King and Rook vs King

King and rook against a lone king is always a win, and it should be the second mate you learn cold after king and queen versus king — it comes up constantly whenever a game simplifies down to an extra rook, and unlike the queen version, a rook can't box the enemy king in on its own in one motion. It only controls a single rank or file at a time, so the technique takes a few more moves and a bit more patience.

A rook cuts off a line, not a box

A queen confines a king to a shrinking rectangle by sitting a knight's-move away and controlling two directions at once. A rook can only ever control the rank or file it's standing on, so instead of a box, the technique is a single dividing line: place the rook on a rank (or file) that the enemy king cannot cross, and the king is now trapped on the far side of it, no matter how it moves.

The rook can't mate by itself

Because a rook only ever covers one line, it can never deliver checkmate on its own the way a queen occasionally can from a lucky angle — the mating square always needs the attacking king's support too. Once the enemy king is confined to the back rank (or the edge file), the attacking king has to walk the rest of the way up the board, one step at a time, while the rook simply holds its line and waits.

The mistake that gives the king back its half of the board

This technique goes wrong most often through a premature check: checking with the rook before the attacking king is close enough to back it up forces the enemy king to move, but if the rook's own king isn't there to control the squares around it, the enemy king can simply step past the rook's rank or file and undo the entire confinement — the game hasn't gone backward on the scoreboard, but the winning side has to start the whole squeeze over from a worse position, and with fewer pawns or move-count cushion than before, that can matter.

Finishing it once the kings are close

When the attacking king has advanced close enough that it and the rook between them cover every square the defending king could step to, the final rook check along the edge of the board is mate — the same idea as the finish in king and queen versus king, just built one rank or file at a time instead of all at once.

This is the more mechanical cousin of king and queen vs king, where a single well-placed queen move does in one step what the rook needs several moves and a supporting king for. If notation like Ra7 still looks unfamiliar, that page covers exactly what every move label on this site means.