GHz
Pentium-M) the Pawn-odds score is about 62%, so the observed difference
corresponds to 10cP +/- 35cP. It thus seems there is hardly any synergy
between Q and N moves, and the values simply add. In other words, Q is
already so powerful that it doesn't really need the Knight moves, and
they provide little 'extra' in terms of making it possible to use the
moves it already had more efficiently.

To make this a hard conclusion, though, I would have to play better
quality games (either 40/5', or 4/2' on my 2.4GHz Core 2 Duo), as the
current setting is at the brink of underestimating the Knight because of
lack of depth in the end-game to use it efficiently, play at least 400 of
them, try sevral other piece combinations (e.g. also against C+B and A+B)
and average over a few different opening setups. That would take a few
days when I have my C2D machine available again.

A short remark on piece values: first, my published model is not my last word, I still am working on that. 

As I have stated already an amount of time ago, piece values are depending from the percentage of emptyness of the board. It concerns the mobility value part of sliding pieces. This would lead to dynamic piece values of sliding pieces slowly growing through a game. SMIRF unfortunately is far away from that.

Then I modified my thoughts on the nature of a bishop pair value bonus, which in fact had not been implemented in SMIRF yet at all. Errornously I derived that value modification from the fact, that a Bishop can reach merely one half of a board. But this is only a legal but misleading view on that strange effect. Today I am relating this paradoxon to the hideability of pieces more valued than a Bishop. Thus there is a chance to positionally devalue an opposite single Bishop by moving ones big pieces preferred on squares coloured oppositely to the Bishop's one. But that view demands the value bonus not to be applied statically by summing up piece values and such a bonus, but by writing an appropriate positional detail evaluation (as I have done intuitively in SMIRF).

To try to find out piece values by having teams of different armies fighting each other seems to be very promising at a first sight. But as you see in those huge table bases: a lot of optimal play is done pure combinatorically and could end contrarily, if placing one piece only a step aside. Thus it is hard to understand why to densly relate outcomes of a games and piece values. In an extreme constellation having King+Knight against King (which is a draw anyway) such an approach would lead to the conclusion, that a Knight is valued to nothing.

I agree that statistics from tablebases is very hard to interpret: more
than half the wins are usually tactical positions where pieces are
hanging, so that the outcome has nothing to do with the piece makeup in
question at all.

But this is a consequence of the inclusion of tactical initial positions
in the data set. The approximately 20,000 games I played to extract the
piece values given below were all played from tactically dead positions
(CRC-like opening positions, with some selected pieces deleted), where it
would take several moves to attack an enemy piece in the first place. Note
that I never played pieces in isolation (which could lead to the KNK effect
you mention), but always in a nearly full opening setup (34 or more Chess
men on the board).

As to the dependence of piece values on the fill fraction on the board:
one would only experience this effect to its full extent if the filling
fraction remained constant during the game (as in Crazyhouse, where indeed
the piece values are totally different from normal Chess). In games without
piece drops, the board will unavoidably get empty. So you will have to plan
to the future. It is true that in the early middle-game a Bishop is much
more dangerous than a Rook, (which, without open files, is almost
completely useless), but the difference is not so large that you can gain
enough material to neutralize the end-game-value difference before the
board gets empty enough that the advantage reverses. So it is still the
end-game value that dominates the piece value early on. The instantaneous
value tells you only the direction of a small correction that has to be
applied, and is very volatile.