Eric because you cannot.
What is the value of the king?

FBloggs: i disagree.
Here the King is disguised as dark squared bishop. The dark squared bishop got captured earlier in the game. So the King steps in as a substitute. In this case the King is worth about 3 point.
Not a good disguise. Looks like a king to me.

In the endgame. when the king can emerge from its fortress to take an active part in the game, he has
about the same value as a bishop or a knight. But if the king is checkmated, the game ends. It is, there-
fore, possible to sacrifice almost all of your pieces in order to deliver checkmate, so no true value can be placed on the king.

LM_player. Say you are playing a 1 hour game and the game, by your estimation and feel for the board state is about 1/4 over. How many points is the King worth then?

I think its 4.
If the rule is is not checkmate to win but rather 1 last piece standing. Or point based time limit
there is an absolute value for the pieces and a relative one. in the case of the king, the relative one goes from zero at the begining and more and more valuable reaching the end game with fewer pieces on the board. check this article https://en.m.wikipedia.org/wiki/Chess_piece_relative_value