Example 22
A unit that holds two
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Chapter 2 of 5
Further Principles in End-Game Play
A unit that holds two, a classical King and Pawn ending, passed Pawns and counting, the opposition, Knight against Bishop, the mate with Knight and Bishop, and Queen against Rook.
Every example is on its own board: click a move or use the arrows, and the notes appear beside the board. The number under the board is Stockfish's evaluation for White (minus means Black is better), or the exact result when few enough pieces are left.
We shall now go back to the endings in search of a few more principles, then again to the middle-game, and finally to the openings once more, so that the advance may not only be gradual but homogeneous. In this way the foundation on which we expect to build the structure will be firm and solid.
9. A cardinal principle
In the position below, White can draw by playing b4 according to the general rule that governs such cases, i.e. to advance the Pawn that is free from opposition. But suppose that White, either because he does not know this principle or because he does not, in this case, sufficiently appreciate the value of its application; suppose, we say, that he plays 1.a4. Then Black can win by playing 1…a5, applying one of the cardinal principles of the high strategy of chess: a unit that holds two.
In this case one Pawn would hold two of the opponent's Pawns. The student cannot lay too much stress on this principle. It can be applied in many ways, and it constitutes one of the principal weapons in the hands of a master.
Example 22. The example given should be sufficient proof. We give a few moves of the main variation:
7210. A classical ending
Example 23. In this position White's best line of defence consists in keeping his Pawn where it stands at h2. As soon as the Pawn is advanced it becomes easier for Black to win. On the other hand, Black's plan to win (supposing that White does not advance his Pawn) may be divided into three parts. The first part will be to get his King to h3, at the same time keeping intact the position of his Pawns. (This is all important, since, in order to win the game, it is essential at the end that Black may be able to advance his rearmost Pawn one or two squares according to the position of the White King.)
Example 23
The classical ending, in three parts
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The next subject we shall study is the simple opposition, but before we devote our time to it I wish to call attention to two things.
11. Obtaining a passed Pawn
When three or more Pawns are opposed to each other in some such position as the one in Example 24, there is always a chance for one side or the other of obtaining a passed Pawn.
Example 24. In this position the way of obtaining a passed Pawn is to advance the centre Pawn.
Example 24
Obtaining a passed Pawn
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Now if it had been Black's move Black could play:
Example 24
With Black to move
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12. How to find out which Pawn will be first to Queen
When two Pawns are free, or will be free, to advance to Queen, you can find out, by counting, which Pawn will be the first to succeed.
Example 25. In this position whoever moves first wins.
Example 25
Counting the race
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The first thing is to find out, by counting, whether the opposing King can be in time to stop the passed Pawn from Queening. When, as in this case, it cannot be done, the point is to count which Pawn comes in first. In this case the time is the same, but the Pawn that reaches the eighth square first and becomes a Queen is in a position to capture the adversary's Queen when he makes one.
Once again I must call attention to the fact that a book cannot by itself teach how to play. It can only serve as a guide, and the rest must be learned by experience, and if a teacher can be had at the same time, so much the faster will the student be able to learn.
13. The opposition
When Kings have to be moved, and one player can, by force, bring his King into a position similar to the one shown in the following diagram, so that his adversary is forced to move and make way for him, the player obtaining that advantage is said to have the opposition.
Example 26. Suppose in this position White plays 1.Kd4.
Example 26
The opposition
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The opposition can take the form shown above, which can be called actual or close frontal opposition; or this form, which can be called actual or close diagonal opposition:
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or, again, this form, which can be called actual or close lateral opposition:
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In practice they are all one and the same. The Kings are always on squares of the same colour, there is only one intervening square between the Kings, and the player who has moved last "has the opposition."
Now, if the student will take the trouble of moving each King backwards as in a game in the same frontal, diagonal or lateral line respectively shown in the diagrams, we shall have what may be called distant frontal, diagonal and lateral opposition respectively.
The matter of the opposition is highly important, and takes at times somewhat complicated forms, all of which can be solved mathematically; but, for the present, the student should only consider the most simple forms. (An examination of some of the examples of King and Pawns endings already given will show several cases of close opposition.)
In all simple forms of opposition, when the Kings are on the same line and the number of intervening squares between them is even, the player who has the move has the opposition.
Example 27. This position shows to advantage the enormous value of the opposition. The position is very simple. Very little is left on the board, and the position, to a beginner, probably looks absolutely even. It is not the case, however. Whoever has the move wins. Notice that the Kings are directly in front of one another, and that the number of intervening squares is even.
Now as to the procedure to win such a position. The proper way to begin is to move straight up. Thus:
Example 27
The value of the opposition
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Step through the moves with the arrows, or click a move.
Example 28. The following position is an excellent proof of the value of the opposition as a means of defence. White is a Pawn behind and apparently lost, yet he can manage to draw as follows:
Example 28
The opposition in defence
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Step through the moves with the arrows, or click a move.
If the student will now take the trouble to go back to the examples of King and Pawns which I have given in this book, he will realise that in all of them the matter of the opposition is of paramount importance; as, in fact, it is in nearly all endings of King and Pawns, except in such cases where the Pawn-position in itself ensures the win.
14. The relative value of Knight and Bishop
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.
Example 29. In this position White cannot win, although the Black King is cornered:
Example 29
Two Knights cannot mate
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A position to study: explore it from here, or switch on the live engine.
But in the following position, in which Black has a Pawn, White wins with or without the move. Thus:
Example 29
With a Black Pawn, they can
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Step through the moves with the arrows, or click a move.
Example 30. Although he is a Bishop and a Pawn ahead the following position cannot be won by White.
Example 30
The Bishop of the wrong colour
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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.
Example 31. In this position White with or without the move can win. Take the most difficult variation.
Example 31
Knight against two Pawns
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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.
Example 32.
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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.
Example 33. This is about the only case when the Knight is more valuable than the Bishop.
Example 33
A block position
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Editor's note: Stockfish sees no way through for Black here and rates the position as level, with either side to move.
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.
Example 34. 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.
Example 34
Pawns on one side
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A position to study: explore it from here, or switch on the live engine.
Example 35. Now let us add three Pawns on each side to the above position, so that there are Pawns on both sides of the board.
Example 35
Pawns on both sides
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A position to study: explore it from here, or switch on the live engine.
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.
Example 36
Unbalanced Pawns
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A position to study: explore it from here, or switch on the live engine.
Example 36. In the above 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.
Example 37. 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 (the h-pawn for White, the a-pawn for Black). Black should have extreme difficulty in drawing this position, if he can do it at all.
Example 37
Passed Pawns
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Editor's note: Stockfish rates this position as level.
Example 38. Again Black would have great difficulty in drawing this position.
Example 38
The Bishop's advantage
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Editor's note: Stockfish rates this position only slightly better for White, by about a tenth of a Pawn.
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.
15. How to mate with a Knight and a Bishop
Now, before going back again to the middle-game and the openings, let us see how to mate with Knight and Bishop, and, then, how to win with a Queen against a Rook.
With a Knight and a Bishop the mate can only be given in the corners of the same colour as the Bishop.
Example 39. In this example we must mate either at a1 or h8. The ending can be divided into two parts. Part one consists in driving the Black King to the last line. We might begin, as is generally done in all such cases, by advancing the King to the centre of the board:
Example 39
The mate with Knight and Bishop
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Step through the moves with the arrows, or click a move.
16. Queen against Rook
This is one of the most difficult endings without Pawns. The resources of the defence are many, and when used skilfully only a very good player will prevail within the limit of fifty moves allowed by the rules. (The rule is that at any moment you may demand that your opponent mate you within fifty moves. However, every time a piece is exchanged or a Pawn advanced the counting must begin afresh.)
Example 40. This is one of the standard positions which Black can often bring about. Now, it is White's move. If it were Black's move it would be simple, as he would have to move his Rook away from the King (find out why), and then the Rook would be comparatively easy to win. We deduce from the above that the main object is to force the Black Rook away from the defending King, and that, in order to compel Black to do so, we must bring about the position in the diagram with Black to move. Once we know what is required, the way to proceed becomes easier to find. Thus:
Example 40
Queen against Rook
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Step through the moves with the arrows, or click a move.
Example 41. The procedure here is very similar. The things to bear in mind are that the Rook must be prevented from interposing at b8 because of an immediate mate, and in the same way the King must be prevented from going either to a6 or c8.
Example 41
Queen against Rook, again
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A position to study: explore it from here, or switch on the live engine.
Example 42. We shall now examine a more difficult position. Many players would be deceived by this position. The most likely looking move is not the best.
Example 42
A more difficult position
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Step through the moves with the arrows, or click a move.
Other moves here
Note, in these examples, that the checks at long range along the diagonals have often been the key to all the winning manoeuvres. Also that the Queen and King are often kept on different lines. The student should carefully go over these positions and consider all the possibilities not given in the text.
He should once more go through everything already written before proceeding further with the book.