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The distant opposition - an instructive position for beginners

Drazisaur
| 8

I’ve been trying to learn endgame theory lately and have been delighted about how surprising and beautiful endgames can be.  Unfortunately I am very selective about my learning; if something doesn’t seem interesting or immediately easy to understand, I’ll dismiss it as something that I’ll just get by without.  I made this mistake with the distant opposition - until I came across this little position in a book called Chess Endgame Training by Bernd Rosen.

This position appears in a chapter called ‘The Kings Typical Fighting Methods’ and is a superb illustration of how the king can fight for a draw using the concept of the distant opposition as a guide.  I found the distant opposition a difficult concept because grasping it requires a certain level of board vision.  The beginner - i.e me - doesn’t find it easy to see pieces influence of parts of the board that are far away from the action.  When you are in a game it is hard to remember the distant opposition because it seems impossible that pieces separated by a long distance can be influencing each other.

Rosen describes the opposition in a useful way by saying “the kings ‘oppose’ each other when all the corners of the square around the kings are of the same colour”  this rule applies even if kings are more than one square apart.  I didn’t realise the usefulness of this statement until I properly worked my way through this position.

White looks to be in a bind here.  A pawn down and no way to advance his own pawn safely, all seems to be lost, and this may be the case if it weren’t for the distant opposition.    A beginner wants to play 1. Kg3 to go after the black pawns.  He thinks he can get there first because he seems to be closer but...

 

It's possible that a beginner might know of the concept of the 'opposition' and come to the conclusion that this might help him in this position and play 1. Kf1, but this fails too...

There is however hope for white as the 'distant opposition' comes to the rescue.  1. Kh1!  This move seems ridiculous to the beginner because the king is moving further away from the action and seemingly letting the black king take his pawn and win easily but:

So this was all very well, but taking the distant opposition still didn't seem to make sense to me for some reason.  So I decided to play the position against Shredder here and see what happened when I just concentrated on using the distant opposition.  The following endgame battle ensued and I was amazed to witness myself putting up a solid defence against Shredder at 2600 just by applying the concept of the distant opposition!
What I found truly brilliant about this was how Shredder tried every trick to try and make a breakthrough, repeating positions twice but never three times to avoid the draw by 3 fold repetition.  Eventually black is forced to move one of this pawns lest he sucumb to 3 fold repetition and white is able to take both of black pawns ensuring a draw.  It was this 'game' more than anything else that made me appreciate the distant opposition and how in this instance black can try to dance with the king all he likes, but in the end is forced to move a pawn because of the 3 fold repetition rule.  This position also ended up teaching me how much of an influence the 3 fold repetition rule can be in order to force a player to make a move he doesn't want to make... a kind of zugzwang!  
I hope that beginners find this position as instructive as I did.  I'd recommend putting the position into a computer and playing it out just to experience it for your self (watch out at move 11!).
For any of those more experienced players among you who can see any flaws in my calculations please do point them out lest any beginners out there take some bad advice!  
N:B all the moves in the first 4 diagrams are from Rosen except a few additions by myself for completeness sake.  The comments are however all mine!
Have I aroused in you any desire to study the endgame?