King and Rook vs King: the staircase technique

King and rook against a lone king is a forced mate, but the rook cannot do it alone. The rook draws a line the enemy king may not cross; your king takes away his escape squares. The method has three steps: cut the king off, walk your king up until it faces his, and push the barrier one rank at a time until he runs out of board.

Why it is harder than king and queen

A queen covers a rank, a file and the diagonals at once, so she shrinks a box around the enemy king almost by herself. A rook covers one rank and one file, and it can never come close to the enemy king: any square next to him is a square where an undefended rook is taken for free. In the queen ending the danger is stalemate; here it is drifting in circles until you hit the fifty-move rule.

• The rook draws the wall: a full rank the enemy king is not allowed to cross.
• Your king removes the retreat: it stands opposite the enemy king with one empty square between them.
• The rook checks: the wall climbs one rank and it never comes back down.

Step 1: cut the king off

The first useful move is almost never a check, it is a cut. Put the rook on a rank between the enemy king and your side of the board: he is now stuck in a rectangle that will only shrink. Below, the rook on h4 seals the fourth rank and Black is left with 32 squares.

The wall is sacred. If the black king comes over to attack it, going to g5 to touch the rook on h4, do not break the cut: slide the rook along that same fourth rank with Ra4. The barrier is unchanged, and Black spent two moves walking the wrong way.

Step 2: bring the king up and take the opposition

The wall is built and the rook has nothing left to do for a while. Walk the king: 1.Kf3 Kd5 2.Ke3 Ke5. The kings stand face to face on the e file with one empty square between them. That is the opposition, and it is what turns a check into progress.

Play 3.Rh5+ and count the replies: d6, e6 and f6. That is all of them. The squares d4, e4 and f4 belong to the white king on e3, and the whole fifth rank belongs to the rook. Black has no choice: he steps up a rank, and the barrier climbs with him.

Now the classic mistake. After 3...Ke6 4.Ke4 Kd6 the kings are no longer facing each other. If you check anyway with 5.Rh6+, Black answers 5...Kc5, drops back to the fifth rank and undoes your work. Check only when you already hold the opposition.

Step 3: climb the staircase

The rest is a short cycle on repeat. When the enemy king steps sideways instead of backwards, you do not check: you mirror him with your own king. That is what happened in 5.Kd4 Kc6 6.Kc4 Kb6 7.Kb4 Ka6 8.Ka4, White copying every sideways step and squeezing Black toward the a file.

1. Kings face to face and it is your move: check along the enemy king's rank. He drops one step.
2. The enemy king stepped sideways: follow him with your king and rebuild the opposition. No check.
3. The dance repeats and the opposition never falls on your move: play a waiting move with the rook.

That is where the name comes from: every check lifts the barrier one rank and it never slides back.

The waiting move

Mirroring with the king has a limit. After 8...Kb6 the black king shuffles between a6 and b6 and your king between a4 and b4: the opposition always arrives with Black to move, and Black always has one more sideways step. Mirroring again just repeats the position.

The answer is to hand the move back: 9.Rg5. The wall is still up and now Black has to move. If he steps back with 9...Ka6, the kings face each other on your turn and 10.Rg6+ follows. If he retreats to the seventh rank, you gained a step for free. If he steps sideways with 9...Kc6, mirror him again with 10.Kb4: the moment the kings face each other, the check lands on your move. Pick the waiting square carefully: g5 is far from the black king, while Rc5 would lose the rook to Kxc5.

The mate on the edge

Mate only exists at the edge of the board, your king taking the three retreat squares while the rook seals the rank. From the cutting diagram, the whole game lasts 14 moves: 1.Kf3 Kd5 2.Ke3 Ke5 3.Rh5+ Ke6 4.Ke4 Kd6 5.Kd4 Kc6 6.Kc4 Kb6 7.Kb4 Ka6 8.Ka4 Kb6 9.Rg5 Ka6 10.Rg6+ Ka7 11.Kb5 Kb7 12.Rg7+ Kb8 13.Kb6 Ka8 14.Rg8#.

On the last rank the pattern shows up one final time. With the rook on g7, the white king on c6 and the black king on c8, mate is immediate: Rg8#. If the black king sits on b8, play the waiting move Rh7, and after ...Kc8 comes Rh8#. If he goes to ...Ka8 instead, do not check there: Kb6 leaves him only ...Kb8, and then Rh8#.

Why the fifty-move rule matters here

There are no pawns here, and the only capture available is the one that takes your rook. So the fifty-move counter started at the last capture, usually the very capture that created the ending, and it will never reset. Once fifty moves by each side go by with no capture and no pawn move, either player can claim the draw, and online that is normally automatic. With correct technique the mate takes at most 16 moves. Random checks are how half a point gets thrown away: your opponent defends by avoiding the edge and waiting for you to lose the thread.