Knight endgames are like king and pawn endgames. This rule of thumb was given by former world champion Mikhail Botvinnik, who observed that if a king and pawn endgame was winning, the evaluation would be the same with knights on the board. We can infer that protected or outside passed pawns can be a huge asset in knight endgames, because the stronger side can always offer to trade knights, and the defending side will need to retreat in order to avoid the trade.
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[Event "rated untimed match"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "White player"]
[Black "Black player"]
[Result "*"]
[BlackElo "0"]
[FEN "8/p7/3k3p/2p5/2P3P1/1P6/P7/4K3 w - - 0 1"]
[SetUp "1"]
[TimeControl "0"]
[WhiteElo "0"]
{ Winning Technique.|This king and pawn endgame lesson demonstrates winning
technique with a pawn majority. } 1. Ke2 { White activates his king. A king
is a fighting piece in most endgames when the heavy pieces are off the
board. } 1... a6 { Black's king can do little to stop the white king's advance as we
will see in the coming moves. So black temporizes by advancing a meaningless
pawn. } 2. Ke3 { White's king advances further with the intent to invade
black's side of the board, and win. } 2... Ke7 { The black king attempts to use
distant opposition as a means to stop the invasion of white's king. } 3. Ke4 { White's king confidently advances. } 3... Ke6 { Black directly opposes the advance
of white's king. } 4. a3 { White threatens to advance his b-pawn to create a
passer. } 4... a5 { Black stops white's b-pawn. } 5. a4 { White puts black into
zugzwang. Any move that black makes loses. } 5... Kd6 { Black is forced to move and
give way to white's king. } 6. Kf5 { White invades.|White will soon capture
the h-pawn, advance his g-pawn, promote it, and win. } 6... Ke7 7. Kg6 Ke6 8. Kxh6 Kf7 9. g5 Kg8 10. Kg6 Kh8 11. Kf7 Kh7 12. g6+ Kh8 13. g7+ Kh7 14. g8=Q+ Kh6 15. Qg6# *