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 "World Open"]
[Site "Valley Forge, Pennsylvania"]
[Date "2010.??.??"]
[Round "?"]
[White "Jan Gustafsson"]
[Black "Marc Arnold"]
[Result "1-0"]
[BlackElo "0"]
[FEN "1k6/8/1P1p1p1p/K2PpPpP/4P3/5P2/8/8 w - - 0 1"]
[SetUp "1"]
[TimeControl "0"]
[WhiteElo "0"]
{ Most first moves win, but white must take care not to allow black a
stalemate. } 1. Kb4 { This is the fastest winning line of play. Triangulation
protects the b-pawn and allow the king to invade on c6. } ( { White can also win
with: } 1. Ka6 Ka8 2. b7+ Kb8 3. Ka5 { A surprise sacrifice of white's
beautiful passed pawn. } 3... Kxb7 4. Kb5 Kc7 5. Ka6 Kc8 6. Kb6 Kd7 7. Kb7 Kd8 8. Kc6 Ke7 9. Kc7 g4 10. fxg4 Ke8 11. Kxd6 Kd8 12. Ke6 Kc7 13. d6+ Kd8 14. d7 Kc7 15. Ke7 Kb6 16. d8=Q+ { White wins with a large material advantage. } ) ( { White can also win with: } 1. b7 Kxb7 ( 1... Kc7 2. b8=Q+ ( { Any attempt to
protect the pawn is a serious blunder allowing black to draw. For example: } 2. Ka6 Kb8 3. Kb6 g4 4. fxg4 { Stalemate. } ) 2... Kxb8 3. Kb6 Kc8 4. Kc6 Kd8 5. Kxd6 Ke8 6. Ke6 Kf8 7. Kxf6 Kg8 8. Kg6 g4 9. fxg4 Kf8 10. f6 Ke8 11. Kg7 Kd7 12. f7 Kd8 13. f8=Q+ { White wins with a large material advantage. } ) 2. Kb5 Kc7 3. Ka6 Kd8 4. Kb7 Kd7 5. Kb6 g4 6. fxg4 Kd8 7. Kc6 Ke7 8. Kc7 Kf8 9. Kxd6 Kf7 10. Kc7 Ke7 11. d6+ Ke8 12. d7+ Ke7 13. d8=Q+ { White wins with a large
material advantage. } ) ( { White can also win with: } 1. Ka4 Kc8 2. Kb4 Kb8 3. Ka5 Kb7 4. Kb5 Kb8 5. Kc6 Kc8 6. Kxd6 Kb7 7. Kc5 g4 8. fxg4 Kb8 9. d6 Kc8 10. Kc6 Kd8 11. d7 Ke7 12. b7 Kf7 13. d8=Q { White wins with a large material
advantage. } ) 1... Ka8 2. Ka4 Kb8 3. Ka5 { Reaching the same starting position, but
with black to move. } 3... Kb7 ( { Other moves lose even faster. } 3... Ka8 4. Ka6 Kb8 5. b7 Kc7 6. Ka7 Kd7 7. b8=Q Ke7 8. Qc7+ Kf8 9. Qxd6+ Kf7 10. Qc7+ Kg8 11. d6 g4 12. fxg4 Kh8 13. d7 Kg7 14. d8=Q# ) 4. Kb5 Kb8 5. Kc6 Kc8 6. Kxd6 Kb7 7. Kc5 g4 8. fxg4 Kc8 9. Kc6 Kd8 10. b7 Ke7 11. d6+ Kf8 12. b8=Q+ Kg7 13. d7 Kh7 14. d8=Q Kg7 15. Qg8# 1-0