A Mathematical Realization • page 1/1 • General Chess Discussion • lichess.org

The number of squares a bishop controls is linear with how far away it is from the closest edge. If the bishop is on the edge, it controls 7 squares. 1 away, it controls 9. 2 away, it controls 11. If it is in the four center squares, then it controls 13 squares.

With knights, we also use the reference point of the corner. If the knight is in the corner, it attacks 2 squares. If it is one horizontal step away from the corner, it attacks 3 squares. If it is on any other edge square or one diagonal step away from the corner, the knight attacks 4 squares. There is no place for the knight to attack 5 squares. If the knight is one step away from the edge and not on a corner square, it attacks 6 squares. If it is in the 16 central squares, it attacks 8 squares.

The rook always attacks 14 squares no matter where it is.

The queen is a combination of the rook and bishop, so it is essentially the same as the bishop's graph but translated 14 units up.

The king controls 3 squares in the corner, 5 squares if on the non-corner edge spaces, and 8 anywhere else.

The pawn is a special case. The regular pawn can control 1 square if it is on the side, two squares if it is in the center, and controls as many squares as the promoted piece does. It can also control 2 squares if it is on the 5th-rank edge space, but this only applies to other pawns (the en passant rule). Thus, the regular pawn can <technically> control a maximum of 4 squares with any 5th-rank non-edge space, with the two en passant captures and the two regular captures. This is different from the number of moves it has. Add 1 to every value unless the pawn is on the second rank; then add 2.

That concludes our expedition!

The number of squares a bishop controls is linear with how far away it is from the closest edge. If the bishop is on the edge, it controls 7 squares. 1 away, it controls 9. 2 away, it controls 11. If it is in the four center squares, then it controls 13 squares. With knights, we also use the reference point of the corner. If the knight is in the corner, it attacks 2 squares. If it is one horizontal step away from the corner, it attacks 3 squares. If it is on any other edge square or one diagonal step away from the corner, the knight attacks 4 squares. There is no place for the knight to attack 5 squares. If the knight is one step away from the edge and not on a corner square, it attacks 6 squares. If it is in the 16 central squares, it attacks 8 squares. The rook always attacks 14 squares no matter where it is. The queen is a combination of the rook and bishop, so it is essentially the same as the bishop's graph but translated 14 units up. The king controls 3 squares in the corner, 5 squares if on the non-corner edge spaces, and 8 anywhere else. The pawn is a special case. The regular pawn can control 1 square if it is on the side, two squares if it is in the center, and controls as many squares as the promoted piece does. It can also control 2 squares if it is on the 5th-rank edge space, but this only applies to other pawns (the en passant rule). Thus, the regular pawn can <technically> control a maximum of 4 squares with any 5th-rank non-edge space, with the two en passant captures and the two regular captures. This is different from the number of moves it has. Add 1 to every value unless the pawn is on the second rank; then add 2. That concludes our expedition!

Rookitiki

You can count squares on empty board. Next blindfold simul?

What’s the point of this topic?

You can count squares on empty board. Next blindfold simul? What’s the point of this topic?

DestroyerXV

@Rookitiki said ^

You can count squares on empty board. Next blindfold simul?

What’s the point of this topic?

Mapping out geometric movement and spatial value.

For fun.

@Rookitiki said [^](/forum/redirect/post/R8vLZSIg) > You can count squares on empty board. Next blindfold simul? > > What’s the point of this topic? Mapping out geometric movement and spatial value. For fun.

ChessPriyome

Useful if you practice Board Visualization which is related to Blindfold play. It's a heavily underutilized skill to practice.

pmpsoft

Only one en passant move possible because it has to happen immediately?