In chess, why is the queen valued at nine points instead of eight?
In chess, typically chess pieces are valued based on their importance. 
For example, 
Pawn - 1 point 
Knight - 3 points
Bishop - 3 points
Rook - 5 points
Queen - 9 points

Since the queen can move like the bishop and the rook, simple math would suggest that it is valued at 8 points (3 + 5). 
However, the game of chess, involves complex scenarios and strategies and having a single piece that can move in all directions gives it a distinct advantage during various phases of the chess game. 
This is why the queen is given a higher point valuation.