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far1ey 42 ( +1 | -1 )
Numerical value of the King I was just wondering what the numerical value of a king is. Obviously it depends on the situation but just a rough numerical value for the king. Obviously if the king is checkmated its game over so the question is more what is the value of the Kings MOBILITY. In some books it is 5 in others it is 3. I would be thinking that its value is around 3 as I don't think it would be as powerful as a rook. Any Reinfield values? anyone?

Thanks,
Far1ey
ganstaman 21 ( +1 | -1 )
I remember reading somewhere that the king has 4 pawns worth of fighting power. Which is coincidentally an average of your values of 3 and 5.

Worse than a rook, better than a bishop or knight?
ionadowman 54 ( +1 | -1 )
Clearly the game has changed... ...from when I learned the game at 12. There I was told (in a book) that the king's fighting value would be about 2.5 on the Reinfeld scale (which seems to be the ascale being used here). Maybe the fighting value of the King has been appreciated more by players, as I've seen elsewhere the 4-pawn value mentioned.
My guess is that the King's fighting value appreciates as the number of pieces on the board diminishes. in an endgame, no doubt it is worth 4 pawns, but in the opening it is almost a liability, rather than an asset!

far1ey 30 ( +1 | -1 )
Thanks for that ion and ganstaman, it confirms my theroy that the king is not as powerful as a rook.

ion one reason for Reinfeld value of 2.5 may be that the king is vulnerable to checks unlike other pieces ie when another piece is attacked it doesn't have to move but when the king is attacked it must.
ccmcacollister 98 ( +1 | -1 )
Some interesting considerations ... can be made for this Question. And I want to add up some things later.
At the moment, just a couple comments:
far1ey Exactly! Was just pondering that same point; that the king is hindered by the fact it must respond to Every attack whether by a greater or lesser force. Unlike the B,N,R. Certainly seems to me also that the Rook has greater force value than the King, in most circumstances.
{The only exception I've come up with so far would be something like BL= Ka1,Pa3 /WT=Rb7,Rb8,Kg8 so it might be suggested the K+P is at least as strong than 2 Rooks, since the King can produce statemate, deciding the outcome of the game by playing a2. But only for a Draw. Was wondering if you, or anyone, has any good exceptions!?)}
ionadowman My King probably Was worth 2.5 when I was reading Reinfeld ... At that stage of my development, I didnt expect to reach an Endgame! :)
More: Chess
rallyvincent 146 ( +1 | -1 )
Depends... This is an interesting question. The value of The King increases with the rate of disappearence of light and major pieces. In an endgame without any pieces, just pawns, the King is at the same time the strongest and the weakest remaining figure.

The king is weak because he has to move when attacked, he can't take guarded pawns, and he is too slow to catch a pawn two squares away. On the other hand, he is the only one left who can move forward and backward, he can guard his pawns, and he is the only piece that can never be threatened by the other King.

If both players have the same number of pawns, opposed on the same files, only the King can help the pawns for promotion. Therefor, he has to have a "value" at least of a minor piece. The King can guard three files of the way for the promotion (e.g. e6-e7-e8), what one minor piece cannot do. A Rook can't do that alone (he can't denie the opposing King on the eighth rank, if guarding the pawn from behind. So one could say that in the endgame the King has a "value" equal to that of a Rook.

At the same time, the other King has close to no value, if he cannot hinder the promotion. So, as a conclusion I offer this:

Both Kings have a combined "value" of 5 points, due to their double nature. The "value" of one King is variable, depending on the position of the other King. The stronger one King becomes, the weaker the other one gets. The "value" of a King cannot be judged alone.

Any thoughts on this?

Greetings,
Rally V.
migchess20 13 ( +1 | -1 )
Numeric value of king. Since many years. the numeric value of king is infinite because if it is captured the game is lost.

So long.

migchess20
ganstaman 17 ( +1 | -1 )
migchess20 We're all aware of this, I'm sure. But you can still ascribe a value to the king's attacking power. We just got lazy from the first post on and called it the value of the king.
ccmcacollister 19 ( +1 | -1 )
A couple more points: A king covers 8 squares, like a well placed knight.
A king can stop 3 pawns and hold them if far enough from Queening, but cannot win any of the 3 without allowing one to Queen.
loreta 8 ( +1 | -1 )
Just my 2 cents A King can stop 6 pawns and hold them from Queening, at least :-)
kewms 68 ( +1 | -1 )
K vs. 3 pawns? I'd take the pawns and expect to win every single time.

I don't think it's a meaningful question, though. Since both sides always have the same number of kings, king "material" is always balanced and it doesn't matter what number you assign to it.

The suggestion from rallyvincent that the two kings together are worth five points makes the most sense to me. I'm busy playing an endgame where I have a Queen and three pawns against my opponent's Rook and two pawns. My winning chances -- if any -- depend almost entirely on the relative king positions.

Katherine
ionadowman 18 ( +1 | -1 )
Here's a well-known ending ... ... to demonstrate the power - and the vulnerability - of the King in the endgame:
w
With White to play, what is the result?
Enjoy,
Ion
ccmcacollister 171 ( +1 | -1 )
Loreta! Good Point, BUT Only SIX ?! :) Brush up that technique so your King can restrain 8 Pawns! :))
As right here; a completely legal position, although after some very very VERY bad moves ?! {I think it may have been Diamano's Defense...!?}



Black to move & both must settle for a Draw. Of course if the BL pawns were all moved forward a square, and the WT K put back to be at Ke2, then it would be
BL to Play and Win... with Kb8, leaving WT zugzwung, except for his King !
***
kewms Another good point; You could not be checkmated if you had only 3 pawns and no-king on the board! But don't we all tend to take our poor Monarch for granted at times? As I still can't see where you'd win this, as stated with NO King assistance; K vs 3 pawns. So we must assume the other monarch is otherwise engaged & unable to assist his pawns. Let's not leave him off the board completely since he feels unappreciated enough already ... after being called 'weak', lacking meaning, And a "2.5"! But we must tie him up real good, knowing his keen desire to help his subjects at the slightest opportunity; lest he be inclined to jump into the fray to gladly assume even such a lowly role as that of a mere tempo-maker.



BLack to move ...
1. ... c5+ 2.Ka3 c4 3.Kb4
***
Or the third restraining formation

BLack to move again ...
[Having had to be careful to distance the WT K from his own pawns in these diagrams, lest he too attempt service above the call of duty and simply stroll over to Checkmate his rival]
}8-)
ccmcacollister 12 ( +1 | -1 )
Correction ... Meaning to say 'moving the Ke2 back to Ke1' and starting all the BL pawns another
step Southward; regarding Diagram #1 alteration to give BL the win.
kewms 85 ( +1 | -1 )
The position you gave isn't K vs. 3 pawns. It's K + 3 vs K +3. Not the same thing at all.

Which is my point. A King can only restrain three pawns if the opposing king is tied up elsewhere. But if the opposing king is tied up, there must be other material on the board. And if there's other material on the board, you can no longer claim that the King is "equal" to three pawns.

Another way to look at is to consider that a tempo is (allegedly) worth 1/3 of a pawn. So the King's value can be estimated by counting the number of free tempi he has. That is, if my King is right in the middle of the action, and my opponent's King is five moves away on the other side of the board, my King has five "free" moves before my opponent's King can do anything useful. Assuming that I actually have five good squares available, my King is worth 5 tempi, or 5/3 of a pawn.

Katherine
ccmcacollister 181 ( +1 | -1 )
Katherine ... That is my point too; as I said King vs 3 pawns, not King vs 3 pawns and a king helping. An absent king. The presence or absence of other material on the board makes no difference when we say a Knight or Bishop is worth 3 pawns, so I don' t think there is any reason the same does not apply to valuing a King? Is a Bishop no longer of approximate value to a Knight if there are also pawns on the board? Granted such valuations are all approximations, and when it comes down to it, each unique position alters all such arbitrary & general values. Even the comparative value of a tempo changing in the course of the game. The game winning tempo worth more than a Queen. So it would be pointless to claim a 'King is worth 3 pawns' in a strict sense. [And also, while the King may restrain 3 pawns,
sometimes One Pawn may restrain 2 or 3, and more troubling that two Pawns will restrain a King {again, meaning without other material being able to influence that standoff} ]
***
So the example tries to put King vs pawns, purely. Seeking the lowest common denominator; most basic unit. Whereas you wish to add influence of another piece, the opposing King. The extra pawns there have no influence upon the position other than removing the King from the equation. There seems little point to saying K&3P wins against King. And having a King upon the board doesnt guarantee ability to temporize at all times. That is in fact part of what I would wish to measure in King vs Pawns however; the fact that pawns, like Knights, cannot temporize. So putting the other King in the picture gives the pawns an edge that is not implicit to their inherent abilites it seems to me.
loreta 10 ( +1 | -1 )
BUT Only SIX ?! :) ccmcacollister, really I say you, a bare King could stop six pawns (and plus one Bishop, in Addition) :-)
loreta 8 ( +1 | -1 )
Diamano? ccmcacollister: "I think it may have been Diamano's Defense...!?} "
I think, it couldn't :-)
ionadowman 78 ( +1 | -1 )
loreta's right, you know, Craig! If a Damiano were played, there could not have been a pawn at f7. (Note also that every move by a black Q-side pawn had to be a capture, so Sicilians and Caro Kanns are out... Maybe it were (gasp) a Petroff??
***
I don't know whether anyone has looked at the ending I posted last - it's to be found in many chess primers. The point is that the WK doesn't merely hold the 3 Black pawns, but lures them on to destruction. Massacres the lot. So the WK is stronger than 3 pawns.
But once the Black pawns have disappeared, the BK finds himself unable to hold the 2 white pawns, one of which will queen, quite unaided by the WK. So: the BK is weaker than 2 (isolated, be it noted) pawns.
Oh, yeah... White's first move is 1.Kc1
Ain't chess a wonderful game?
Cheers,
Ion
spijker 21 ( +1 | -1 )

White to play and win. Study from Troitzky.
1. the king is a very weak piece
2. a bishop is a very strong piece.
3. discussion useless.
spijker 9 ( +1 | -1 )
wrong diagram The black king is on f7, not on g8, and there's a whit pawn missing on g7.
But after 1. g8=Q Kxg8 the diagram is OK.
ganstaman 47 ( +1 | -1 )
spijker So black is going up the board it seems. To fool the FEN and get the board going the right way, just tell it that it's the other players turn to move. That is, at the end of the FEN is either a 'w' or a 'b.' Switch that and the board flips.

Anyway, following 1. g8=Q+ Kxg8 comes 2. Ke6 (must keep the black king trapped!) Kh8 3. Kf7 e5 4. Bg7#.

Of course, though, you could always set up positions where one piece's value is very different from its average value. Still a nice puzzle, though.
spijker 11 ( +1 | -1 )
Thanks for the tip. So it must be:


White to move and wins.
ccmcacollister 4 ( +1 | -1 )
spijker I dont see where WT can win the final diagram ?!
thunker 34 ( +1 | -1 )
Check the last board diagram Craig, Just set up the board and follow ganstaman's moves. Interesting but works mostly around forced moves. The power of position.
Note spijker 's last diagram was viewed from white's side.... the previous diagrams were in error it seems....
ccmcacollister 93 ( +1 | -1 )
Thanks Thunker Now the blind can see... That's a nice one spijker !
It was reading your 10/29 note under the diagram that threw me off. When it says "study from Troitzky" ; and having set into my mind that anything being a "study" must be full of long tedious variations and obscure means ... Well it Can be said this one only wins the one way, definately not the other! :) It was definately interesting to see WT's improper tries , & how BL holds vs them, too. I believe I've learned more from approaching it wrong, than otherwise!

(And I was just telling another player, I always seem to start at the wrong-end of analysis these days ... and so it goes)
}8-)
PS// Anyone looking to see another interesting K&P's ending, that baffled a couple of GM's for a time, look at bogg's posting to the Coaching Club Forum about it.
ccmcacollister 98 ( +1 | -1 )
Link
Link to bogg's K&P ending (with many pawns) in Coaching Club forum. {btw, he also made what I feel is a Very interesting offer there, to answer some Chess Questions from others. Which seems sadly underutilized for such a generous offer from someone who knows so much about the game. I'd have a dozen for him, but for the unfairness of that since we play in the same region.}

-> gameknot.com

***
loreta / ionadowman
So NOW you KNOW why I cannot play Diamano's Defense, don't you ! :))
But really, I just didn't want anyone to know That Position CAN be reached from a Petroff ...now Everyone will be playing it! !? :( --sigh-- }8-))