The ‘wrong bishop’ is a rook’s pawn together with a bishop that does not control the pawn’s queening square, a famous case where bishop-and-pawn versus king is only a draw.
Bishop and pawn against a lone king normally wins easily. The exception is a rook’s pawn (a- or h-file) whose promotion square is the opposite colour to the bishop. The bishop can never cover that corner.
If the defending king reaches the corner in front of the pawn, it can never be driven out: the bishop can’t attack it there, and any attempt to push the pawn either stalemates the king or lets it shuffle in the corner. The result is a draw despite the extra piece.
Knowing this saves and steals half-points. If you’re defending down a bishop and a rook-pawn, race your king to that corner. If you’re winning, check the bishop’s colour before trading into such an ending.
Because it’s the wrong colour for the job. The pawn promotes on a corner square, and the bishop only covers one colour. If that corner is the colour the bishop can’t touch, the bishop is useless for evicting the king.
Yes. With any other pawn the bishop can help shoulder the king away and the side with the extra piece wins. The drawing trick relies on the corner being a safe haven, which only a rook-pawn provides.
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