Thx guys for the positive reactions.
I have yet to post the sequel on the knight endings. There has been a
delay because I had to put in rather a lot of overtime at work.

At MUbas:
Great that you recognized the quote! Indeed I love Chesterton
(favourite book: The man who was Thursday).
Here is another quote for you, that would raise some eyebrows 
if connected to chess:
"I am going to base the defence on the fact that the judge has a bald head"

Hear, Hear, to all those who thought this was a fantastic revision!  I had to double-check a couple of lines, but everything is laid out clearly and I didn't see any mistakes at all!  

WOW!

Thanks!

Thanks for posting this, with enough diagrams so it was easy to follow in my head! I look forward to the Knight ending.

pawn endgame second plan: white king invasion

after 43....g5 



The invasion-plan is bound with some risk. White can no longer catch up with black kingside pawns in case of a pawn race.
As we see later, this is a good reason for keeping the knights on the board. 


44.Kb6, f5
45.Kxa6
(It is not to late to repent:  45.Kc5 still holds the draw)
45......., h5
Now black is ready for the pawn race. White has two choices:
variant 1: promote the b-pawn
variant 2: promote the a-pawn

variant 1 white promotes the a-pawn
46.b4,g4
47.fxg4!

47.b5 is no good: 47...,gxf3 48.K6,f2 49.b7,f1+ 
Again an example how important it is to head promotion with check in your calculations.
The text move asks black a not to simple question:
Which pawn are you going to promote?



The answer to the question above should be simple, if black asks himself another:
Which pawn can I promote with check?
The answer then becomes clear
47........f4!
Note that the natural reply 47....hxg4 doenst win
47....hxg4? 48.b5! (position before material: after 48.fxg4??,f4! white again is lost) 48...gxh3 49.b6,h2 50.b7,h1Q (no check!) 51.b8Q=


48.b5
48.gxh4,f3 doenst help: black's king is in the square of the h-pawn
48..........,  f3
49. b6     , f2
50. b7     , f1Q+ -+
Black has achieved his goal, he promotes first and with check.
The rest is technique: to bring first his queen and than his king as close to the b-pawn as possible:
51.Ka7, Qf2+ 52.Ka8,Qf3! (pinning the b-pawn and threatening Kd7-c7-Qxb7#) 53.Ka7,Qe3+ etc.


variation 2 white promotes the a-pawn

46.a5,g4



Now we get to three subvariations:
variation 2.a 47.fxg4
variation 2.b 47.hxg4
variation 2.c 47. various king-moves.

variation 2.a. 46.a5,g4 47.fxg4

47.fxg4,
Black should again think about which pawn he wants to promote.
White's king is blocking his pawn and has to move to the b-file.
If he should play Kb7, the answer is obvious: the h-pawn promotes with check. 
But what if white plays Kb6/b5?
The answer remains the same: the h-pawn. The reason is that if the h-pawn promotes first, the new queen will cover the promotion field of the a-pawn!. 
Note that this reason is unique for a pair of a- and h-pawns.
47.....,fxg
Preserving the h-pawn! 
Instead 47....hxg4 would throw away the win:
47...hxg4 48.fxg4,fxg4 49.Kb7,g3 50.a6,g2 51.a7,g1Q 52.a8Q=
48. hxg4
White has no choice: after 48.K?, gxh3 black has two h-pawns!
48......., h4!
Again 48...hxg4 would have thrown away the win.
49.Kb7, h3
50.a6,h2
51.a7,h1Q+ -+
And black wins by bringing his queen close to the a-pawn:
52.Kb8 (52.Kb6?,Qa8!), Qh2+ 53.Kb7,Qg2+ 54.Kb8,Qg3+ 55.Kb7,Qf3+ 56.Kb8,Qf4+ 57.kb7,Qb5+ 58.Kc7,Qa6 59.Kb8,Qb6+ 60.Ka8,Kd7 etc.


variation 2.b white promotes the a-pawn 46.a5,g4 57.hxg4


Now black must take care, because one condition isnt fulfilled.
At the moment the f-pawn blocks the a8-h1 diagonal so the h-pawn doesnt promote with check, which makes a difference!

47.hxg4, fxg4!
After 47...h4? black doesnt win 
47...h4 48.Kb6!,h3 49.a6,h2 50.a7,h1Q (no check!) 51.a8Q=

48.Kb7
After all, the h-pawn isnt close enough, is it?
48.fxg4, (now the diagonal a8-h1 is cleared, so) 48...h4! 49.Kb7,h3 50.a6,h2 51.a7,h1Q+ and wins.
Note that if white had played 49.Kb6 (iso Kb7) white cant promote after 51...h1Q since 52.a8Q,Qxa8!
48.Kb6 (which pawn is black going to promote now?) 48...g3! (now this pawn promotes with check) 49.a6,g2 50.a7,g1Q+ and black wins.

48.......gxf3!
Black still clears the a8-h1 diagonal, with a specific purpose in mind.
49.a6,f2
50.a7,f1Q
51.a8Q
It seems that white has achieved his goal, both sides have promoted their pawns

Unfortunately for white
51.....Qh1+ !
Still wins for black, after the queens come off, white loses the pawn endgame.

variation 2.c white king invasion 47.K?



If white clears the way for his a-pawn at once, the position of the king determines blacks reply. If you worked through the previous variations you should have no difficulty to understand the variations:

47.Kb6, g3! (the g-pawn promotes with check)
47.Kb7, gxf3! (black will exchange queens after both sides promote their pawn, leaving him with a won pawn endgame):
47.Kb7,gxf3 48.a6,f2 50.a7,f1Q 51.a8Q,Qh1+ 52.K?,Qxa8 53.Kxa8, Kd6! etc.

This completes my analysis of the pawn-endgame from Rechel-Hebden
I hope you agree with me that there was something to learn from it.

I intend to post  the analysis of the Knight endgames during the next week.

I examined the main lines of this endgame in another thread:

http://www.chesspub.com/cgi-bin/yabb2/YaBB.pl?num=1210712688/0/#13

There I allready remarked that there was more to say about this endgame. First I will return to the pawn endgame that might have occured after:
38.Ke3,Nd5 39.Kd4,Nc7 40.Nb7,Ne6 41.Kd5,Ke7 42.Nc5 and now
42....Nxc5! (iso Nf4?) 43.Kxc5

But before I do so I want to introduce a basic endgame that is very practical and explains some of the variations presented later.


This position is a fortress, black can make no progress.
1.Kg1,g2 2.Kh2,Kf2 stalemate.
1.Kg1,Ke3 2.Kh1,Kf2 stalemate.
With black to play it also draws:
1....g2+ 2.Kg1,Kg3 stalemate.

With this position in mind, you shoud quickly find the easiest method to 
draw in the next diagram. 

This postion and its solutions is in the first (German) edition of Awerbach's monograph on pawn endings. And this is what he has to say about it:
"We encounter this type of endgame quite often in practice and therefore it deserves our attention"

Now that we are warmed up lets look at the pawn endgame from Rechel-Hebden:


It's black's move. And it should be obvious that he must find some active defence. If black remains passive white captures the a6-pawn and wins easily with his connected passed pawns. Thus he must distract white and create a passed pawn of his own. But it matters greatly how he sets his own pawn majority on the kingside in motion.
The 'golden' rule is to move the potential passed pawn first.
It is the pawn that is not opposed by an enemy pawn, in this case the g-pawn. According to this rule, 43....g5! is the right move.

To prove this I will first show that neither 43...f5 nor 43...h5 are insufficient to draw. 
variation 1a.
43.....,f5 
44.f4!,      
(white makes it hard for black to create a passed pawn)
Note that moves like 44.Kb6 or 44.b4 would throw away the win, as black can correct his error playing 44.....g5!
44.... , a5  
(black tries to returns the favour)
45.b4!,       
45....., axb4
46. Kxb4, Kd6
White immediately creates a passed pawn. Black can stop this pawn with his king, and hold off whites king from the critical b7 square. But now white's king goes pawnhunting on the other side of the board.


47. Kc4!
The white monarch starts his journey to the kingside (47.a5 wins as well).
47........, Kc6
Still blocking whites king  (47.....g6 48.a5! and black's king must make way as he has to stop the runaway a-pawn)
48. Kd4, Kc6
49. Ke5, g6
50. Kf6 , Kb5



51. h4!
Note that white can still throw the win away with the greedy and impatient 51.Kg7?? when black draws with 51....g5! creating a passed pawn of his own.
After 51.h4 its all over:
51.h4,Kxa5 52.Kg7,Kb5 53.Kxh7 and the black king is too late to rescue the pawns he deserted.

I have explained this example at some length, so that you should have no difficulty to comprehend the other side variations:
From the starting postion


variation 1b.
43...f5?  44.f4,h6 (black tries to activate his kingside first iso improving the position of his king with Kd6 as in the variations above) 45.h4! (a preemptive move to render g5 harmless), g5 (after any king move white plays h5!) 46.fxg5!,hxg5 47.hxg5, a5! 48.Kd5! (and white picks up the f-pawn; note that 48.b4 is a blunder: 48...f4!=)



variation 2.
43....h5 44.f4!,a5 45.b4,axb4 46.Kxb4, Kd6 47.Kc4 (is very similiar to variation 1a.
Just note that 47..., f5 48.h4! +- and 47....,f6 48.f5 +-

In the next post in this thread I will examine 43...g5 in detail.
The remaining two posts will be devoted to various knight endgame variations.