A wrong rook pawn is a rook pawn whose promotion corner is the color the bishop does not control, so king, bishop and pawn cannot beat a lone king that reaches that corner.
King, bishop and one pawn against a bare king is normally a trivial win, with one giant exception. If the pawn is a rook pawn and the bishop travels on the opposite color from the promotion square, the defender draws by planting the king in the corner. That combination is called the wrong rook pawn, or simply the wrong bishop.
The mechanism is stalemate. The bishop can never cover the corner square, so the defending king shuffles between the corner and the square beside it. Push the pawn to the seventh with the king boxed in and you deliver stalemate, not mate; keep the pawn back and the king simply cannot be evicted. For a white h-pawn you need the dark-squared bishop, for a white a-pawn the light-squared one.
The practical lesson comes before the endgame: check the corner color when you simplify. Defenders a piece down can save games by giving back material to reach the wrong corner, and attackers must avoid cashing in to a position where their extra bishop and pawn are worth half a point.
The one that controls the promotion square. For a white h-pawn that square is h8, a dark square, so you need the dark-squared bishop; for a white a-pawn you need the light-squared bishop. With the right bishop the win is elementary.
Get the king to the promotion corner and stay there, shuffling between the corner and the adjacent square the bishop cannot cover. The attacker can never evict the king without allowing stalemate, so the game is drawn.
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