Bishop vs Knight and Pawn: The One Drawing Move

Watch the method: press play to see the winning idea run, or step through it move by move.

A bishop can hold a passed pawn on its own, even with its king out of play. What it needs is a square that the knight cannot attack.

Guard the crossing square, not the queening square. The bishop is light-squared and d8 is dark, so the promotion square is out of reach forever. The pawn is stopped on d7 instead.

Only Be8 works. The knight on e5 covers both c6 and d7, so the natural blockading and guarding squares simply hang the bishop: Bd7 Nxd7, Bc6 Nxc6. From e8 the bishop watches d7 from safety.

The rule behind the trick. Why can a lone bishop hold at all? It is arithmetic. King and knight together can screen only four squares of a stopping diagonal, two each. A five-square diagonal always leaves one square free, so as long as the pawn has not reached the seventh rank the bishop needs no help from its king. Shorten the diagonal to four squares and the attacker can screen the whole of it: now the defending king must be near, or the bishop is driven off. Below four squares the knight's chances grow further still, though a king close by can still save the bishop, as the rook pawn corner draw shows.

Change diagonals under pressure. When the white king evicts the bishop from e8, it reroutes with Bg6-f5-c8 and keeps d7 covered from the other side. The attacker never makes progress.

The safety net. The bishop can always be given for the pawn: king and knight against a bare king cannot mate. In this drill, hold the square and the half point is yours.