Every other ending leans on king and pawn play, so four rules come first: the square of the pawn, the opposition, key squares and the rook pawn exception. Each one gives a quick way to read a position and know the result before calculating.
Verdict The pawn queens. The black king cannot step into the square.
Decide at a glance whether a king can catch a passed pawn, by drawing the square from the pawn to its queening square.
The white pawn on f4 needs four moves to queen, and the white king on a8 is too far to help. The yellow corners mark the square: f4, f8, c8 and c4. With Black to move, the king on c2 cannot step into the square, so the pawn queens. With the king on c3 it plays ... ♚d4 and the position is a draw.
1... ♚d3 2. f5 ♚d4 3. f6 ♚c5 4. f7 ♚d6 5. f8=♕+
Forgetting the double step. A pawn on its starting rank is already one move closer, so draw the square from the third rank.
Black to move. Win or draw?
Draw. The king steps into the square with ... ♚d4 and catches the pawn.
1... ♚d4 2. ♔b8 ♚e4 3. ♔c8 ♚xf4
After ... ♚d4 the white king is too far away to help, and the pawn is lost, which leaves only the kings.
Copy the position into any board or engine to practice it:
K7/8/8/8/5P2/8/2k5/8 b - - 0 1
Verdict With Black to move, White wins. With White to move, the same position is a draw.
Win the opposition: put your king directly facing the enemy king, with one square between them, and leave the opponent to move.
The kings face each other on e5 and e7. The red squares are the squares the white king cannot use while Black holds the king there. Black has to move and must step aside, so the white king walks past with ♔d6 and the pawn follows. With White to move, the same position is a draw, because White cannot pass the move.
1... ♚f7 2. ♔d6 ♚f8 3. ♔d7 ♚f7 4. e5 ♚g6 5. e6 ♚f5 6. ♔d6 ♚f6 7. e7 ♚g5 8. e8=♕
Thinking the opposition belongs to the side that moves into it. It belongs to the side that does not have to move, so the player to move often has to give way.
White to move. Win or draw?
Draw. White is the side to move, so Black holds the opposition.
1. ♔e5 ♚e7 2. d5 ♚d7 3. ♔d4 ♚c7 4. ♔c5 ♚d7 5. d6 ♚d8
The black king mirrors the white king, and White can never make the black king step aside.
Copy the position into any board or engine to practice it:
8/4k3/8/4K3/4P3/8/8/8 b - - 0 1
Verdict White wins, whoever moves. The king stands on a key square.
Bring the king to a key square in front of the pawn, because from there the pawn queens by force.
For the pawn on e5, the squares d6, e6 and f6 are key squares. The white king stands on e6, so the black king cannot stop the pawn, whoever is to move.
1. ♔d6 ♚f8 2. e6 ♚g7 3. e7 ♚f7 4. ♔d7 ♚g6 5. e8=♕+
Walking toward the pawn instead of the key squares. In the exercise position, 1. ♔e5 only draws.
White to move. Win or draw? Find the first move.
White wins with ♔f5, heading for the key square f6. The natural 1. ♔e5 only draws.
1. ♔f5 ♚d6 2. ♔f6 ♚c6 3. ♔e6 ♚c5 4. e5 ♚d4 5. ♔f5 ♚c4 6. e6
The king reaches f6, a key square for the pawn on e4, and then the pawn advances.
Copy the position into any board or engine to practice it:
4k3/8/4K3/4P3/8/8/8/8 w - - 0 1
Verdict Draw. The black king holds the corner.
Know that a rook pawn cannot win when the defending king reaches the corner in front of it.
On the edge file the pawn has only one side to pass. The black king reaches the corner a8, and the white king cannot drive it out. Pushing the pawn only leads to stalemate: after a7+ ... ♚a8 and ♔a6, Black has no legal move.
1. a6 ♚b8 2. a7+ ♚a8 3. ♔a6
Bringing the king close and pushing the pawn. After 1. a6 ♚b8 2. a7+ ♚a8 3. ♔a6??, the position is stalemate.
White to move. Win or draw?
Draw. The black king reaches the corner and White cannot make progress.
1. ♔g5 ♚h7 2. ♔f6 ♚h8 3. ♔f7 ♚h7 4. h6 ♚h8 5. h7 ♚xh7
The pawn can only advance to h7, where the black king simply takes it.
Copy the position into any board or engine to practice it:
k7/8/1K6/P7/8/8/8/8 w - - 0 1