Saturday, January 13, 2007

Differential View

This idea was behind a short comment of mine to a post of Temposchlucker. It was too short to make the point clear. But I think it is so important that it deserves a full post. I begin with some trivial definitions and remarks.

The general goal of a move
Every move should make the own pieces better and/or the opponent pieces worse. Making a piece better is making it safer and/or more active. A better piece has a higher dynamic value, as opposed to its static value. Example: If the dynamic value of a bishop is higher than that of a rook, the sacrifice of the Exchange will add value.

Safety and activity
Safety is a tactical issue and always must be considered first. Activity is a positional issue. If more activity is accumulated on the board, the safety is diminished. In other words, positional superiority leads to more tactics. The opposite is also true: More safety often leads to less activity (example: the King in the middlegame vs. in the endgame). All this is not new, I only mention it as a starting point of my reasoning.

What is the best move?
Attempt of a definition by differential view: The best move is the one that maximizes the dynamic value difference between the own pieces and the opponent pieces, either in safety or in activity or in both.

Yes, it is trivial, but ...
Every cheap chess software does this all the time: It evaluates the position and calculates a value in pawn units for one or the other side. What should be done is easily said but not so easily done. The problem is that we flesh-and-blood players are not very fit for multitasking and balanced thinking. We like to simplify. We like to look at our own plans or at the plans of the opponent, but not both at the same time. One more difficulty is that the differential view must not only take place between own and opponent position, but also between safety and activity. If I see it right, things get four-dimensional. Plus two of these dimensions, safety and activity, are reciprocal which makes the thing non-linear or chaotic. The outcome is everything else than trivial, I would say.

Simple scenarios (positional)
Trade a bad bishop (knight) against a good knight (bishop). Take your worst piece and make it better (say, by 0.9 pawn units) while there is no possibility to make an opponent piece worse. Take the best piece of the opponent and make it worse by 1.3 pawn units while making your worst piece better would only add 0.9 pawn units in your favour.

Not so simple scenarios (tactics involved)
Adding much more activity to an own piece at the price of security, adding some dynamic value also to opponent pieces. Pawn break in a previously quiet position, making the board burn at once.

Chess is not an easy game. But sometimes it may be easier than we think. Maybe it becomes easier if we adopt a strictly differential view, always looking at a position from both sides, every time. We should not be lawyers for our own party, we should be judges.


At 3:17 PM, Blogger Temposchlucker said...

This week I noticed something peculiar. If you want to trade a passive bad bishop against a good bishop, you have to make your bad bishop active first. Is I said earlier, the pathways are neutral, if you can't reach a pathway, you can't trade bishops. Active/passive is a feature during the whole game, while good and bad bishops are a feature of the endgame solely. Often a passive and bad bishop coincide, when the bishop is inside the pawn chain.

At the moment I'm building theory I forget about tactics to simplify matters.

At 1:54 PM, Blogger Mousetrapper said...

Hm, hm, Tempo, I see it a bit differently: I have had bad bishops in the opening and in the middlegame, not only in the endgame. With your other point I agree: Sometimes you must invest into a bad bishop only to make it ready for trade. Once you have done it, you often begin to feel sorry for the child after so much care. But nevertheless, often you should stick with your first decision and trade it.


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