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H.G.Muller wrote on Sat, Apr 19, 2008 08:15 AM UTC:

'Also, you might try to figure out the strength of a piece that can move
as
a queen and a knight. Call this piece say 'General' or G. One might use
an 12x8 board. One setup might be (white pieces)
  R C N B A Q K G B N C R
It is derived by imposing the condition that all pawns are protected by a
quality piece in the start position.'

I prefer to call this piece 'Amazon': the name 'General' is already
taken by several Shogi pieces, where the various brands of Generals are
all more or less handicapped Kings. Furthermore, Ferz means 'General',
and indeed can be described as a handicapped King. Although in English one
uses the Persian name for this piece (like for the Rook), most other
languages don't, and overloading the name 'General' would cause
problems in translation.

That being said: I ran a preliminary test for determining the Amazon value
(on a slow laptop, as my main PC is tied up in running the 'Battle of the
Goths' Championship), by playing games where one side had an Amazon in
stead of Q+N. I did this on 10x8 from the Capablanca setup (removing the
Queen's Knight and replacing Queen by Amazon), because there the piece
values are accurately known. I did not want to use 12x8, because I have no
piece values there for the pieces against which I would compare the
Amazon.

After 116 games, the Amazon is leading by 51.3% (52+ 49- 15=). The
statistical error over 116 games is 4.3%, though, so this difference with
equality if far below significance. At these settings (40/2' on a 1.3GHz
Pentium-M) the Pawn-odds score is about 62%, so the observed difference
corresponds to 10cP +/- 35cP. It thus seems there is hardly any synergy
between Q and N moves, and the values simply add. In other words, Q is
already so powerful that it doesn't really need the Knight moves, and
they provide little 'extra' in terms of making it possible to use the
moves it already had more efficiently.

To make this a hard conclusion, though, I would have to play better
quality games (either 40/5', or 4/2' on my 2.4GHz Core 2 Duo), as the
current setting is at the brink of underestimating the Knight because of
lack of depth in the end-game to use it efficiently, play at least 400 of
them, try sevral other piece combinations (e.g. also against C+B and A+B)
and average over a few different opening setups. That would take a few
days when I have my C2D machine available again.

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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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