Relative values of squares, files, ranks and layers of the chessboard.

From an entry of my blog, enjoy!

Hi all:

We know that the center is worth more, but how much more? I had the idea to try calculate that.

I recently published the entry "The exact relative value of chess pieces and fairy chess pieces", those values were important to calculate the values of the squares, files, ranks and the concentric layers of the chessboard (including the center).

The first step is to use the values of all simple or unique pieces moving in a free or empty board, and then the same in a crowded board. The piece that combines these movements is the Vizier (a piece that does not exist in traditional/classical chess but exists in Supercharged Chess), it is a Queen Knight compound. In the image below are the two boards, note that the board of the right also shows the maximum number of pieces that can attack a single square (although in Supercharged Chess the total number of pieces that can attack a central square is 24 not 16! This is due to the Supercharged Knight).

The second step is to sum up these values in a single board in order to calculate the values of each square. As these numbers would not have any meaning for most chess players, I used percentages with regard to the whole board (as in the image below on the right).

The third step is to calculate the values of each file, rank and the concentric layers of the board, again in percentages so it can make sense to most chess players. Note that file a = h, b = g, c = f, d = e and rank 1 = 8, 2 = 7, 3 = 6 and 4 = 5. Also note that the center is the most internal and valuable layer, its value is 29% with regard to the whole board.

So, the values are there, of course these values are very relative, meaning that the position matters more always.

And now it is up to us to play games that can take advantage of these subtle details. 

Your feedback is welcome and is appreciated.

Take care.

Mobility can be thought of as proportional to the probability a piece will find something useful to do at some point during the game... so it's a means not an end. You can stay mobile all game long and never do anything useful. Focusing on mobility might be a convenient way to make an educated guess at the values of pieces in variants like fairy chess though, I don't know.

As for strategy, the fundamental unit, as far as I'm concerned, is piece activity... which is closely related but not the same. An active piece may not control as many squares as a less active piece, but the squares it does control are more important. The easiest example of a high value square (or group of squares) is slow moving (or immobile) enemy pieces that can't be defended quickly. In normal chess these are usually weak pawns or the king.

Thanks for your comment. Theoretical studies like this are more part of the science and math of the game, they have less impact on strategy.

Great valuation technique...

Back rank and 7th rank are the most important ranks.

These are relative values according to the power of the pieces. If it is the opening or middle game, then this back rank is very important.

Also in the endgame because it is the ppromotion rank.

Thanks.

All these come from the relative value of the pieces which I discovered many years ago.

When you get the exact values of the pieces, everything else is easy. 

Very interesting, however I don't think chess can really be divvied up like this. The position on the board is too important to lay down these generalized ideas.

I commented more elaborately on this calculation method in your blog about it. But methods like this in general produce piece values that are very far off, because they ignore too many aspects that are important in practice. Sorry I have to be so harsh, but the method presented here is no exception. You don't even get good values for the classical pieces (in particular Q vs R + B).

• Relative values can be exact because they are relative. The method is also exact because two pieces (say Rook and Bishop) are worth less than any pieces that combine the power of the two. Moskalenko put these into factors. I have explained all this in my article.