How do you checkmate with a rook and king?
Here is the mistake almost every learner makes. They check with the rook on every single move, and the enemy king never gets any closer to the edge. Most of the moves in this method are not checks at all.
A rook is weaker than a queen, so the plan needs one extra idea. Here is the whole method in four steps.
1. Build a wall. Put the rook on a rank or a file that the enemy king cannot cross. Do not give check. You are drawing a line, not attacking.
2. Walk your king up. March it straight at the enemy king. The rook stays where it is.
3. Take the opposition. Stop when the two kings stand on the same line with exactly one empty square between them.
4. Check. The rook's check now pushes the enemy king back one row, because your king covers the squares it would run to.
Repeat steps two to four until the enemy king is on the edge of the board. The check on the edge is checkmate.
What is the box method with a rook?
The wall makes a box. The enemy king lives inside it and every rook check makes the box one row smaller.
The important part is that the rook only checks when your king is directly opposite. A check on its own does nothing. The king simply steps sideways, and worse, your wall has moved, so it can slip back through.
That is the single biggest mistake in this endgame. Learners check with the rook on every move and never make progress.
What is the opposition?
Opposition means the two kings stand on the same rank, file or diagonal with one empty square between them. It is then the other player's turn to move.
Kings can never touch. So when they face each other like this, the player to move has to give ground.
In this endgame the opposition is what makes the rook's check work. Your king already covers the three squares behind the enemy king, so the check leaves it only one direction to go: backwards.
If you check without the opposition, the enemy king steps sideways and nothing has changed.
What is a waiting move?
Sometimes you have the opposition the wrong way round. The kings face each other, but it is your turn, and any king move would break the shape.
The answer is a waiting move with the rook. Slide the rook along the rank it is already holding, far away from the enemy king. The wall stays. The move passes to your opponent. The opposition is now yours.
One safety rule goes with it. Always slide the rook to the far side of the board, never onto a square the enemy king could reach next move. A lost rook turns a won game into a draw.
Can you use the ladder method with one rook?
No, and it is worth knowing why. The ladder method needs two rooks. One rook holds a row while the other checks on the next row, so neither rook is ever alone.
With one rook, the rook cannot hold a row and give check at the same time. Your king has to do the holding instead. That is exactly what the opposition is for.
So the two mates look similar but the work is shared differently. If you have two rooks, the ladder is much faster and needs no thinking at all.
How long should it take?
A rook and king can mate a lone king from any legal position in at most sixteen moves, if both sides play the best moves.
That matters because of the fifty-move rule. If fifty moves go by with no capture and no pawn move, either player can claim a draw. Sixteen is comfortably inside fifty, but only if you are following a method instead of chasing.
Here is a test of your own play. If five moves pass and the king's box is no smaller, you are chasing.
The stalemate that ruins this endgame
The danger square is the corner. When the enemy king is stuck on a1, a8, h1 or h8, it often has only one or two squares left.
Move your own king to the wrong square and the enemy king suddenly has none. It is not in check, so the game is an immediate draw.
Before every king move in the corner, ask the one question: after this move, does the black king still have a legal move? If the answer is no, your move has to be check.