As i have stated in previous posts,
analysis of knight endgames is quite difficult.
There are few general rules, and the number of analysed positions in literature is quite limited. For instance in Dvoretzky's endgame manual knight endgames are allowed only seven pages.
The next example is from Awerbakhs monograph on pure knight and pure bishop endgames.
Kan – Goldenov, 1946 (diagram 466)
Awerbakh concludes the position is drawn,
Averbakh concluded that this position was drawn.
1.Nc8+ Kf6! The actual game continued 1....Kd8? 2.e7!,Kd7 3.Ke5 and white walked his king to f6-f7 to clinch te win.
2.e7 2.Kd6,Nc4+ 3.Kd7 (3.Kd5,Nb2 repeats the position), Ne5+ 4.Kd6,Nc4+=
2.Nd6,Nd3! Threatening Nf4+ followed by Nxe6=
2.... Kf7
3.Ke5 3.Kc5, Nd3! 4.Kd6,Ke8= (or 4.Kc6,Ne5=)
3..... Nd3 And white can make no further progress. The knight is bound to defence of the e7-pawn. And attempts by the king to take over this obligation fail:
(4.Kd6,Ke8! 5.Ke6,Nf4+ 6.Kd6,Nd3=)
(4.Kc5,
And yet there is a win.
1.Nf5+! With two basic lines
1..... Ke8 (1....Kd8 2.e7,Kd7 transposes, while 2....Ke8 3.Ke6 is an immediate mate)
2.e7+ Kd7 (2.....Ke8 2.Ke6 and mate)
3.Ke5! White executes the same plan as in the actual game: he walks his king to f7.
3........, Nd3 (3....Ke8 4.Ke6 and mate)
4.Kf6, Nf4
5.Kf7! And promotion can not be stopped.
1.............Kf6 It turns out that Averbakhs rescue plan does not work any longer.
The key point is that the knight is more actively posted. On f5 it restricts the freedom
of movement of the Black knight and more important: it now has two squares in reach from which it controls e8 (d6/g7) That decides the game.
2.e7, Kf7
3.Kc5!! 3...... Na4!? 3....Ke8 4.Kd6 (threat Ng7+ followed by e8) ,Kf7 (4....Nc4 5.Ke6+-)5.Kd7 and the pawn promotes
3....Nd3 4.Kd6 (and Black is in Zugzwang) He cant move his king (4...Ke8 5.Ng7+-). And on any knight move 4...N? 5.Kd7+- and the pawn promotes.
4.Kc6!! 4.Kd6??, Nb6! Would throw the win away in view of Nc8+
4........., Nc3 Black was in zugzwang. Again he cant move his king:
4...Ke8 5.Kd6! (With the dual threats 6.Ng7+ and 6.Ke6 followed by mate), Kf7 6.Ng7! And the pawn promotes.
5.Kd7 +- And the pawn promotes (with check)
Actually I have found several other errors in Averbakhs book: all concerning simple knight endgames. If there is any interest i will add some to this thread. For now I leave you with a little puzzle:
What is Blacks drawing move in the position below (Reti)