On the road to invasion

 A line of attack writhe from an attacker on its original square to the sitting duck that tries to escape him. Along the way, there might be a few twists in the line of attack, what we called the pivotal points. Vukovic calls them the additional focal points.

The pivotal points that lie in the enemy camp are especially interesting. It are the invasion squares. It might be difficult to work directly on a sitting duck (the king, for instance). It might be easier to work on an invasion square first. It is a kind of sitting duck of the second order.

What are the features of an invasion square?

First of all, it can't be protected by enemy pawns. Otherwise a pawn can kick you out. Secondly, you have to fight for the balance. The balance is represented by the balance between the amount of attackers compared to the amount of defenders. Only when you have a positive balance, you can occupy the invasion square.

You have the current balance. Which tells you whether you are currently able to occupy the invasion square.

And you have the future balance. Which tells you whether you can maintain the occupation of the invasion square. Here you have to count the potential defenders in comparison to the potential attackers. Here the element of time comes in. Maybe you can occupy the invasion currently, but after a few moves you can be kicked out. Take for instance a white knight on e5 and a black knight on f6. Maybe you are currently safe on e5, but in the future, you might be kicked out by f6. So whatever you have to do on e5, you have to do it fast.

For the balance on an invasion square of a certain color, especially the bishops are interesting. By trading the right enemy bishop, you can change the balance forever. This turns exchanging pieces into a weapon.

What when there is no invasion square yet?

The advice is to conquer the center first. I have no clear picture of this wrinkle in the line of attack yet. That is what I'm trying to figure out with my search for an algorithm. When the center pawns start to become mobile, they tend to leave pivotal points in their wake. And often they are the cause of the creation of invasion squares. I'm trying to get the total picture.