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Anonymous wrote on Fri, Apr 18, 2008 01:58 PM UTC:

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.

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Comments

Aberg variation of Capablanca's Chess. Different setup and castling rules. (10x8, Cells: 80)

💡📝Hans Aberg wrote on Sat, May 3, 2008 04:43 PM UTC:

H.G.Muller:
| But the point is that this does not alter the piece values.

Right, though that might be just a preferred way to structure theory because it suits human thinking. Essentially, define contexts, and attach values to them. First define piece values in nutralk settings. Then observe that the bishop pair gets an added value. Then try to figure out values for good and poor bishops. And so on. By contrast, computers tend to be very poor at handling such contexts, so other methods might be suitable for programs.

Derek Nalls wrote on Sat, May 3, 2008 03:26 PM UTC:

Muller:

You have my best regards toward your worthwhile effort to publish your
empirical, statistical method for obtaining the material values of pieces
in the ICGA Journal.  My assessment is that it will surely be a much
better paper than the junk [name removed] published in the same journal
regarding piece values.

[The above has been edited to remove a name and/or site reference. It is
the policy of cv.org to avoid mention of that particular name and site to
remove any threat of lawsuits. Sorry to have to do that, but we must
protect ourselves. -D. Howe]

H. G. Muller wrote on Sat, May 3, 2008 03:22 PM UTC:

Sure, this is what people do and have done for ages. It is well known that the advantage of having the move is worth 1/6 of a Pawn, (corresponding in normal Chess to a white score of 53-54%) and that, by inference, wasting a full move is equivalent to 1/3 of a Pawn.

But the point is that this does not alter the piece values. It just adds to them, like every positional advantage adds to them. In my test the advantage of having the lead move is neutralized by playing every position both with white to move and black to move.

💡📝Hans Aberg wrote on Sat, May 3, 2008 11:50 AM UTC:

H.G.Muller:
| As piece values are only useful as strategic guidelines for quiet
| positions, they cannot be sensitive to who has the move.

At the beginning of the game, white is thought to have a slight advantage, and the first task of black will be attempting to neutralize that. And it might be possible set a picee value to that positional advantage, just as when reasoning in terms of getting positional compensation for a sacrifice. Somewhat less han a pawn, perhaps. If one knows about the black/white winning statistics, one might be able to set a value on it that way. It may not be usable for a computer program as it does not change sides, but only computes the relative values of moves.

H. G. Muller wrote on Sat, May 3, 2008 10:34 AM UTC:

As piece values are only useful as strategic guidelines for quiet positions, they cannot be sensitive to who has the move. A position where it matters who has the move is by definition nont quiet, as one ply later that characteristic will have essentially changed. So at the level of piece-value strategies, Chess is a perfectly symmetric game.

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