http://mywebpages.comcast.net/danhe...

Based on a million games, it has statistical evaluation of many material imbalances. Although some calculations are feasible only by computer programs (like the increase / decrease of bishop and knight values when the number of pawn on the board diminuishes) it has many valuable information.

It is the first place where I found a convincing explanation of why exchanging a bishop and a knight for a rook and a pawn (that typically happens on f2/f7) is not such a good deal.

Dan Heisman reviews the book on Chessville.

So after any series of exchanges, players often add up the remaining material (or more simply just count what was taken off) to see who is ahead. In this game and most games, however, that isn't enough. Things such as pawn structure matter a lot, as does king safety and piece activity. Look at the board at move 24. Ignoring any material inequalities, the position appears to favor black. The white king has few defenders while the black king has those 3 pawns to hide behind. The black rooks and queen are all sitting in front of the white king (imagine what that king must be thinking). Whatever the material adds up to, it appears to me that black is making more of his pieces, and is therefore far ahead.

Hello <Fulkrum> & I hope all is well. :) Thanks much for the book. :) I will certainly look for it. :) Take very good care & have a great day. :) Cheers mate! :)

<ganstaman> <Why do we assign values to pieces?> Of course, as you said, to help evaluate the position. But I would strengthen that a little: material is in most cases the most important factor. Just think that one of the main positional advantages (and the easiest to evaluated) like the bishop pair only amount to half a pawn in Kaufman's evaluation, and you realize that normally many factors have to sum up to give compensation for just a pawn.

King safety is an exception, but I wouldn't agree that players' time is well spent in evaluating pawn structures, the least valuable aspect unless you're close to an endgame, and that not only in my opinion.

I got the impression that many people (not talking of anybody specifically) find it fashionable to disregard material when just writing on forums, and then watch their pawns like the chessic equivalent of Uncle Scrooge when playing tournaments.

At least, that's my otb experience! I find less and less gambiteers around, and the few left just play their own beloved gambit backed up by countless hours of home analysis.

I guess my point is this: Interesting as the article was, I don't like the idea behind it. It makes counting material too complex, while not actually being complete. I'm having trouble wording this, so maybe I'll try two examples.

Example one, using the article's info.
First note that we're now dealing with fractions (not really difficult, but it's easier to make errors and will take some more time). Secondly, the value of pieces change with the amount of material on the board. So when considering an exchange, you have to look at how the value of what's left changes as well. Things are getting complicated. Additionally, you still have to guess the quantified value of positional factors, such as pawn structure, king safety, piece mobility/activity, threats, etc.

Now for example 2, using what we already knew. We quantify the values of pieces using the 1, 3, 3, 5, 9 system. Every exchange is simple to calculate. We still have to guess the quantified value of positional factors, such as pawn structure, king safety, piece mobility/activity, threats, etc.

I hope I'm being clear. Regardless of what method you chose to calculate material, you should come to the conclusion that black is better in this game. This is because his pieces are doing more against a less safe king (and he's up the exchange). I think that when considering a material imbalance, you shouldn't concern yourself with whose ahead by fractions of a pawn, and instead make a rough estimate (using 1,3,3,5,9) and see if you can make your material do more than your opponent's.

Coming to your points, I already said in a previous post that parts of the article are only valuable to chess engines. Knowing that a knight decreases its value by 1/8 pawn for any pawn removed from the board doesn't mean that one should calculate the new value of its pieces that way during the game. But for sure knowing that the value somehow dicreases IS of great importance to any player.

I once saw a player lose an endgame with K+N vs K+3P (the pawns were connected). At the end he was very surprised by the outcome ("what? can't a knight draw against 3 pawns?"). He wouldn't be surprised had he read that article.

Where I disagree with you is of the little relevance you give to the 3 vs 3.25 matter. Using 3.25 as the (average) value of knights and bishops adds very little to the complexity of the evaluation of material imbalances, and avoids the very common beginner mistake of exchanging 2 minor pieces for a rook and a pawn.