Bishop vs Knight and Pawn: Holding the Long Diagonal

This is the mirror of the knight blockade: a lone bishop against knight, pawn and king. The bishop cannot sit on the stop square the way a knight does; it defends from a distance instead, and distance is exactly where a bishop out-duels a knight.

The crossing square. Pick the square the pawn must cross next and check which diagonals pass through it. Here e7 lies on the a3-f8 road, six squares long, and on the d8-h4 road, five squares long, and it is the SHORTER of the two that settles the evaluation: when both run to five squares or more, as here, the bishop holds with no help at all from its king, patrolling from beyond the reach of king and knight, and the pawn can never take the step. When the short road shrinks to four squares or fewer, the knight and king can hunt the bishop off and the defending king has to be close. The audit is the same one Centurini taught for bishop endings: long diagonal, defensible; short diagonal, doomed. Rook pawns near the rim are the dangerous case for exactly this reason.

Why roadblocks fail. The knight's only idea is to interpose on the diagonal and cut the bishop's view of e7. But a knight standing in the road is just a piece en prise: it cannot protect itself, the pawn does not defend the blocking squares, and the king cannot babysit the knight and escort the pawn at once. The bishop captures the free ones and sidesteps the defended ones, and the road always reopens.

The practical rule: defending a piece down against a passer, put the bishop on the LONGEST diagonal through the pawn's next stop, at maximum distance, and then make the laziest legal moves available. Activity is the attacker's burden here. Every bishop wander off the road, including checks that feel forcing, is the full point walking away.