Endgames where each side has a king, one or more pawns, and a single minor piece fall into four categories - knight vs knight, bishop vs knight, bishop vs bishop where the bishops are on the same coloured square, and bishop vs bishop where the bishops are on opposite coloured squares. Each has its own character, so we will look at each separately.
In many ways, knight vs knight endgames are similar to pure pawn endgames, as the knight is a fairly slow piece. Usually, the side with an extra pawn will win, just as in pawn endgames, and the technique is much the same - centralise your king and knight, and push your pawns where you have a majority to create a passed pawn. One thing to look out for is opportunities to sacrifice the knight in order to promote a pawn, such as in the following typical example:
Usually, the bishop is the preferred piece in the endgame, because its long range movement allows it to influence events on both sides of the board, whereas it can take the knight several moves to cross from one flank to the other. In general, knights become weaker over the course of the game; as more pieces are exchanged, their ability to jump means less and less, while their slow speed becomes an issue as wide spaces open up on the board. Meanwhile, the bishop increases in strength as more diagonals open up. On an open board, with pawns on both wings, the knight is often unable to keep up with the bishop, as the following example shows.
When both sides have only a bishop, the game can be difficult to win even when you have an extra pawn. This is because it can be difficult or even impossible to budge the enemy king from a square that the bishop cannot attack. Here is an example:
There is even an infamous case where a bishop and pawn against a bare king are not enough to win. If the pawn is a rook pawn, and the queening square of the pawn is of the opposite colour to the bishop's square, then it is actually impossible to force the enemy king out of the corner, as the following example shows:
Bishop endgames aren't always a draw, but they can be difficult to win. The most important thing to do is to make sure you avoid getting your pawns fixed on the same colour as your bishop. Instead, try to fix your opponent's pawns on the same colour as his bishop. As in the middlegame, a bad bishop is a major weakness, but that weakness is greatly magnified when the bishop is your only remaining piece besides the king and pawns. If you can place your pawns on the opposite coloured square to the bishops, that means your opponent will never be able to attack them with his bishop, and if you fix his pawns on the same coloured square as the bishops, your own bishop will be able to attack them and tie the enemy down to defending.
Opposite coloured bishop endgames are notorious for their drawishness. It can be impossible to win, even when you are two pawns up. The problem is that the enemy king and bishop can make a blockade on the opposite coloured square to your bishop, leaving you with no way to break through. Here is an example where even three extra pawns are not enough to win:
In general, if you have extra pawns, you should try to avoid trading down into an opposite coloured bishops endgame. On the other hand, if you're behind on pawns, look out for opportunities to exchange down to opposite coloured bishops, as the opposite coloured bishop endgame is a good place to try and save a draw.
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