Pivot squares

Sofar, the framework I developed consists of:

• PoPLoAFun
• 2 sitting ducks (weak pawn, king)
• invasion square (3rd duck)
• attack on two fronts

I have a pretty good idea where I'm weak (endgame, assault) and how to address it. It will take about two years to get to the level I imagine to be good enough in these areas. I know what to do and how to do it.

At the same time, I look at the future in order to get an idea what I should improve next. I don't want to work for two years on my endgames and then to find out that I'm stuck again.

That a crucial piece of the puzzle is still missing.

So I'm working my way through all positional ideas in order to deem whether they will fit easy in my framework or not. Only positional ideas that I'm able to fit in my framework I consider to be mastered. Otherwise it are just loose ideas with no connection to the rest of my game.

The past eleven days I worked on the center. Because a lot of positional elements play a role in the center, it takes time to dissect the complexity to a reasonable level. The treatment of the center by renowned authors tend to be notoriously vague and abstract.

For the first time, I think that I have found the beginning, though.

• Moves in the center must be judged by their effect on the activity of your pieces and the restriction of your opponents' pieces
• Before you can get to an invasion square, you need pivot points
• I need a way to express the stability of a pivot point in order to judge whether they are stable long enough, without the need to look for eternal squares only

When there are invasion squares in the enemy camp, something is already wrong. But before your opponent creates an invasion square for you, you must work on your center. You can do that by focusing on the pivot points. A pivot point is a square on the LoA (line of attack) where the LoA changes direction. When your pieces have pivot points, they are ready to jump to an invasion square whenever they emerge.

So this is the nomenclature of squares along the LoA:

• pivot square
• invasion square
• focal square (= PoP = point of pressure)

The pivot square can be on your own half of the board, behind your own pieces or in no man's land. 

I prefer focal square (which is the name Vukovic coined) above PoP,

The pivot square and the invasion square are the most powerful when they are in the center. This is due to statistical chances in relation to the board geometry and the movement of the pieces. The focal points are next to the king. Maybe the term PoP can be reserved for tactics. Like where the knight forks the royals.