First with all endings we think about possible simplifications. We note that if we swap B and N, the position is won since we can force the black K to g3 and play the f pawn to f3 and win the h pawn. So lets think about how black can make progress.

1. Sac knight for 2 pawns on h3- this ending is not a win for black as a bishop is too good at setting up a light square blockade, and we have an h pawn.

2. Win the g pawn- this is impossible without white blundering.

3. Play for the pawn break on g4- white can just capture the pawn and with not losing g2, he can then swap 1 more pawn off with the pawn on g2 if black wants to make progress, so this achieves little. Btw it's a general theme in similar endings that the player trying for a win should refrain from swapping his g/b pawn for a/h pawns unless there is a tactical reason, or in some cases when we create a passed pawn.

So this only leaves the final option- playing the f pawn to f3.

The plan:

We play Kf4 next move, then manoeuvre the N to e4 and force Ke3. Then if white turtles still we play Ke2-e1 and play Ng3-e2 and force the black K onto f2. We have to be careful of some g3 hxg3 Kg2 moves, and can stop this at any time with f7-f5-f4. If white plays K to f1 it remains to be seen if we have a winning continuation.

Once we get our K to f2 we can force it onto g3, and play the aforementioned plan of f7-f3, gxf3 Nxf3, then winning the h pawn and the game.

The actual key line (from a game):

1...Kf4 2.Kf2 Nf5 3.Bb7 Nd6 4.Bd5 Ne4+ 5.Kg1 f6 6.Bc6 Ke3 7.Be8 g5 8.Kf1! (white's most resilient try)



8...Kf4 9.Bc6 Nc5 10.Kf2 Nd3+ 11.Ke2 Ne5! 12.Bb7 Kg3 and the rest should follow.

Note that if white kept his bishop on the a8-h1 diagonal (specifically a8), black would have been able to waste a tempo with a pawn move on the K side to force the B onto b7 c6 or d5 to carry out his double attack of the B and the ...Kg3 threat.

So the endgame rests on a knife's edge. Had black's pawns been too far advanced the position could well be a draw.

what can we learn from this? It's very important to not set pawns to be the same colour of your bishop in B vs N endings, and also just how bad a/h pawns are in endings (if you didn't know already) both for the attacking side and the side playing for a draw.

In same side pawns (with 1 extra pawn) as the attacking side, we should therefore try to go for the h pawn break if possible to create weaknesses, and if not, we play for the pawn break on the other side of the pawn chain.

A very important defensive "formation" in rook and pawn endings is the following:



Because it's a rook ending, white doesn't have any meaningful light-squared weakness. This formation makes it very hard for black to make progress. He really wants to push the h pawn forward himself, but now can only go for the e3 break. Although this ending is very different to a minor piece one, the pawn structure theme is the same.

B+3p vs R+2P:

Obviously there are 2 scenarios, but in both cases the B side only actually requires 2 pawns to draw and not 3 (knight and 2 pawns however is usually lost against R and 2 pawns).



Note the familiar trend with the h pawn forwards! The key here is that black cannot keep his K on g4 (be careful where you place the bishop- it needs to give check once black has K on g4).

For the other coloured bishop we have:



Here black finds it even harder to make progress. Even after h7-h4 and swapping pawns, white will then keep his K on h2 and move the B on the a7-g1 diagonal for days (note that the ending against the lone h pawn without f2 pawn is still a draw, as long as black's h pawn is advanced too far at h4).

Now for the more difficult N fortress:



This position (or with the pawn back on h4) is a slightly different take on the usual advanced h pawn defensive formation. Although not as aesthetically pleasing as the bishop fortresses, white can hold an easy draw. The only way for black to make progress is to get his K to f1 (note he can't keep it on e2 since white will check him away with his N), but by then white can move his pieces forward and force trade of pawns for an easy draw.

If white tries to set up on f2, g3, h4, it's possible that black can advance his pawn to g4 and trap either trap the N on g1, or force an exchange sac for the N and f pawn into a winning ending.