King and rook against a bare king is always a win. A rook isn't as strong as a queen and can't mate on its own, so it has to team up with the king. The rook cuts the enemy king off on one side, your king walks over to confront it, and whenever the two kings face each other, a rook check sends the enemy king back one rank. Once you've learned it, you won't panic when this ending shows up while you play chess against the computer.
Key position
How to play it
Step 1: cut the king off with the rook, then bring your king
First the rook goes to the 4th rank, and the black king can't cross it. Then the white king walks up and tries to stand face to face with the black king (same file, one square between them; this is called "the opposition"). Now a rook check forces the black king back.
If the black king avoids facing your king, make a waiting move with the rook along the same rank (like Rg4 above), so the box doesn't get bigger. Sooner or later the black king has to come back or retreat on its own.
Step 2: push the king to the back rank
Keep pushing one rank at a time in the same way until the black king is stuck on the 8th rank. The white king follows it, and the rook guards the 7th rank.
With the rook far away on a7, the black king can't get near it. The farther your rook is from the enemy king, the safer it is.
Common mistakes
Just like the queen mate, the classic mistake at the end is stalemate. The other one is putting the rook next to the black king without protection.
In the same position, Rg8+?? leaves the rook unprotected and the black king takes it, also a draw. The right idea is to play Kf7 first (or another move that leaves the black king a square) and mate with the rook next move.
Practice puzzles
Show answer
1. Ra8# The rook goes to a8 and checks along the back rank. The white king covers f7, g7 and h7, so the black king has nowhere to go.
Show answer
1. Rh7 For example, slide the rook along the 7th rank to h7 (Re7, Rf7 and Rg7 also work) and let Black move. If the king goes to d8, it faces your king and Rh8 is mate. If it goes to b8, play Kc6 and mate comes soon. Watch out: Rb7?? lets the black king take the rook, and it's a draw.
FAQ
How many moves does the rook mate take?
According to the tablebase, at most 16 moves from the worst starting position. With the cut-off-and-opposition method it usually takes about 20 moves in a real game, well within the 50-move rule.
Why wait until the kings face each other before checking?
When the kings face each other, your king covers the three squares in front of the enemy king, so a rook check can only send it backward. Check at any other time and the king just slips out to the side, and you've wasted moves.
What if the enemy king keeps chasing my rook?
Move the rook to the far end of the same rank or file, as far from the enemy king as possible. As long as it stays on that rank, the cut-off works just the same.
Try it yourself
The opposition you used in the rook mate comes up again and again in pawn endgames. All the endgames are in Chess endgames. To practice it yourself, open free chess and, when you're down to a lone rook, don't stop until you've mated.