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H.G.Muller wrote on Wed, Apr 23, 2008 11:49 AM UTC:

As to the Amazon value: I guess you are right worrying about undefended
Pawns when designing a variant that is more fun to play. For the
determination of piece values, however, this is hardly important. In the
first place, I have to delete pieces from the nominal opening setup to
create a difference, sometimes multiple pieces (such as Q+N to balance the
Amazon), and this usually this leaves some undefended Pawns anyway. It is
more important to shuffle the pieces, to create as many different initial
positions as possible. That some of them have extra weaknesses is not so
important, as both sides have that same weakness, and I play it twice with
different sides starting.

I was never able to see a clear effect of the opening array anyway. Not
even when starting one side with Knights or Bishops in the corner, against
a normal setup. I guess this would only show up by really making opening
theory for the specific position. It is just too difficult to find ways to
exploit such weaknesses 'behind the board' at any reasonable time
control.

BTW, I terminitad the initial experiment with the Amazon after 441 games.
The Amazon was leading 52.6% over Queen + Knight, while the standard error
is about 2%, and Pawn-odds advantage 12%. This suggests Amazon to be about
20 cP stronger than Queen + Knight. But it is very possible that on this
slow laptop at this TC the Knight is underestimated by 10 cP.

Anyway, there seems to be very little to no synergy between the Queen and
Knight moves. I guess most synergy in compound pieces results from
crossing a certain threshold, needed for qualifying as 'super-piece'.
Rooks, Knights and Bishops on an empty board can all go to a given target
square along two paths (if it is reachable at all). A Queen can do that in
general in 12 ways (if the board is large enough). This huge jump in
manoeuvrability is what makes the super-pieces so much more valuable. A
superpiece can attack a Pawn chain in several places at once from several
positions, so that normal pieces cannot defend all attacked Pawns, and in
stead have to worry about their own survival. So a super-piece is much
more than just a stronger piece. It is used in in an essentially different
way. E.g. in the early end-game, chasing the King with checks while having
enough freedom to at the same time manoeuvre to get a clear shot at some
other undefended piece.

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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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