Black White (1) ... 20-24 (2) 11-15 24-27

12-8 would be of no use as 19-23 would force 8-12 again.

(3) 15-11

If 15-18 White wins by 27-31

(3) ... 27-32

27-31 would admit of a draw by (4) 19-23, 28-24; (5) 23-27, 24- 20; (6) 27-23, 12-16; (7) 11-15, etc.

(4) 11-15 12-8 (5) 15-18 32-27 (6) 18-15 27-31 (7) 15-18 8-11 (8) 18-23 11-7 (9) 19-15

This is better than allowing the Kings to get together.

(9) ... 28-24 (10) 23-27 24-20 (11) 27-23 7-2 (12) 15-11 2-6 (13) 23-19 6-10

If he moved the other King, Black would draw by 19-16.

(14) 19-23 10-14 (15) 23-19

Black would lose easily if he allowed the man to advance

(15) ... 14-18

Threatening to exchange

(16) 19-24

The only move to avoid the exchange.

(16) ... 18-23 (17) 24-28 23-19 (18) 28-32 31-26 (19) 32-28 26-23 (20) 28-32 23-18 (21) 32-28 19-15 (22) 11-8 20-16

and White cannot be prevented from getting another King.

An earlier setting of third position is shown in Diagram 100.

32 31 30 - o o 29 - 28 * * - * 21 - 20 oo - 13 - 12 - 5 - 4 - 3 2 1

DIAGRAM 100.

White wins by

(1) ... 19-24 (2) 27-31 32-28 (3) 23-27 30-23 (4) 27-32 23-18 (5) 32-27 24-20 (6) 27-23 19-15, etc.

THE FOURTH POSITION

Although White is a piece ahead he has great difficulties in winning on account of the weak position of the man on 12. Black's man on 3 holds

32 31 30 - 29 - 28 - 21 - 20 - oo 13 - 12 o oo oo - 5 - 4 * ** ** - 3 2 1

DIAGRAM 101.—White to Move and Win.

him in check without being impaired in his effectiveness towards the center of the board. If Black had the move, White could not win at all, as he would be unable to dislodge Black's Kings. As it is, he wins by means of a sacrifice which often occurs in endings with 4 Kings against 3.

Black White

(1) ... 14-9 (2) 1-5 9-13 (3) 5-1 11-15 (4) 2-6 10-14 (5) 1-5 15-18 (6) 5-1

32 31 30 - 29 - 28 - 21 - 20 oo - oo oo 13 - 12 o - ** 5 - 4 * ** - 3 2 1

DIAGRAM 102.

It would not help Black to play 6-2 on account of 13-9; (7) 5-1, 9-5; (8) 2-6, 14-17; (9) 6-2, 17-13; (10) 2-6, 18-15; (11) 6-2, 15-10, etc.

(6) ... 14-9 (7) 6-2 9-5 (8) 2-6 18-15 (9) 6-2 15-10

This is the important move, which forces the win.

(10) 2-6

If 2-7, White exchanges by 13-9

(10) ... 10-7

Only with this pretty sacrifice can White win the game. After (11) 3-10 White plays 5-9 and should Black answer (12) 6-2, White would get "two for one" by 9-6. Therefore, Black can do no better than play (12) 10-15, 9-2; (13) 15-19, etc., and get a King in each double corner. White then wins as explained in the chapter on elementary endings.

Fourth position results in a draw only when the man is held on 12 or 21, according to whether the weaker side is Black or White. In third position it is useless to hold the man on the above squares, but sometimes a draw is obtained by holding him on 20 or 13.

In defending a game with two Kings against two Kings and a man, the weaker side must have the move in the system in which the man is pinned. The following position for instance is drawn with White on the move.

32 31 30 - 29 - 28 oo - oo 21 - 20 - ** * 13 - 12 - 5 - 4 ** - 3 2 1

DIAGRAM 103.

Black, on the move, would win by (1) 13-17, 22-13; (2) 14-9.

In Diagram 104 the drawing move is 27-31. The game ought to run like this:

(2) 20-24 23-27 (3) 24-28 27-32 (4) 30-26 31-27 (5) 22-18 27-24

32 31 30 - ** 29 - 28 oo - oo ** 21 - 20 * - 13 - 12 - 5 - 4 - 3 2 1

DIAGRAM 104.—WHITE TO MOVE.

(6) 26-23 24-20

and White moves back and forth between 24 and 20. In the position of Diagram 105 White draws by:

(1) ... 23-19 (2) 28-32 19-24 (3) 7-2 24-19 (4) 2-6 19-24 (5) 6-9 24-19 (6) 9-14 19-24 (7) 14-17 15-19

32 31 30 - 29 - 28 ** - oo 21 - 20 - oo 13 - 12 * - ** 5 - 4 - 3 2 1

DIAGRAM 105.—WHITE TO MOVE.

Changing the guard

(8) 17-22 19-23

and Black can make no progress.

THE FIFTH POSITION

White is on the move, and it is evident that he loses if he moves the man on 27 permitting black to reply 11-15. The only way to save the game is to sacrifice the man on 20 by 20-16. The following play would ensue.

32 31 30 - 29 - 28 o - o o 21 - 20 o o - * * 13 - 12 * * * - 5 - 4 - 3 2 1

DIAGRAM 106.

(2) 11-2O 27-23 (3) 20-24 22-18 (4) 24-27 18-9 (5) 10-14

Preventing 23-18

(5) ... 9-6 (6) 27-31 6-2K (7) 31-27 2-6

White cannot save the piece and so he runs his opponent.

(8) 27-18 6-9 (9) 13-17 19-15 (10) 18-11 9-18 (11) 17-22 18-25 (12) 11-15 25-22

Drawn. White would lose by 21-17, as after (13) 15-18, 17-13; (14) 18-14, 25-22; (15) 12-16 he cannot gain the double corner.

The following has been suggested as a suitable problem to be called SIXTH POSITION.

32 31 30 - 29 - 28 - oo 21 - 20 - o ** 13 - 12 o - ** 5 - 4 * - 3 2 1

DIAGRAM 107.—BLACK TO MOVE AND WHITE TO DRAW.

Black plays

(1) 7-2

threatening (2) 3-7 and (3) 15-11. White can prevent this only by

(1) ... 24-20

Now 3-7 would only draw on account of 16-11.

(2) 2-6 20-24 (3) 6-10 24-20

Again 3-7 had to be prevented.

(4) 10-14 20-24 (5) 14-17 24-27

This time 24-20 would have lost, as Black would have replied (6) 17-13, 20-24; (7) 3-7, 12-8; (8) 15-11.

(6) 17-13 27-32

Avoiding 27-24 which would lose by (7) 3-7

(7) 13-9 32-27 (8) 9-14 27-24 (9) 14-18 24-27

Drawn. White has to watch 3-7 and to take care to play 24-20 at the right time so as to exchange 16-11 if 3-7 is played. At the same time he must beware of playing 24-20 when the Black Kings are on squares 15 and 5 or 15 and 13, as otherwise Black would reply 5-9, 20-24; 3-7, 12-8; 15-11.



IV

GENERAL PRINCIPLES AND ILLUSTRATIVE GAMES



It is possible to apply general strategic principles to the game of Checkers, just as well as the game of Chess, even though there is not the scope in Checkers for strategic maneuvers on the grand scale on which they can be carried out in Chess.

Again it is naturally the principle of greatest mobility which should govern the plan of mobilization in any opening, and it is consequently more desirable to have the men work in the center of the board, than on the edge, where part of their range is cut off.

The advantage of center squares over side squares is not so marked in Checkers as it is in Chess. There is no doubt that a piece has more mobility in the center, where there are two or four moves to choose from, than on the side where only one or two moves are possible; but a man on the side has an advantage in so far as he is backed up by the edge of the board so that he is safe from being captured until he moves. However, a player who keeps his men in massed formation in the center will in almost all cases be able to make them protect each other and to win the upper hand against an opponent whose army is divided into two parts, one on the left and the other on the right side of the board.

When playing with the white men, it is advisable to occupy such squares as 14, 18, 19, 30, 31 and 32, and it is not advisable to occupy 5 and 12 whenever the opponent has a man on 1 or 3 respectively, as in that case the men have a tendency to act as supports for the enemy instead of helping their own side. In the position: Black 1, 7 and 9; White 5, 14, 18 and 22; for instance, White's man on 5 supports Black's man on 9 and White, on the move, has to surrender a piece by 22-17, to which Black replies 9-13.

It is naturally a good thing not to touch the men of the back row mentioned above, as they will prevent the opponent from getting Kings. White's man 29 and Black's man 4, however, are better off in the middle of the board, as the squares 25 and 8 are adequately guarded by 30 and 3 respectively. Moreover, there is danger of the first position arising from openings in which a player keeps his man in the single corner.

A formation which very often occurs in the middle game is the so- called "elbow." It consists of three men arranged like the white pieces in Diagram 108.

32 31 30 - 29 - 28 o - o 21 - 20 * o - * 13 - 12 * - 5 - 4 - 3 2 1

DIAGRAM 108.

When adequately supported an elbow forms a solid position which cannot easily be attacked. An example of a strong elbow will be found in the following game:

32 31 30 - o o 29 - 28 o - o 21 - 20 o o - * o 13 - 12 * * * - * * 5 - 4 * - 3 2 1

DIAGRAM 109.

Black White

(1) 10-15 23-19 (2) 6-10 22-17 (3) 1-6 25-22 (4) 11-16 17-13 (5) 16-23 26-19 (6) 7-11 29-25 (7) 11-16 22-17 (8) 16-23 27-11 (9) 8-15 24-19 (10) 15-24 28-19 (11) 4-8 25-22 (12) 8-11 31-26 (13) 3-7 22-18 (14) 9-14 18-9 (15) 5-14

The men on 6, 10, 13, 14, 17 and 21 form the elbow, the strength of which becomes apparent on the 19th move.

(15) ... 26-23 (16) 11-15 32-28 (17) 15-24 28-19 (18) 7-11 30-26 (19) 2-7 19-16 (20) 12-19 23-16 (21) 11-20 26-23 (22) 7-11 and wins.

The danger involved in an elbow, which is not sufficiently backed up, is shown in the following game.

Black White

(1) 10-15 23-19 (2) 7-10 22-17 (3) 3-7 25-22 (4) 9-14 29-25 (5) 5-9 17-13 (6) 1-5 22-17 (7) 11-16 26-22 (8) 16-23 27-11 (9) 7-l6 31-26 (10) 8-11 24-19 (11) 16-23 26-19 (12) 11-15 30-26

and White wins through the threat to get two for one by 19-15 after the exchange. Black cannot help the loss of a man.

The reader, who has thoroughly acquainted himself with the fundamental endings, will have no difficulty in playing a good game of checkers, if he follows at every move the general principles discussed in this chapter. When playing over the countless variations, which are offered in the majority of checker books, he would find that they are merely illustrations of the application of those principles to the various openings.

Following are two examples from master play, the careful study of which will do more good to the student than the perusal of a great number of games that lack adequate annotation.

Black White

(1) 9-14

The best opening move is probably 11-15, as this enables a speedy development of the man on 4, who, as previously explained, should not be kept in the back row. The variations resulting from 11-15 have been so thoroughly analyzed that it is practically impossible to defeat a player who chooses this opening and knows the possible variations by heart. It has, therefore, been found necessary to restrict the players in matches and tournaments by balloting the first move of Black and White, in order to avoid too many draws. This is a serious drawback, as it curtails the freedom of decision, to which a player should be entitled in any game.

(1) ... 22-17 (2) 11-15

It is hard to tell whether this move of 11-16 or 5-9 is the best. 6-9 and 10-15 are considered weak.

(2) ... 25-22

More aggressive than 23-19, which can safely be played.

(3) 15-19

8-11 or 17-13 or 23-19 are also good moves.

Black White

(3) ... 24-15 (4) 10-19 23-16 (5) 12-19 17-1O (6) 6-15 21-17 (7) 5-9 29-25 (8) 8-12 25-21 (9) 7-10 17-13 (10) 1-6

32 31 30 - o o o 29 - 28 o o o - o o 21 - 20 * - * o 13 - 12 * * * - 5 - 4 * * * * - 3 2 1

DIAGRAM 110.

At first sight, it might seem unwise to break up the King row, when 9-14 could be played; but the advantage of holding the man on 13, instead of allowing him to complicate matters by 13-9, more than counterbalances the disadvantage of moving a back man. Black could also play (10) 2-6, but this admits of the following strong attack: (10) 2-6, 27-23; (11) 4-8, 23-16; (12) 12-19, 32- 27; (13) 9-14, 27-24; (14) 3-7 (8-12 would lose), 22-17; (15) 14- 18 (again 8-12 would lose), 17-14; (16) 10-17, 21-14; (17) 1-5, 31-27; (18) 6-10, 24-20; (19) 10-17, 26-22; (20) 18-25, 30-14; (21) 7-11 (Probably the only move to draw—8-12 would lose on account of 20-16).

Black White

(10) ... 27-24 (11) 4-8 32-27

22-18 could also be played.

(12) 9-14 27-23

or 22-17 or 24-20.

(13) 3-7 23-16 (14) 12-19 22-17 (15) 7-11 26-23

31-27 would lose through (16) 8-12, 26-22; (17) 11-16, 24-20; (18) 19-24, 20-11; (19) 24-31, 11-8; (20) 14-18.

32 31 30 - o o 29 - 28 o - o o o 21 - 20 * o - * * o 13 - 12 * * - * * 5 - 4 * - 3 2 1

DIAGRAM 111.

(16) 19-26 30-23 (17) 8-12 24-20 (18) 15-18 23-19

20-16 cannot be played on account of (19) 20-27, 16-7; (20) 2-11, 31-24; (21) 12-16.

(19) 11-15 20-16

White can, of course, draw here by 31-26; but 20-16 also draws in spite of Black's seemingly invincible elbow.

Black White

(20) 15-24 28-19 (21) 2-7 31-26 (22) 18-23

If 18-22, White draws by 19-15; (23) 12-19, 13-9.

(22) ... 26-22

32 31 30 - 29 - 28 - * o o 21 - 20 o o - o * o 13 - 12 * * - * * 5 - 4 - 3 2 1

DIAGRAM 112.

Playing for a brilliant finish. He could also draw by 16-11; (23) 7-16, 26-22; (24) 14-18, 22-15; (25) 23-26, 17-14.

Black White

(23) 23-27 16-11 (24) 7-23 22-18

Drawing, although two men down.

The following game illustrates first position:

Black White

(1) 11-15 22-18

This move is not considered as strong as 23-19.

(2) 15-22 25-18 (3) 8-11

12-16 can also be played.

(3) ... 29-25 (4) 4-8 25-22

24-20 is another good move.

(5) 12-16

If 10-15, White obtains a strong game by 23-19.

(5) ... 24-20

Considered best. 24-19 or 22-17 are also playable.

(6) 8-12

He could lay a trap by (6) 10-15. If White replies 27-24 or 28- 24, Black wins by (7) 15-19. 24-15; (8) 16-19, 23-16; (9) 9-14.

Black White

(6) ... 27-24 (7) 10-14 24-19

32 31 30 - o o 29 - 28 o o - o o o 21 - 20 o o o - * * * 13 - 12 * * * - * * 5 - 4 * * - 3 2 1

DIAGRAM 113.

In answer to 31-27, Black would win by (8) 7-10, 24-19; (9) 9-13, 18-9; (10) 5-14, 28-24; (11) 13-17, 22-13; (12) 3-7 or (10) ..., 27-24; (11) 1-5, 22-18; (12) 3-7.

(8) 7-10 28-24

32-27 or 19-15 are considered stronger.

(9) 3-7 32-28

This loses. The only drawing move is 30-25.

Black White

(10) 9-13 18-9 (11) 5-14 22-18

32 31 30 - o o 29 - 28 o - o o o 21 - 20 o o * - * * 13 - 12 * * - * 5 - 4 * * - 3 2 1

DIAGRAM 114.

Four variations are possible here. If 31-27 or 30-25, Black wins by (12) 13-17, 22-13; (13) 14-18, etc. (11) ..., 22-17 loses on account of (12) 13-22, 26-17; (13) 14-18. The sacrifice (11) ..., 21-17; (12) 14-21, 22-18 is met by (13) 10-14, 18-9; (14) 1-5, 26-22; (15) 5-14, 31-26; (16) 13-17.

Black White

(12) 13-17 18-9 (13) 6-13 21-14 (14) 10-17 26-22

In answer to 30-25 Black wins by (15) 7-10, 25-22; (16) 2-6; but with 31-27 White can offer prolonged resistance, thus:

32 31 30 - o o o 29 - 28 o o - o o o 21 - 20 o o o - * * 13 - 12 * * * - * * * 5 - 4 * * * - 3 2 1

DIAGRAM 115.

(14) ..., 31-27; (15) 17-22, 26-17; (16) 13-22, 19-15; (17) 11- 18, 23-14; (18) 1-6, 20-11; (19) 7-16, 27-23; (20) 16-19, 23-16; (21) 12-19, 24-15; (22) 6-10, 15-6; (23) 2-18, 28-24; (24) 18-23, 24-19; (25) 23-27, 19-15; (26) 27-32. 15-10; (27) 32-27, 10-6; (28) 27-23, 6-1; (29) 22-26, 1-6; (30) 26-31, 6-9; (31) 30-26, 9- 13; (32) 26-22, 13-9; (33) 23-18. Black has now received first position and wins.

Black White

(15) 17-26 31-22 (16) 7-10 30-25 (17) 2-6 25-21 (18) 6-9 22-18 (19) 1-5 18-15

White must give up a piece to get through, and Black can then exchange at his leisure and win without difficulty.

(20) 11-27, etc.



V

PROBLEMS



Checker problems, unlike the Chess problems, are intimately related to the game itself and do not enable combinations different in kind from those which occur in the actual fight over the board.

PROBLEM No. 1. WHITE TO MOVE AND DRAW.

32 31 30 - 29 - 28 o - o o 21 - 20 - * * 13 - 12 - 5 - 4 - 3 2 1

DIAGRAM 116.

They usually represent an end game and are distinguished from ordinary endings only by an unexpected initial move, mostly embodying a sacrifice of several men. Diagrams 116, 117 and 118 furnish some examples:

PROBLEM No. 2. WHITE TO MOVE AND WIN.

32 31 30 - ** 29 - 28 - oo o o 21 - 20 o - * 13 - 12 * - * 5 - 4 - 3 2 1

DIAGRAM 117.

If, in Diagram 116, White tried to reach the King row with his man 27, Black would win by first position thus: (1) . . ., 27-23, (2) 16-20, 24-19; (3) 20-24, 19-15; (4) 24-27, 23-19; (5) 27-24, 19-16; (6) 24-19, etc. The only way to draw is to sacrifice first the man on 21 by 21-17; and then to continue as above. This enables White to play 23-18, instead of 19-15, exchanging the King for a man.

The first move in Diagram 117 is 24-28, to which Black must reply (2) 29-25. White then sacrifices his three men by 17-14 and after (3) 25-27 (or 9-27) plays 28-32. Black must take the third man, and White recaptures two men by 32-14, pinning both of the remaining black men.

PROBLEM No. 3. BLACK TO PLAY AND WIN.

32 31 30 - o o o 29 - 28 o o o - o o * 21 - 20 * o * - * o o 13 - 12 o * * - * * * 5 - 4 * * * - 3 2 1

DIAGRAM 118.

This is the longest stroke known to have occurred in actual play. The game from which the above position arose went as follows:

Black White

(1) 12-16 21-17 (2) 16-20 17-13 (3) 10-14 23-19 (4) 14-17 19-16 (5) 17-21 16-12 (6) 11-16 22-18 (7) 8-11 25-22 (8) 7-10 26-23 (9) 10-14 24-19 (10) 14-17 31-26 (11) 4-8 19-15

Now the position of the diagram is reached, in which Black wins by

(12) 21-25 30-14 (13) 16-19 23-7 (14) 3-19 12-3 (15) 19-24 28-19 (16) 2-7 3-10 (17) 6-31 13-6 (18) 1-17 22-13 (19) 31-15

Completing a stroke, which removes 18 pieces from the board.

(19) ... 32-27 (20) 15-10 29-25 (21) 5-9

To get the move

(21) ... 13-6 (22) 10-1 25-22 (23) 1-6 22-18 (24) 6-10 27-23 (25) 20-24 23-19 (26) 24-27 18-15 (27) 10-7 19-16 (28) 27-31 15-11 (29) 7-3 16-2 (30) 31-27 11-8 (31) 27-24 8-4 (32) 24-19 4-8 (33) 19-15 8-4 (34) 15-11 and wins.

THE END