CHAPTER II
FURTHER PRINCIPLES IN END-GAME PLAY
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 shown above, White can draw by playing P - Kt 4 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 {36} does not, in this case, sufficiently appreciate the value of its application; suppose, we say, that he plays 1 P - Q R 4. Then Black can win by playing 1... P - Q R 4, 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:--
1. P - R 4 P - Q R 4 2. K - Kt 2 K - B 5 (Best; see why.) 3. P - Kt 4 P x P (Best.) 4. P - R 5 P - Kt 6 5. P - R 6 P - Kt 7 6. P - R 7 P - Kt 8 (Q) 7. P - R 8 (Q) Q - K 5 ch 8. Q x Q K x Q
This brings the game to a position which is won by Black, and which constitutes one of the classical endings of King and Pawns. I shall try to explain the guiding idea of it to those not familiar with it. {37}
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10. A CLASSICAL ENDING
EXAMPLE 23.--In this position White's best line of defence consists in keeping his Pawn where it stands at R 2. 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 K R 6, 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.)
1. K - Kt 3 K - K 6 2. K - Kt 2
If 2 K - Kt 4, K - B 7; 3 P - R 4, P - Kt 3 will win. {38}
2. ........ K - B 5 3. K - B 2 K - Kt 5 4. K - Kt 2 K - R 5 5. K - Kt 1 K - R 6
The first part has been completed.
The second part will be short and will consist in advancing the R P up the K.
6. K - R 1 P - R 4 7. K - Kt 1 P - R 5
This ends the second part.
EXAMPLE 24.--In the above position the way of obtaining a passed Pawn is to advance the centre Pawn.
1. P - Kt 6 R P x P If B P x P; P - R 6, 2. P - B 6 P x B P 3. P - R 6
and as in this case the White Pawn is nearer to Queen than any of the Black Pawns, White will {41} win. Now if it had been Black's move Black could play
1. ........ P - Kt 3 2. B P x P B P x P
It would not be advisable to try to obtain a passed Pawn because the White Pawns would be nearer to Queen than the single Black Pawn.
3. P x P P x P
and the game properly played would be a draw. The student should work this out for himself.
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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 26.--Suppose in the above position White plays
1. K - Q 4
Now Black has the option of either opposing the passage of the White King by playing K - Q 3 or, if he prefers, he can _pass_ with his own King by replying K - B 4. Notice that the Kings are directly opposed to each other, and the number of intervening squares between them is odd--one in this case.
The opposition can take the form shown above, {44} which can be called actual or close frontal opposition; or this form:
which can be called actual or close diagonal opposition, or, again, this form:
which can be called actual or close lateral opposition.
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_." {45}
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.--The above position shows to advantage the enormous value of the opposition. The {46} 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:
1. K - K 2 K - K 2 2. K - K 3 K - K 3 3. K - K 4 K - B 3
Now White can exercise the option of either playing K - Q 5 and thus passing with his King, or of playing K - B 4 and prevent the Black King from passing, thereby keeping the opposition. Mere counting will show that the former course will only lead to a draw, therefore White takes the latter course and plays:
4. K - B 4 K - Kt 3
If 4...K - K 3; 5 K - Kt 5 will win.
5. K - K 5 K - Kt 2
Now by counting it will be seen that White wins by capturing Black's Knight Pawn.
The process has been comparatively simple in the variation given above, but Black has other lines of {47} defence more difficult to overcome. Let us begin anew.
1. K - K 2 K - Q 1
Now if 2 K - Q 3, K - Q 2, or if 2 K - K 3, K - K 2, and Black obtains the opposition in both cases. (When the Kings are directly in front of one another, and the number of intervening squares between the Kings is _odd_, the player who has moved last has the opposition.)
Now in order to win, the White King must advance. There is only one other square where he can go, B 3, and that is the right place. Therefore it is seen that in such cases when the opponent makes a so-called waiting move, you must advance, leaving a rank or file free between the Kings. Therefore we have--
2. K - B 3 K - K 2
Now, it would be bad to advance, because then Black, by bringing up his King in front of your King, would obtain the opposition. It is White's turn to play a similar move to Black's first move, viz.:
3. K - K 3
which brings the position back to the first variation shown. The student would do well to familiarise himself with the handling of the King in all examples of opposition. It often means the winning or losing of a game.
{48} 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:
1. K - R 1 !
The position of the Pawns does not permit White to draw by means of the actual or close opposition, hence he takes the distant opposition: in effect if 1 K - B 1 (actual or close opposition), K - Q 7; 2 K - B 2, K - Q 6 and White cannot continue to keep the lateral opposition essential to his safety, because of his own Pawn at B 3. On the other hand, after the text move, if
1. ........ K - Q 7 2. K - R 2 K - Q 6 3. K - R 3 ! K - K 7 {49} 4. K - Kt 2 K - K 6 5. K - Kt 3 K - Q 5 6. K - Kt 4
attacking the Pawn and forcing Black to play 6... K - K 6 when he can go back to Kt 3 as already shown, and always keep the opposition.
Going back to the original position, if
1. K - R 1 P - Kt 5
White does not play P x P, because P - K 5 will win, but plays:
2. K - Kt 2 K - Q 7
If 2...P x P ch; 3 K x P, followed by K - K 4, will draw.
3. P x P P - K 5
and mere counting will show that both sides Queen, drawing the game.
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,[3] 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.
{50}
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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 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:
1. Kt - Kt 6 P - R 5
{51} White cannot take the Pawn because the game will be drawn, as explained before.
2. Kt - K 5 P - R 6 3. Kt - B 6 P - R 7 4. Kt - Kt 5 P - R 8 (Q) 5. Kt - B 7 mate
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._
EXAMPLE 30.--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. {52}
EXAMPLE 31.--In the above position White with or without the move can win. Take the most difficult variation.
1. ........ K - R 7 2. Kt - Kt 4 ch K - R 8 3. K - B 1 P - Kt 4 4. K - B 2 P - R 7 5. Kt - K 3 P - Kt 5 6. Kt - B 1 P - Kt 6 ch 7. Kt x P mate
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, {53} 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.
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. {54}
EXAMPLE 33.--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 {55} 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.
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 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 (K R P for White, Q R P for Black). Black should have extreme difficulty in drawing this position, if he can do it at all. {58}
EXAMPLE 38.--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. {59}
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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 Q R 1 or K R 8. 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:
1. K - K 2 K - Q 2
Black, in order to make it more difficult, goes towards the white-squared corner:
2. K - Q 3 K - B 3 3. B - B 4 K - Q 4 {60} 4. Kt - K 2 K - B 4 5. Kt - B 3 K - Kt 5 6. K - Q 4 K - R 4 7. K - B 5 K - R 3 8. K - B 6 K - R 2 9. Kt - Q 5 K - R 1
The first part is now over; the Black King is in the white-squared corner.
The second and last part will consist in driving the Black King now from Q R 8 to Q R 1 or K R 8 in order to mate him. Q R 1 will be the quickest in this position.
10. Kt - Kt 6 ch K - R 2 11. B - B 7 K - R 3 12. B - Kt 8 K - R 4 13. Kt - Q 5 K - R 5
Black tries to make for K R 1 with his King. White has two ways to prevent that, one by 14 B - K 5, {61} K - Kt 6; 15 Kt - K 3, and the other which I give as the text, and which I consider better for the student to learn, because it is more methodical and more in accord with the spirit of all these endings, _by using the King as much as possible_.
14. K - B 5 ! K - Kt 6 15. Kt - Kt 4 K - B 6 16. B - B 4 K - Kt 6 17. B - K 5 K - R 5 18. K - B 4 K - R 4 19. B - B 7 ch K - R 5 20. Kt - Q 3 K - R 6 21. B - Kt 6 K - R 5 22. Kt - Kt 2 ch K - R 6 23. K - B 3 K - R 7 24. K - B 2 K - R 6 25. B - B 5 ch K - R 7 26. Kt - Q 3 K - R 8 27. B - Kt 4 K - R 7 28. Kt - B 1 ch K - R 8 29. B - B 3 mate
It will be seen that the ending is rather laborious. There are two outstanding features: the close following by the King, and the controlling of the squares of opposite colour to the Bishop by the combined action of the Knight and King. The student would do well to exercise himself methodically in this ending, as it gives a very good idea of the actual power of the pieces, and it requires foresight in order to accomplish the {62} mate within the fifty moves which are granted by the rules.
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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 {63} 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:
1. Q - K 5 ch
Not 1 Q - R 6, because R - B 2 ch; 2 K - Kt 6, R - B 3 ch; 3 K x R. Stalemate. (The beginner will invariably fall into this trap.)
1. ........ K to R 1 or to R 2 2. Q - R 1 ch K - Kt 1 3. Q - R 5
In a few moves we have accomplished our object. The first part is concluded. Now we come to the second part. The Rook can only go to a White square, otherwise the first check with the Queen will win it. Therefore
3. ........ R - Kt 6 4. Q - K 5 ch K - R 1 best 5. Q - R 8 ch K - R 2 6. Q - Kt 7 ch K - R 1 7. Q - Kt 8 ch R - Kt 1 8. Q - R 2 mate
(The student should find out by himself how to win when 3...R - Kt 8; 4 Q - K 5 ch, K - R 2.) {64}
EXAMPLE 41.--The procedure here is very similar. The things to bear in mind are that the Rook must be prevented from interposing at Kt 1 because of an immediate mate, and in the same way the King must be prevented from going either to R 3 or B 1.
EXAMPLE 42.--We shall now examine a more difficult position.