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H.G.Muller wrote on Sat, Apr 19, 2008 02:34 PM UTC:

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.

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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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