The King's endgame value

Quoting my pal sollevy10: In the endgame, when there is little danger of checkmate, the fighting value of the king is about four points (Lasker 1934:73). The king is good at attacking and defending nearby pieces and pawns. It is better at defending such pieces than the knight is, and it is better at attacking them than the bishop is (Ward 1996:13).

Source: http://en.wikipedia.org/wiki/Chess_piece_relative_value

I'm beginning to think this is a moot pt because it's impossible to have a situation such as K vs B or K vs N, but I still can't believe a King is worth 4 points no matter how many programmers or mathematicians think so, although I do respect the opinions of IMs and GMs in this matter.

Any other thoughts here?

As usual, everything is absolutely dependent on the specific position.

Actually I don't bother how much my king is worth, since I cannot trade him for something!

although the king is the most important piece, Lasker and others estimated its fighting value to be four points in the endgame, which means that it is less powerful than the rook but more powerful than either the N or B. i think the estimate is logical. it tells us too that in the endgame, our king has to be active defending or attacking. you are in check by my king!

I think that Lasker's idea of giving those 4 points to the king is just to underline the idea he expressed that it is better than knight or bishop regarding defending and attacking the pieces, and since the knight and bishop is normally regarded as 3 points, you have to give the king more than that when comparing the value in such situations.

To me it simply means that he underlines the idea that the king is an important active piece in end games. Whether the points value of the the king is considered better or worse than knight or bishop wouldn't be the big deal for me. The big deal would be that the king actively participates in the end game. The difference between losing and winning in end games is often determined by whether the king is passive or active.

There are some endgame situations where mating attacks can occur and mate threats can change the evaluation of a position. An active king can help in making mate threats and mating nets against the enemy king (though this won't happen in most endgames).

A king has to move when threatened, but it is free to enter any square and therefore is not limited on what it can support.  A knight is pretty limited on which squares it can support and pieces cannot be directly protected by a bishop on the opposite color.  A rook is slightly better than a king. While it is not as free as a king in its movement, it has a long range advantage and it also does not have to move when threatened.

So the idea that a king is a 4 seems about right. I would agree that developing a king at the endgame is probably going to more worthwhile than developing a knight or bishop, and that a king usually has more tactical opportunities at the endgame than a knight or bishop. 

It hardly matters if the king's value in the end game is 3.363 or 4.197. As pfren explained, you're not going to trade your king for a rook! The important thing is that in the endgame your king is a strong piece! And you need to use it. I've seen countless games where the stronger player wins an "even" ending because he gets his king up the board and uses it aggressively. He is playing a king up!

Ceteris Paribus

Let's imagine that your opponent's king is anchored in the corner and your own is free and active in the middle of the board. This I would say to be a King up. Equivalent to +3 in piece power.

I would say 2-3 points, but it depends on the position