What is the wrong-coloured bishop?
A bishop stays on one colour for the whole game. A bishop that starts on a light square only ever stands on light squares.
A rook's pawn is a pawn on the a-file or the h-file. It promotes in a corner: a1, a8, h1 or h8.
Put those two facts together. Suppose your bishop is on the other colour from that corner. It can never guard the corner, and it can never attack a king sitting there.
That is what players mean by the wrong-coloured bishop. With a rook's pawn and nothing else, the game is a draw, however far ahead you look.
Why can the light bishop not force the king out?
Look at the black king's two squares, h8 and g8. The bishop on light squares can attack g8, but it can never attack h8.
So the king simply steps between the two squares. Whenever the bishop covers g8, the king stands on h8 and waits.
White cannot bring more force. There is one bishop, one pawn and one king, and the king cannot take h8 from the black king on its own.
The stalemate that ends every attempt
Pushing the pawn does not help either. It makes matters worse.
After 1.h7 the black king on h8 has nothing at all. The pawn covers g8, the white king covers g7 and guards the pawn, and taking on h7 is not allowed.
Black is not in check and has no legal move. That is stalemate, and stalemate is an immediate draw.
The only way to avoid the stalemate is to move the white king away from the pawn, and then Black takes the pawn. A king and a bishop cannot checkmate a lone king.
The same position with the right bishop wins at once
Now move the bishop from d1 to c1. It is the same piece and almost the same square, but c1 is dark, so this bishop travels on dark squares and can reach h8.
White mates in three moves.
1. 1.Bg5 and the black king has only one square, g8.
2. 2.h7+ and the check drives the king back to h8.
3. 3.Bf6 is checkmate. The bishop checks along the long diagonal, the king covers g7, and the pawn covers g8.
The difference between a draw and a win here is one square of colour.
The question to ask before you trade pieces
Ask one question: does my bishop stand on the same colour as the corner my pawn is heading for?
If the answer is no, that ending is a draw, so do not walk into it. Three things save you.
- Keep a second pawn. With another pawn anywhere on the board the win usually comes back.
- Keep the pawn off the rook's file. A knight's pawn or a bishop's pawn does not promote in a corner, so the defence does not work.
- Get your king to the corner first. If the black king cannot reach h8, White wins even with the wrong bishop.
If you are the defender, run for the corner. The corner and the square next to it are the safe squares.
The mistake we see learners make
Learners count material, see a bishop and a pawn against a bare king, and trade everything down.
Material is not the question here. The question is the colour of one square.
The other half of the mistake belongs to the defender. Many players resign this position or wander away with the king. The corner is the draw, and walking out of it loses at once.