Rook against bishop: the corner decides

The key idea

Rook against bishop is a draw if the defending king goes to the corner of the OPPOSITE colour to his bishop. In the corner of the same colour as his bishop there's forced mate. Before steering your king to a corner, check what colour the square is and what colour your bishop is.

Example 1 · The right corner: there's no way in

Black's bishop is dark-squared and his king is on a8, which is light. Correct corner — and that alone is enough to draw.

1. Rg1 White manoeuvres looking for a way in. Before defending, do the colour count: my bishop is dark-squared and my king is on a8, which is light. That's the correct corner, and that's why this position is saved before it starts.
2. Bh6 The bishop takes a diagonal from which it watches the entry squares. Notice how little I have to calculate: as long as the king doesn't leave a8 and b8, mate doesn't exist.
3. Rb1 The rook tries the other file.
4. Ka7 The king moves inside its shelter. Here's the key to why it's a draw: to mate on a8 that square would have to be the colour of my bishop, and it isn't — my bishop can never be forced off, or forced to cover, the squares that matter.
5. Rf1 White keeps trying, and has nothing.
6. Kb7 And back again. A clean draw a rook down. Keep the rule, which is the only thing to know: king to the corner of the OPPOSITE colour to your bishop, and the endgame more or less defends itself.

Example 2 · The wrong corner: mate in five

The same material, the same dark-squared bishop… and the king on h8, which is also dark. Now White is teaching.

1. Kf7 The same material as in the previous example, the same bishop, the opposite result: here there's forced mate. The only thing that has changed is the colour of the corner — h8 is dark, like the black bishop, and that condemns it. My king comes closer to take squares away.
2. Kh7 The black king moves where it can, which isn't far.
3. Rh1+ Check along the corner file. The bishop will have to interpose, because the king has no free squares left.
4. Bh6 And there's the problem with the wrong corner: the bishop is forced to block on a square of ITS OWN colour, right in front of its king, where the rook can take it or the king runs out of squares. In the right corner this forced interposition doesn't exist.
5. Rh5 The rook takes up position to finish. No rush, and without allowing stalemate, which is the defender's only remaining resource.
6. Kh8 The king returns to the corner and mate arrives a couple of moves later. Keep the whole contrast: same pieces, same technique, and the result changes purely because of the colour of the corner. When you have to defend this endgame, your first decision — which corner you run to — is worth more than the next twenty.

Practice

The black king has sheltered on h8 and his bishop is dark-squared: the same colour as the corner. That's the wrong corner. Make it count.

1. King first, to take squares away. With the corner the colour of his bishop, mate genuinely exists. Bring your king closer to take escape squares from the black king.
2. Check along the corner file, and the bishop is forced to block on a square of its own colour. Check with the rook along the file his king lives on.
3. And the rook takes up position to finish, without allowing stalemate. Mate arrives in a couple of moves. Place the rook on the h-file to prepare mate, taking care not to stalemate him.

Rook against bishop is decided before it starts, which is why this lesson works for both sides: if you're defending, look at your bishop's colour and run to the OPPOSITE corner — no technique beats you there. If you're attacking, check whether your opponent has picked the wrong corner, because that's the only way this endgame gives you the full point.