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H.G.Muller wrote on Wed, Apr 23, 2008 11:16 AM UTC:

All very true. But in practice, I never have seen piece values that were
extremely different in the opening from what the are in the end-game. The
rason is probably that in the beginning there are so many pieces that even
being one or two behind does not immediately decided the game by checkmate.
The opponent can almost always fight it off for a long time by trading
material. And by the time the board is half empty, most pieces start
approaching their end-game values. So if the disadvantage of two pieces
was only transient, the pieces being present, but merely useless on the
full board, he would effectively have earned them back.

In addition, pieces are seldomly totally useless. The Rook, which is the
most notorious example of a piece that is difficult to develop early,
still make itself very useful as a defender behind the Pawn line,
preventing your position to collapse under the attack of quickly developed
pieces of the enemy. It would perhaps be different if a CV had pieces that
by rule were not allowed to move at all before 75% of the Pawns had been
captured, but than suddenly became very powerful. For such pieces it would
be very questionable if you could survive long enough for them to be of
use. But with Rooks as defenders, you can realistically expect to survive
to the point where the Rooks live up to their full potential at least 90%
of the cases. R for N or B gambits are almost non-existent. It is very
questionable if the instantaneous advantage of having N in stead of R
would allow you to win a single Pawn before the advantage evaporates.

I did make an early end-game test on the Archbishop, though, because it
was the compound of two 'early' pieces, and some players suggested that
it had its main use in the early middle-game. So I set up a tactically
dead A+5P vs R+N+6P position (
http://home.hccnet.nl/h.g.muller/BotG08G/KA5PKRN6P.gif ), and let it play
a couple of hundred times to see who had the advantage. Turns out the
position was well balanced. This could be considered as a direct
measurement of the end-game value of the involved pieces.

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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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