King Mobility 9
I am going to type this in a rush with no editing, but I am working on an article on King Mobility. The most a king can move is 1 of 8 squares. So I number the squares in a 3 by 3 grid, and the King resides on square 5 (the center of a tic tac toe board).
So to gain awareness of a King's vulnerablity. I am creating a term called "barriers". A barrier is a piece of a King's own team. If a Black King is on e8 and a black rook is on d8. Then the rook is known as occupying "barrier 4", because in the tic-tac-toe sceme, this is the 4th square. Obviously the King cannot move to squares 1,2,3, because on e8, those squares are off the board. So In such a position the King's mobility is lowered to 4.
If a white rook were on d8, it may not be a barrier if it is not protected by white, because the King on e8 could just capture the rook. In such case the King on e8 would have a mobility of 5.
If the white rook on e8 is protected, then the King on e8 cannot move to d8, nor d7, nor f8. So the King's highest mobility is 2.
Of course if the rook on d8 is being protected by a bishop or queen along the d8-h4 dark diagonal then the King's mobility is only to 1 square = f7. For the queen or bishop is covering e7 the 8th square of the King's tic-tac-toe box. f7 is the 9th square of the King's tic-tac-toe box and the only move;
....more on King Mobility, and barriers, and mating nets later.....