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H.G.Muller wrote on Wed, Apr 23, 2008 09:38 PM UTC:

Well, this is basically how I got the empirical values I quoted. Except
that so far I only did it for opening positions, so the values are all
opening values. But, like I said, they don't seem to change a lot during
the game. For the complete list of exchanges that I tried, see
http://z13.invisionfree.com/Gothic_Chess_Forum/index.php?showtopic=389&st=1
.

Compensating with Pawns is kind of difficult, though. The Pawn value is
the most variable of all pieces, and the most non-additive. You have
passers, defended passers, edge Pawns, backward Pawns isolated Pawns,
Pawns of the King's Pawn shield. One can be worth more than twice as much
as the other. And the problem is that deleting a Pawn in the opening, you
don't know where it is going to end up on the average. In addition, in
the opening you have all kinds of compensation for deleting a Pawn, in
terms of acceleration of development. In the end-game position I gave, at
least you know which type of Pawn the extra Pawn (c5) is. I would be
inclined to count that as the 'average Pawn', and deleting it does not
significantly weaken your Pawn structure.

But in general, it is much more reliable to try Queen vs 3 minors or vs 2
Rooks. That way you get relative piece values that are not very sensitive
to the value of the Pawns that you used to 'equalize'.

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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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