In the fight of King, Bishop and Knight against the King the mate can be enforced only in a corner controlled by the Bishop, if the lone King always makes the best move.  Diagram 12 may serve as an example of this ending.  White has a black Bishop and so he will have to drive Black’s King to either h8 or a1 as it is not possible to mate him in the white corner a8, unless he makes a blunder.

After (1) B-e5 for instance, Black must of course not go into the corner as Kt-b6 would mate him.  He will play K-c8 and White will have to prevent the flight of the black King into the middle of the board.  It is easy to see, by the way, that the Kt cannot be placed so as to control the square c8, thereby forcing the King into the corner, and to threaten the mate on b6 at the same time.  For he can control c8 only from a black square while he would have to stand on a white square to be able to reach b6 in one move.

After (1) B-e5, K-c8; (2) K-b6, K-d7; (3) Kt-f4 Black’s King is confined to the seventh and eighth ranks and it is only a question of time when he will be forced to h8.

+---------------------------------------+
8 |    | #K |    |    |    |    |    |    |
|---------------------------------------|
7 |    |    |    |    |    |    |    |    |
|---------------------------------------|
6 | ^K |    |    |    |    |    |    |    |
|---------------------------------------|
5 |    |    |    | ^Kt|    |    |    |    |
|---------------------------------------|
4 |    |    |    |    |    |    |    |    |
|---------------------------------------|
3 |    |    | ^B |    |    |    |    |    |
|---------------------------------------|
2 |    |    |    |    |    |    |    |    |
|---------------------------------------|
1 |    |    |    |    |    |    |    |    |
---------------------------------------
a    b    c    d    e    f    g    h

Diagram 12.

White’s Bishop being only capable of commanding black squares the Knight will have to be used to drive the King from white squares.  For instance:  K-c8; (4) K-c6, K-d8; (5) Kt-g6, K-c8; (6) Kt-e7, K-d8; (7) K-d6, K-e8; (8) K-e6, K-d8; (9) B-h2.  A waiting move.  White wants to place the Bishop on c7 so as to make d8 inaccessible to Black. (9) K-e8; (10) B-c7, K-f8; (11) Kt-f5, K-e8; (12) Kt-g7, K-f8; (13) K-f6, K-g8; (14) K-g6, K-f8; (15) B-d6, K-g8; (16) Kt-f5, K-h8; (17)

+---------------------------------------+
8 |    | #K |    |    |    |    |    |    |
|---------------------------------------|
7 |    |    |    |    |    |    |    |    |
|---------------------------------------|
6 |    | ^K |    | ^Kt|    |    |    |    |
|---------------------------------------|
5 |    |    | ^Kt|    |    |    |    |    |
|---------------------------------------|
4 |    |    |    |    |    |    |    |    |
|---------------------------------------|
3 |    |    |    |    |    |    |    |    |
|---------------------------------------|
2 |    |    |    |    |    |    |    |    |
|---------------------------------------|
1 |    |    |    |    |    |    |    |    |
---------------------------------------
a    b    c    d    e    f    g    h

Diagram 13.