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How many points is the king worth

So according you, the King is on par the rook in the endgame.
I haven't read all the replies but if you were to only consider the number of squares a king controls in the centre of the board, it's the same as a knight, 8 squares.

I read some saying it's 0 and some saying it's infinite (which is not a number, it's a concept) both sound equally good and better to me than 3.
3.5 in term of piece activity! (not for exchange) :D
I wonder what alpha zero thinks of the king? From what I understand, alpha zero doesn't give pieces a fixed score, I've seen a game against stockfish where it could have gone up an exchange for a number of moves, but must have calculated its bishop in its position and future positions was worth more than their rook in its position and future positions.
scientifically speaking, the king has about 1.4142 points in the middlegame and about 3.1415926 at the endgame.

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