Why Are Rooks More Important Than Bishops?

To evaluate the bishop vs. rook comparison, you need to look at a basic evaluation of both pieces to see how you can compare them, only then will you be able to answer Why Are Rooks More Important Than Bishops?
While both pieces can move from one end of the board to another (as long as there’s no obstruction), the rook has some advantages over the bishop to give it more evaluation points in the game.
No matter where rooks are placed on an empty chessboard, you have an option to make up to 14 valid moves with them; they have 7 possible squares on the file and 7 possible valid squares on the ranks. The bishop on the other hand can make a maximum of 13 possible valid moves at the centre of the board, but when placed in the centre or on the flank this is reduced to only 7 squares
You can only move your bishops to squares of the same colour as they begin on, this means they can only move on half the squares of the board (32). With your rook, you can move to any square on the board (all 64). This is the second reason why a rook is more important than a bishop.
No single piece can checkmate on its own, it has to happen with the assistance of other pieces, it could be your king or any of your other pieces. Only a rook and a king or a queen and a king can checkmate the opponent’s king on their own, you’ll need re-enforcement from at least one more piece to checkmate with a bishop and a king. This is why bishops and knights are referred to as minor pieces and the queen and rooks as major pieces.
Sometimes your opponents may use some of his pieces to constrain their king’s movement, this is the only instance when you can checkmate your opponent with a single piece or a minor officer and a king.
A rook has an additional way of moving when it combines with the king to castle, since castling helps protect the king, it is logical for you to give more value to the piece that gives the king extra protection against your enemies’ pieces. The bishop doesn’t have a special way to protect the king.
When combined, a pair of rooks can create a battery along a file/row, but bishops can only create batteries with the queen, or other promoted bishops of the same colour but those are not always a given. This also answers your question of why are rooks more important than bishops?
Conclusion
So now, when you are asked, why are rooks more important than bishops? You can list the utilities or the rook over the bishop below:
A rook’s movement is not restricted to colour, unlike the bishop.
Assuming an empty board, the rook can always see 14 other squares from any other square, whereas a bishop’s scope of legal moves varies between 7 to 13 depending on the square, the latter only reached when the bishop is centralised
A king and rook are sufficient to checkmate, but bishop+king vs king is a draw, as, unlike the rook, a bishop cannot cut off the king’s path as it can always escape via the opposite square colour of the bishop. Additionally, this difference allows a rook to achieve stalemate setups that a bishop cannot, as the rook can continuously check the king no matter where it goes.
When combined, a pair of rooks can create a battery along a file/row, but bishops can only create batteries with the queen, or other promoted bishops of the same colour but those are not always a given. But now we’re getting into more advanced details, so let’s stop here.
A rook has an additional way of moving when it combines with the king to castle, the bishop doesn’t.
All of these make it clear why rooks are more important than bishops.
Check out Can Bishops Jump in Chess?
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