Put a queen on d4 of an empty board and count the squares she attacks. Seven along the fourth rank, seven up and down the d-file, and thirteen more on the two diagonals through d4. Twenty-seven, which is nearly half the board from one square.
2 The rest of the count
A rook attacks 14 squares from anywhere on an empty board, corner or centre, because seven plus seven never changes. That constancy is why rooks are happy to sit at home in the opening and terrifying once a file opens.
Everybody else pays for where they stand. A bishop gets 13 squares from d4 and 7 from a1, a knight 8 and 2, a king 8 and 3. The knight has the steepest fall of the lot, and that arithmetic is the whole of the old line about a knight on the rim. The pawn is the exception at the bottom: two squares attacked wherever it stands, one if it is on the a-file or the h-file.
So the order of raw power runs queen, rook, bishop and knight together, king, pawn, which is roughly what the point values say too: 9, 5, 3, 3, and 1 for the pawn.
Powerful is not the same as important
The king is the piece the entire game is about. Lose it and nothing else matters, which is why it gets no point value at all and why you spend the opening tucking it away on g1.
It is also a genuinely good attacking piece once the queens are gone. In a king and pawn endgame, getting your king in front of its own pawn on the sixth rank is usually the difference between a win and a draw, and in king and queen against king the mate is impossible without the king walking up to help. Strong, and irreplaceable, but not powerful in the queen’s sense.
Then why not bring the queen out on move two?
Because power and safety pull in opposite directions. Every piece on the board can attack a queen, and she has to run from all of them.
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h 1 Count what each side got for four moves. Black has two knights out and a pawn on g6 with a bishop ready to follow it. White has a bishop on c4 and a queen that has been to h5 and back to f3 because 3…g6 threw her off the diagonal. The tempo went to Black for nothing, and it always will: a queen has to run from whatever attacks her, and everything on the board attacks her.
That is the whole of the opening principles in miniature: knights and bishops first, queen when there is something for her to do. Let her out on the right move and she does what nothing else can, forking a king and a rook from a square four ranks away, which is where most of the fork patterns at beginner level come from.