Monday, May 07, 2007

King and pawn endgames...confused as usual...

To my horror, Chess Tactics for Beginners actually includes king and pawn endgames. Who do they think they are, insinuating crucial endgame knowledge into tactical software?

I am finding these KP endgames to be quite challenging. Hence, I'm using it as an opportunity to bone up on the theoreticals. In particular, the opposition. I used to think that once you have the opposition, you win. Obviously, this is false, as the following position demonstrates: Black to move, white has the opposition, so white wins right? Obviously, since white's king is outside the square of black's pawn, the opposition doesn't matter. So when does it matter? It matters, for one, when the defender's king is inside the square of the pawn (I use 'defender' to denote the side without the pawn, 'attacker' to denote the side with the pawn).

In those cases where the defender is in the square of the pawn, the attacker needs to get his king in front of the pawn with opposition to win. The opposition isn't even necessarily a useful way to get in front of the pawn. The only absolute is that you want the king in front of the pawn with opposition. Unfortunately, this means you have to do a lot of calculation, a lot of counting squares, to time it just right so that you achieve the holy grail of landing in front of your pawn with opposition. Is this right? If so, crap. I hate calculating, especially in the endgame when my brain wants to go to Hawaii. I was hoping for a simple square-of-the-pawn-style shortcut algorithm that would protect my precious brain from having to think in these simple endings. Am I right that no such algorithm exists? Also, what is the definition of being 'in front of' a pawn? Does it always mean on the same file in front of it?

Another apparently cool factoid I learned about is the opposition when the kings are not aligned on the same diagonal, file, or rank, the so-called 'misaligned' opposition. A player in this case has the opposition if it is the opponent's move and the rectangle drawn around the kings has the same color at each corner. So, for instance, in this example whoever isn't moving has the opposition (note same color of each corner of rectangle, which will happen whenever there is an odd number of ranks and files between the kings):This is nice and simple. So, if it is white to move, black must be very happy, as black has the opposition and is in the square of the pawn, right? Much to my dismay, wrong. White or black to move, white wins from this position. So my question is, what good is the misaligned opposition for the defender, and does anyone have an example where having the misaligned opposition actually does some good for the defender. That is, is the concept only apparently cool? (I found a similar problem with the diagonal opposition: put the black king on e6 in the above and it is still a win for white, with white to move).

Confused as usual...

24 Comments:

Blogger The Rise and Shine Good Knight said...

hmmmmmm

5/07/2007 09:17:00 PM  
Blogger The Rise and Shine Good Knight said...

that same color corner concept sounds cool with the misaligned opposition, but if white wins than that isn't really opposition right? I too am confused..

5/07/2007 09:19:00 PM  
Blogger chessloser said...

damn endgames baffle me, even when i think i understand them. i've seen the colored corner box thingy, i just wish i "knew it in my bones."

5/07/2007 10:23:00 PM  
Blogger Bill said...

Once again, Dan Heisman has relevant material:
http://www.chesscafe.com/text/heisman26.pdf

I think where opposition can be confusing is when its viewed as being a good in itself as opposed to being a means to an end -- that end might be to draw, or invade the enemy camp, or whatever, but its only a tool (one that may or may not be powerful enough to offset other factors of the situation).

For example, in the 2nd diagram (where the king is on c4), the answer to "who has the opposition?" is irrelevant to the outcome because regardless, the white king can advance into (as Heisman refers to it) the "tic tac toe" zone (with a pawn move to spare) and so control the queening square. Black can't prevent his advance to c6.

Looked at another way, In this position, black is powerless to prevent white from getting two squares in front of his pawn (and Black can't reach the pawn) so white will queen.

Only if the black king were on c6 would opposition enter into it (then Black to move loses, White to move draws).

So, no (well not much) calculation needed -- just more principles. :-)

5/07/2007 10:57:00 PM  
Blogger hisbestfriend said...

Um that diagram is wrong, right? How can white win? doesn't black win no matter who goes first? What am I missing?

5/08/2007 12:13:00 AM  
Blogger likesforests said...

King and Pawn endings are the bread and butter of a chess player. You must master them if you want to make a stand in more complicated endings! Rook vs Rook and Queen vs Queen are always threatening to simplify. For example, a recent game I played arrived at this position:

View Online Diagram

Should I play 40...Qd6 (defending my b-pawn, but allowing a queen exchange) or 40...Kf7 (abandoning my b-pawn, but avoiding an exchange)? You can only answer that for certain if you *know* whether the resulting pawn endgame would be won, lost, or drawn.

5/08/2007 12:42:00 AM  
Blogger likesforests said...

"Also, what is the definition of being 'in front of' a pawn? Does it always mean on the same file in front of it?"

The answer is here:

http://www.beginchess.com/category/endgame/

Good post. :)

5/08/2007 12:53:00 AM  
Blogger Blue Devil Knight said...

hisbestfriend: you must be referring to the first diagram. That was the point. Opposition doesn't matter in that case. In the second diagram, white wins easily.

Bill/Likeforests: that is a good point: the King can reach the 'key squares' (TCT language). I'll check out the Heisman, as I intellectually know about key squares but never really got so I can just know instantly what square I need to reach (instead of 'in front of', which Silman says, he should say 'key square', which for some reason he doesn't describe: the first major shortcoming I've seen in his otherwise excellent book).

(likeforests, note that at that link beginchess provides the definition of the misaligned opposition, but like Silman with no example. Anyone have such an example? Why should we care about this misaligned opposition? There must be an example, otherwise why would it be taught by all these masters?).

5/08/2007 09:09:00 AM  
Blogger Blue Devil Knight said...

So to sum up, Silman is in ways misleading. The goal isn't to get "in front of" the pawn with opposition. The goal is to use the opposition to reach a key square.

5/08/2007 09:12:00 AM  
Blogger ShakhMat said...

I allways see opposition as a case of zugzwang. So, in 2nd diagram, when white moves and lose the opposition, black moves and takes it, then white has another move to put black in zugzwang. A pawn move. I have 3 important thing in mind when on "endgame mode" 1) zugzwang 2) piece activity 3) double threads. The lastone is the most important for me, when I have 2 real threads that my opponent cannot meet both at same time, then I know I have a win. Hope this helps. Sebastian.

5/08/2007 10:07:00 AM  
Blogger likesforests said...

Dvoretsky's writes clearly on the subject of pawn endings:

"The stronger side gets the opposition in order to execute an outflanking (where the enemy king retreats to one side, and our king then attacks the other way). The weaker side gets the opposition in order to prevent this outflanking. ... If outflanking is not possible, then possession of the distant opposition is worthless."

The general guideline is, anytime you can draw a rectangle where corners touch both kings, and all four corners are the same color, the kings are in opposition. Vertical, horizontal, and diagonal opposition all follow this guideline.

Silman may have a different naming convention, but most authors call the above simply opposition and not 'misaligned opposition'.

Pandolfini and Lowery refer to the following as either knight's move or misaligned opposition. It's also an example of when it's useful!

Pandolfini Endgame 108

5/08/2007 02:37:00 PM  
Blogger likesforests said...

Here's another interesting one. Taking the vertical opposition with Ke1 loses. J. Drtina 1907.

5/08/2007 02:59:00 PM  
Blogger Blue Devil Knight said...

Likeforests: those are good examples, and I'm pretty clear on those (the diagonal even: the reason the example I showed it doesn't work is because the king can make it to a key square).

But Silman isn't using an unusual example (he also discusses the case where the kings are on the same rank, file, or diagonal: the standard definitions). For instance, Muller and Lamprecth on p 24 of 'fundamental chess endings' call the case where they are not on the same R/F/D the 'virtual opposition' (what I have called the 'misaligned opposition' (and which Silman doesn't actually name)). Like Silman and beginchess here, though, Muller doesn't give an example where this would actually be useful.

At any rate, I am starting to appreciate the complexity here.

Strangely, Flear's book on Pawn Endgames doesn't mention key squares!

Muller and Lamprecht give the following rule, which perhaps may be the best summary of all the principles for KP vs K I have seen (not it applies only for non rook pawns):

The attacker wins if two of the following three are true--
1. King in front of the pawn.
2. Opposition.
3. King on the 6th rank.

5/08/2007 03:34:00 PM  
Blogger likesforests said...

You want to see virtual opposition in action? A great example is the ending from Shirov-Areschenko, Aerosvit Foros 2006:

FEN: 8/8/1p5k/pP2K3/8/8/8/8 w - - 0 76

To hold the draw, Shirov must stay close to the pawns while maintaining the opposition. Can you guess his next move?

*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****

Kd4! *Every* other move loses as they either allow a4,a3,a2,a1/Q or lose the opposition.

5/08/2007 08:28:00 PM  
Blogger likesforests said...

To explain more fully, the square of the pawn extends from a1 to a5 to e5 to e1. White's king must remain within that square or Black can play a4,a3,a2,a1/Q.

To maintain the opposition and so prevent Black's king from outflanking him, White must play f6 (horizontal, close opposition), f4 (diagonal, close opposition), d4 (virtual, distant opposition), or d6 (horizontal, distant opposition).

The only move meeting both criteria is Kd4. Shirov knows this, and so proves he's worthy of the title of super-grandmaster.

5/08/2007 08:35:00 PM  
Blogger Blue Devil Knight said...

Likeforests: great--what's the position? I have a feeling all that stuff after "FEN" gives a position, but I don't understand that language.

5/09/2007 08:49:00 AM  
Blogger likesforests said...

Diagram

5/09/2007 10:04:00 AM  
Blogger Blue Devil Knight said...

Likeforests: thanks. I'll have to look at all this useful information you provided when I get home tonight. I see you provided that example earlier, and I didn't see it because I think I was constructing a comment in response to your first message while you posted the second message.

Anyway, I'll take a look at all this.

5/09/2007 10:15:00 AM  
Blogger Cratercat said...

Nice post BDK. Yeah, I think your diagram example highlights the notion of playing principles, and when exceptions to those principles occur due to positional factors. Also, I don't know if you own it or not (I don't yet) but there's supposed to be a great book out by Mueller "Secret of Pawn Endings" which I imagine might help in clarifying nebulous topics like "misaligned king opposition". For some reason when it comes to learning about endgame, I need to read about it from more than one author in order for the concepts to really take hold.

5/10/2007 03:59:00 PM  
Blogger Cratercat said...

BTW - Thanks for referring me to J'adoube's post on the modern benoni. A very entertaining read :o)

5/10/2007 04:01:00 PM  
Blogger J'adoube said...

Ah, young padawan. . .

:)

The important point to remember here is whether or not White can reach the 6th rank in front of his pawn. If he can, he wins, opposition be damned.

5/11/2007 08:54:00 AM  
Blogger Roger Coathup said...

We've been posting a fair bit about king and pawn endgames over on Chess Tales.

Chess Endings: Essential Knowledge by Averbakh is a must read.

5/11/2007 04:08:00 PM  
Blogger HardDaysKnight said...

This is a great post; I grow more and more to appreciate the endgame; I just wanted to add that I played chess for many years thinking I understood King and pawn endings, and the opposition. Then I discovered (from Muller and Lamprecht or Dvoretsky, I don't remember) that the opposition didn't matter if the king is on the sixth rank in front of the pawn. And my understanding continues to grow. But importantly, even with that knowledge, I hadn't gotten a lot of practice in the endgame until I started using PCT with the endgame modues (and I assume Convekta offers something similiar); gaining skill (i.e., the ability to apply knowledge to a given situation) is crucial. Armed with more endgame confidence, my overall approach to chess is changing for the better.

Speaking of those authors, Dvoretsky's Engame Manual is a wonderful, captivating book; Muller and Lamprecht’s Fundamental Chess Ending is also excellent. I also own Basic Chess Endings, but I find the others more accessible.

6/12/2007 12:32:00 PM  
Anonymous Anonymous said...

in the 2nd diagram, you can easily tell that white wins because the opposition only applies when there are only king moves left. white can lose a tempo by moving the pawn instead of the king, taking the opposition at the opportune time.

rule: opposition applies when there are only king moves or if any other non-king move is detrimental to its position.

6/25/2009 09:31:00 PM  

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