Dicover how to draw the ending with a knight vs two pawns. When you have some knowledge of the basic pawn endgames, this is easy to understand.
Consider the following position.
It looks pretty grim for white. The black pawns threaten to queen very soon.
Luckily you are able to defend this position with 1.Kf1!
Black can't win this ending. He can try to make progress in different ways.
Variation A: 1...g2+;
Variation B: 1...f2;
Variation C: 1...Ke4;
Variation D: 1...Kd2;
Black wants to advance the pawns without losing both of them.
You've got only one move to start the defence succesfully.
Now Black has to bring his king in, to help promote one of his pawns.
Here you'll discover how (where) to place your knight in this type of ending.
The knight has to prevent the king from helping its pawns.
2....Ke2; (after 2...f2+, 3.Kxg2, Ke2; 4.Nf4+, Ke1; there's Nd4+, winning the pawn).
This is the move you'll have to anticipate when playing this ending of knight vs two pawns. If your knight can't prevent the king from helping the pawns, you'll lose.
Here you already have two drawing options.
4.Nxg2+; chopping off the g-pawn. After 4...Ke2; 5.Nf4+ the game will probably end in a draw by repetition.
The other option is 4.Nd3+, Ke2; 5.Nf2, and you've set up a very good blockade. You can keep on hopping your knight on and off the f2-square.
Black has no way to advance his pawns any further.
Here 2.Kg2, is a good defence.
Once again, the black king has to help its pawn promote. Your knight is on the right square to intervene in time.
The threat is to queen the f-pawns and this has to be prevented.
After 3. Nf4+, Ke1; 4.Nd3+
Black has no other options than to retreat the king to e2 (otherwise the knight takes the f-pawn). This allows a draw by repetition.
Here you're able to draw by taking the f-pawn.
2. Ng5+, Kf4; 3.Nxf3, Kxf3;
You'll be able to secure a drawn position after 4. Kg1, (See pawn endings).
This isn't Black's best try.
After 2.Ng5, f2;
3. Ne4+ (don't make the mistake of 3. Kg2?, Ke2; losing), Ke3;
4.Nxg3, the draw is already secured.
In the endgame of knight vs two connected pawns, you have to place your knight on a favourable square.
The knight has to prevent the opponent's king from helping its pawns.
When you have your knight on a favourable square, you'll be able to draw this endgame.