Count the Diagonal, Then Block It

Bishop against knight and pawn usually holds, and the reason is always the same: the bishop controls the square in front of the pawn from a distance. Take that diagonal away and the ending collapses.

Count the diagonal. Black's bishop guards c7 from a5, along a5, b6, c7, d8. Four squares. A diagonal that short can be blocked by a single piece, and Nb6 does exactly that.

The push is an only-move. After Nb6 there is exactly one winning move, c7, and every alternative draws. Play it a move too early and Bxc7 ends the game; play it a move too late and the bishop swings around to the b8-h2 diagonal.

The colour of c8. The promotion square is light and the defending bishop is dark-squared. It could never fight for c8, only for c7. That is why one knight move settles the position.

The companion draws. Our position "Only Be8 Stops the Pawn" is the same material with the bishop able to reach a long diagonal in time. There it holds. Counting the diagonal is what tells the two apart.