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H.G.Muller wrote on Wed, Apr 30, 2008 06:24 PM UTC:

Hans Aberg:
| You do not get a theory that predicts winning chances, as chess 
| isn't random. If the assumption is that opponents will have a 
| random style similar in nature to the analyzed data, then it might 
| be used for predictions.
This is where we fundamentally differ, and it makes it completely
pointless to discuss anything in detail as long as we argue based on such
mutually excusive axioms. Chess as we play it is a game of chance, as
players don't have perfect knowledge, and thus randomly choose between
positions they cannot distinguish based on the knowledge they have. And
there is no logical necessity for the condition of similar randomness that
you impose. It is well known that the eventual distribution of  random
walker does not depend on the details of the steps he can make. Only on
the variance. (The central limit theorem of probability theory!) In
particular, it is an empirical fact that statistical analysis of
computer-computer games, as I did, produces the same winning probabilities
as analyzing GM games (as Kaufman did). So even if you were in principle
right (which I doubt) that sufficiently different nature of the randomness
would produce different overall statistics, observations then apparently
show that computers and Human GMs are not 'sufficiently different'.

| It is clear that Larry Kaufman does not think of his theory in 
| terms of 'x pawns ahead leads to a winning chance p'. You can 
| analyze your data and make such statements, but it is an incorrect 
| conclusion it will be a valid chess theory predicting future games 
| - it only refers to the data of past games you have analyzed.
For one, this is not clear at all, and very unlikely to be true. Anyway,
you cannot know what Kaufman thinks or doesn't. Fact is that he
translates the statistics into piece values in exactly the same way I do.
The rest of you statement is totally at odds with standard statistical
theory, which maintains that probabilities of stochastic events can be
measured to any desired accuracy / confidence by sampling. This is really
to ridiculous for words.

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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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