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H.G.Muller wrote on Mon, Apr 28, 2008 07:06 AM UTC:

Hans Aberg:
| I describe how a piece value theory might be developed without 
| statistics. Since one P or R ahead generically wins, set them to 
| the same value. Now this does not work in P against R; so set the 
| value higher than P. Then continue this process in order to refine 
| it, comparing different endings that may appear in play, taking away 
| special cases, always with respect to tournament practice, using 
| postmortem game analysis.

It seems to me that in the end this would produce exactly the same
results, at the expense of hundred times as much work. You would still
have to play the games to see which piece combinations dominantly win. But
now you would throw away the information on how much, making the outcome of
65% equivalent to one of 95%.

While in fact there is very much information in this, as tsmall advantages
turmn out to be additive to a high degree of accuracy. If Pawn odds is 62%,
and Q vs A is 59%, I can be pretty sure that A+P vs Q will be 53%. In the
system you propose, you would have to actually play A+P vs Q before you
would know if A is worthe more or less than Q minus P.

This in particular applies to the fractional advantages. If a B-pair wins
56% from a B anti-pair, and you would only interpret that as 'B-pair is
good', you would have to explicitly test the B-pair against any other
fractional advantage (e.g. Q+BB(unpaired) vs C+BB(paired), Q+BB(unpaired)
vs A+BB(paired), etc to know that the pair advantage was half a Pawn,
rather than 3/4 or 1/4.

Why do you think this is an attractive method, and why would you expect it
to give different results in the first place? Can you construct a
hypothetical example (of score percentages) where your analysis method
would produce different results from mine?

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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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