Before turning our attention to this matter it is well to state now that two Knights alone cannot mate, but, under certain conditions of course, they can do so if the opponent has one or more Pawns.
In the above position White cannot win, although the Black King is cornered, but in the following position, in which Black has a Pawn, White wins with or without the move. Thus:
The reason for this peculiarity in chess is evident. White with the two Knights can only stalemate the King, unless Black has a Pawn which can be moved.
Although he is a Bishop and a Pawn ahead the following position cannot be won by White.
It is the greatest weakness of the Bishop, that when the Rook's Pawn Queens on a square of opposite colour and the opposing King is in front of the Pawn, the Bishop is absolutely worthless. All that Black has to do is to keep moving his King close to the corner square.
In the following position White with or without the move can win. Take the most difficult variation.
Now that we have seen these exceptional cases, we can analyse the different merits and the relative value of the Knight and the Bishop.
It is generally thought by amateurs that the Knight is the more valuable piece of the two, the chief reason being that, unlike the Bishop, the Knight can command both Black and White squares. However, the fact is generally overlooked that the Knight, at any one time, has the choice of one colour only. It takes much longer to bring a Knight from one wing to the other. Also, as shown in the following Example, a Bishop can stalemate a Knight; a compliment which the Knight is unable to return.
The weaker the player the more terrible the Knight is to him, but as a player increases in strength the value of the Bishop becomes more evident to him, and of course there is, or should be, a corresponding decrease in his estimation of the value of the Knight as compared to the Bishop. In this respect, as in many others, the masters of to-day are far ahead of the masters of former generations. While not so long ago some of the very best amongst them, like Pillsbury and Tchigorin, preferred Knights to Bishops, there is hardly a master of to-day who would not completely agree with the statements made above.
This is about the only case when the Knight is more valuable than the Bishop.
It is what is called a "block position", and all the Pawns are on one side of the board. (If there were Pawns on both sides of the board there would be no advantage in having a Knight.) In such a position Black has excellent chances of winning. Of course, there is an extra source of weakness for White in having his Pawns on the same colour-squares as his Bishop. This is a mistake often made by players. The proper way, generally, in an ending, is to have your Pawns on squares of opposite colour to that of your own Bishop. When you have your Pawns on squares of the same colour the action of your own Bishop is limited by them, and consequently the value of the Bishop is diminished, since the value of a piece can often be measured by the number of squares it commands. While on this subject, I shall also call attention to the fact that it is generally preferable to keep your Pawns on squares of the same colour as that of the opposing Bishop, particularly if they are passed Pawns supported by the King. The principles might be stated thus:
When the opponent has a Bishop, keep your Pawns on squares of the same colour as your opponent's Bishop.
Whenever you have a Bishop, whether the opponent has also one or not, keep your Pawns on squares of the opposite colour to that of your own Bishop.
Naturally, these principles have sometimes to be modified to suit the exigencies of the position.
In the following position the Pawns are on one side of the board, and there is no advantage in having either a Knight or a Bishop. The game should surely end in a draw.
Now let us add three Pawns on each side to the above position, so that there are Pawns on both sides of the board.
It is now preferable to have the Bishop, though the position, if properly played out, should end in a draw. The advantage of having the Bishop lies as much in its ability to command, at long range, both sides of the board from a central position as in its ability to move quickly from one side of the board to the other.
In the following position it is unquestionably an advantage to have the Bishop, because, although each player has the same number of Pawns, they are not balanced on each side of the board. Thus, on the King's side, White has three to two, while on the Queen's side it is Black that has three to two. Still, with proper play, the game should end in a draw, though White has somewhat better chances.
Here is a position in which to have the Bishop is a decided advantage, since not only are there Pawns on both sides of the board, but there is a passed Pawn ("h" for White, "a" for Black). Black should have extreme difficulty in drawing this position, if he can do it at all.
Again Black would have great difficulty in drawing this position.
The student should carefully consider these positions. I hope that the many examples will help him to understand, in their true value, the relative merits of the Knight and Bishop. As to the general method of procedure, a teacher, or practical experience, will be best. I might say generally, however, that the proper course in these endings, as in all similar endings, is: Advance of the King to the centre of the board or towards the passed Pawns, or Pawns that are susceptible of being attacked, and rapid advance of the passed Pawn or Pawns as far as is consistent with their safety.
To give a fixed line of play would be folly. Each ending is different, and requires different handling, according to what the adversary proposes to do. Calculation by visualising the future positions is what will count.