Once the basic rules are known, king and pawn endings are won by timing and by using every pawn. Triangulation loses a tempo with the king, the outside passed pawn pulls the enemy king away, and shouldering and the breakthrough open the way for a pawn.
Verdict White wins by losing a tempo.
Reach the same position with the opponent to move. The king walks around a triangle of three squares while the opponent can only shuffle.
With Black to move, this position is won for White, because every black king move loses. With White to move it is not enough to wait: every move except ♔f4 loses. White goes round the triangle e4, f4, e3 and is back on e4 after three moves, with Black to move.
1. ♔f4 ♚h6 2. ♔e3 ♚g6 3. ♔e4 ♚h7 4. ♔d4 ♚g6 5. ♔c5 ♚f5 6. ♔d6 ♚f4 7. ♔xe6 ♚g4 8. ♔f6 ♚xh4 9. e6 ♚g4 10. e7 h4
Making any other king move. In the position above, 1. ♔d4?? and 1. ♔e3?? both lose.
White to move. Win or draw? Find the first move.
White wins. The same position mirrored, with the triangle d4, c4, d3. Only ♔c4 wins.
1. ♔c4 ♚a6 2. ♔d3 ♚b6 3. ♔d4 ♚a7 4. ♔e4 ♚b6 5. ♔f5 ♚c5 6. ♔e6 ♚c4 7. ♔xd6 ♚b4 8. ♔c6 ♚xa4 9. d6 ♚b4 10. d7 a4
The king leaves d4 and comes back with Black to move. Every other first move loses.
Copy the position into any board or engine to practice it:
8/8/4p1k1/4P2p/4K2P/8/8/8 w - - 0 1Verdict White wins. Without the outside passed pawn, the same pawns are a draw.
Create or keep a passed pawn far from the other pawns, so that the enemy king has to leave its own pawns to stop it.
The pawn on a4 is an outside passed pawn: it stands far from the kingside pawns. Black's king cannot guard its pawns and stop the a-pawn at the same time, and the white king walks to b7 to escort the pawn to the queening square.
1. ♔d5 ♚e8 2. ♔c6 ♚d8 3. ♔b7 ♚d7 4. a5 ♚d6 5. a6 ♚d7 6. a7 g6 7. a8=♕
Treating every passed pawn as decisive. Only a pawn far from the other pawns decoys the king. Without it, the same pawns are a draw, as the exercise shows.
White to move. Win or draw?
Draw. There is no outside passed pawn, so neither king can break through.
1. ♔e5 ♚e7 2. h3 ♚f7 3. ♔f5 ♚e7 4. ♔e5
White cannot make progress: every king move is answered by the matching black king move.
Copy the position into any board or engine to practice it:
8/5kpp/8/8/P2K4/8/6PP/8 w - - 0 1Verdict White wins.
Win positions that look equal. Shouldering uses the king's body to keep the enemy king away from a pawn. The breakthrough sacrifices pawns to create a passed pawn.
The white king takes the square d5 in front of its pawn with 1. ♔d5. From there it controls e5 and e6, so the black king cannot get in front of the pawn. Pushing the pawn at once with 1. d5 only draws.
1. ♔d5 ♚e7 2. ♔c6 ♚e6 3. d5+ ♚e5 4. d6 ♚e4 5. d7 ♚f5 6. d8=♕
Three white pawns face three black pawns on the same wing, and the black king is far away. White wins with 1. b6!: after 1... axb6 comes 2. c6! bxc6 3. a6, and after 1... cxb6 comes 2. a6! bxa6 3. c6. In both lines a white pawn gets through.
1. b6 axb6 2. c6 bxc6 3. a6 ♚g7 4. a7 ♚f6 5. a8=♕
Pushing the wrong pawn. In the breakthrough position, 1. a6? and 1. c6? both lose. In the shouldering position, 1. d5? only draws.
White to move. Win or draw? Find the first move.
White wins with ♔e5. The natural pawn push 1. e5 only draws.
1. ♔e5 ♚g7 2. ♔e6 ♚h6 3. e5 ♚g6 4. ♔d6 ♚f5 5. e6 ♚f6 6. ♔d7 ♚e5
The king steps in front of the pawn and shoulders the black king away, and then the pawn follows.
Copy the position into any board or engine to practice it:
8/8/5k2/8/3PK3/8/8/8 w - - 0 1