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Hans Aberg wrote on Sun, Apr 27, 2008 10:23 AM UTC:

Me:
| So in general, one P ahead does not win, but in special circumstances 
| it can be,  ...
H.G.Muller:
| This is already not true. In general, one Pawn ahead does win in a Pawn ending. KPK
| is an exception (or at least some positions in it are).

My statement referred to this particular ending. For other endings, I indicated it depends on the playing strength, noting that a GM would make sure to win whenever possible, but a weaker player may prefer more material. It is classification for developing playing strategies, not the theoretically best one.

| But is is still completely unclear to me how this has any bearing on piece values.

Change the values radically, and see what happens...

| KPK is a solved end-game (i.e. tablebases exist), so the concept of piece value is
| completely useless there. In solved end-games it only matters if the position is
| won, ...

It is true of all chess positions, not only end-game.

| ...and having KPK in a won position is better than having KQK in a drawn position.

So here one the point-system would be useless, if one faces the possibility of having to choose between those two cases. But the point system will say that KQ will win over KP unless there are some special circumstances, not that it will win in a certain percentage if players of the same strength are making some random changes in their play.

| I don't see how you could draw a conclusion from that that a Pawn has a higher value
| than a Queen.

I have no idea what this refers to.

| Piece values is a heuristic to be used in unsolved positions, to determine who has
| likely the better winning chances.

Only that the 'winning chances' does not refer to a percentage of won games of equal strength players making random variations, which is what you are testing. It refers to something else, which can be hard to capture giving its development history.

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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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