I'm trying to truly understand why Rooks are more valuable than Bishops. Yes, they control more squares. But why?
I understand that a rook forms a line that pieces cannot pass through, and this is related to the fact that it controls squares of multiple colors. A diagonal does not block a piece in the same way.
But I just cannot wrap my head around why controlling all squares in a cardinal direction is any better than controlling all squares in an ordinal direction. Does anybody have a mathematical or logical explanation for this? Why does controlling squares cardinally result in more total squares controlled than doing so ordinally?