Single Comment

M. Winther
| Muller, to get piece values at ~3% exactitude you would need to 
| presuppose that piece values are static properties. But they are 
| really changeable with regard to tactical and strategical context. 

Not necessarily. I always measure piece values in a well-defined context,
e.g. opening values, end-game values. Piece values are by definition
strategic quantities, I avoid starting in tactical positions, and for an
accurate measurement I average over many non-tactical initial positions
with similar peiece makeup. This usually gives quite consistent results,
when you keep the number of pieces and the total value of present material
approximately constant. (i.e. the difference of the performance of two
diffent pieces is hardly dependend on the details of the makeup of the
opponent or its allies.)

That piece values change as the board empties, because. e.g., Rooks get
more freedom of movement and Cannons can find fewer platforms, is
something that can be measured separately. If the piece values found for
the various qualitatively different situations differ, you can try to add
material-interaction terms in the evaluation. (The best known example of
such a term in normal chess is one proportional to the product of the
number of Bishops and number of Pawns, making the effective B-N difference
dependent on the number of Pawns.)

| This means that you would probably have to foresee the future in, 
| say, ten moves in order to get a ~3% exactitude. 

I am not sure what you mean by 'forsee the future'. By playing out the
game until checkmate or legal draw, I effectively make a Monte-Carlo
sampilng of all plausible futures. But it is important that the sample is
generated under conditions of reasonabe tactical accuracy, or you would
not be sampling a representative set of realistic positions, which then
would distort the results.

| One obvious example is XiangQi. Chinese Chess masters are hard pressed
| to reveal the relative values of pieces. Those pieces which are 
| completely lousy, like the elephant and the mandarin, are sometimes
| very valuable while they provide protection for the general, function 
| as screens for the cannon, or can block enemy pieces. So, in a certain
| context they become very valuable. 

I have not built an engine to play Xiangqi yet (I am in the preliminary
design stage now of an engine that could play Shogi, Chess and Xiangi with
arbitrary Chess men on boards upto 10x10.) So I have not done any
measurements for tuning. Quite possibly the material-interaction terms in
Xiangqi are much larger than in Chess, due to the peculiar capture mode of
the Cannon and the restricted access pieces have to the board. It seems to
me that the effects you describe can be described reaconably well by
cross-product terms of number of Cannons and number of other pieces. This
transcends pure piece values, but can be measured just as easily.

| Ten moves later, the elephant or mandarin is useless. Probably, in 
| chinese chess, only a human is capable of evaluating a piece.

Such a fast change is usually tactical, and then has little to do with
strategic piece values. Unles the strategic situation completely changed
in those ten moves, e.g. because all heavy material got traded, or all
hoppers got traded. But in that case such differences can easily be
expressed by terms that are proportional to the amount of heavy material /
number of hoppers.

I doubt if Humans could do this job better than computers. This is why I
would like to build a Xiangqi engine, so that I could do similar tests on
piece values as I am doing now for Chess.