Need help solving 5th exercise in Pawn Endgames intermediate draws

The move Kg3 leads to zugzwang if black and white play correctly

The principle at work is that of shouldering, opposition and spare tempi. Spare tempi are pawn moves that you can use to make it your opponent's move. That usually makes you win the opposition. This is a very difficult example though.

What you need to realize is that black has 2 spare tempi with ...g6 and later maybe ...h5 to win the opposition. So say you've reached the position with white Kf4, h4, black Kf6, g7, h6 and black to move. White has the opposiiton, but black can use the move ...g6 to make it white's move. If you look at that position, you'll see that black can always shoulder the white king back down the board. Say Ke4, Ke6, Kf4, Kd5, Kf3, Ke5, Ke3, Kf5, Kf3 (white again has the opposition, but black has another 'spare tempo' with ...h5 making it white's move again and black will walk over to the h-pawn to win it. 

Black needs to be aware that white has 1 spare tempo that will kill his 2 spare tempi. So say you've reached the position 1. Kg3, Ke7; 2. Kf3, Kf7? black has the distant opposition, but white plays 3. h5 taking the opposition, killing black's spare tempi and drawing by keeping the opposition (black can't pass). 

White needs to realise that the 2 black spare tempi mean that white can't keep the opposition. The solution then becomes to not take the opposition (and to not let the black king go past and shoulder the white king away). So after 1. Kg3, Ke7; 2. Kf3, Kf6 white needs to play 3. Ke4! This prevents shouldering (after 3. Kg4, black just plays 3. ...Ke5 winning). White declines the opposition and keeps the black king out. If black tries 2. ... Ke6 white just plays 3. Kf4, again declining the opposition and preventing the shouldering move. If black does go for 3. ...Kd5 he's too far away from the pawns and with 4. Kf5 white is actually shouldering the black king to lose an important tempo in the race to the kingside pawns. 

To summarize: if the white king is on the 4th rank and black has the opposition, white can play h5 to take over the opposition and draw. If the white king is on the 4th rank and has opposition, black can first play ...g6 to take over the opposition, then should the king back, before using ...h5 as another spare tempi to take over the opposition once again.

Thank you RAU4ever, I finally understand the problem. Very well explained!

Hello, this is an interesting topic, and I was wondering : 

How do you memorize this kind of stuff ? 

If White king and is on 3rd rank and there is a pawn on xx and he has opposition then ....

I just cannot. There are too many endings to "know". On the other hand, I do not think you compute all of them when playing. 

So does my deficient brain is doomed to fail in endgames ? 

You will learn as you play.

Observing master games will also help you in these problems

You don't memorize. Pawn endgames have some fundamental principles, like the opposition, spare tempi and shouldering which should be learned. Apart from that, pawn endgames rely heavily on calculation. They can get very, very tricky.

hmm, then no escape from calculation I guess, which in a way, good news  

White to play, Kg3 draws according to Lomonosov TB. Only move.

I am also having trouble with this one. It seems 1.Kg3 is mandatory, but can anyone explain what white can respond with after 1.Kg3, g6?
(And why?)

...g6 just wastes an extra tempo. 2.Kf4 takes the opposition and now Black has neither ...g5 nor ...h5.

Thanks for answering

What do you propose to do for white if black answer with 2. Kf4, Kd7?

I guess you mean ...Ke7. Since Ke5 does not work because of ...h5, Ke3 keeps the distant opposition. I never would have found that in a Blitz game.

Thanks for sharing. Really interesting endgame position.

I searched my endgame book for this position and this seems to be a very difficult example of a pawn endgame. A study by Richard Reti & Dr. A. Mandler published in "Tidskrift," 1921.

Another wrinkle is that if after g6 is already played and you take the opposition, if black's King goes to say d7, you cannot move to d5 to maintain the opposition as the black King will go e7, f7 and you can't maintain opposition due to the black pawns. So you need to go to d3. (You also can't naively oppose the black king all the way to the A file )