Chapter 4

THE GAME OF CHECKERS

I

THE RULES OF THE GAME

The game of Checkers (English: Draughts) is played on the 32 black or white squares of the Chess board by two opponents, each of whom has twelve men of the same kind. The object of the game is to capture all opposing men or to block them so that they cannot move.

The original position of board and men is shown in Diagram 85. It will be seen that the board is placed in such a way that the players have a vacant square at their lower right hand corner. This corner is called the DOUBLE CORNER because two men are located in its immediate neighborhood while the left hand corner, the SINGLE CORNER, is occupied by only one man.

The squares of the Checker board are usually described by numbers as shown in Diagram 86. This is a rather crude method when compared with the simple notation by means of a system of coordinates as used in Chess, but as it is universally employed in Checker books and Checker columns in daily papers it will be adhered to in the following explanation of the game.

The black men are placed on the squares 1 to 12, the white men on the squares 21 to 32. The first move must invariably be made by the player of the black men.

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

DIAGRAM 85.

The move of the Checker men is a diagonal step forward, one square at a time. If a hostile man is in his way and if the square beyond the hostile man is vacant, he must capture him by jumping over him on to the vacant square, and he must continue capturing from the square on which he lands as long as this is possible according to the above rule. Captured men are removed from the board.

WHITE

+---------------------------------------+ | | 32 | | 31 | | 30 | | 29 | |---------------------------------------| | 28 | | 27 | | 26 | | 25 | | |---------------------------------------| | | 24 | | 23 | | 22 | | 21 | |---------------------------------------| | 20 | | 19 | | 18 | | 17 | | |---------------------------------------| | | 16 | | 15 | | 14 | | 13 | |---------------------------------------| | 12 | | 11 | | 10 | | 9 | | |---------------------------------------| | | 8 | | 7 | | 6 | | 5 | |---------------------------------------| | 4 | | 3 | | 2 | | 1 | | +---------------------------------------+

BLACK

DIAGRAM 86.

If a man reaches the opposite edge of the board he automatically becomes a King and must be "crowned" by the opponent, who must place another man on top of him. A King may move and capture backward as well as forward. A man, who reaches the "King row" in capturing, cannot, however, continue capturing on the same move with the newly made King.

The position of Diagram 87 may serve to illustrate the above rules. White, on the move, plays 14-9. Black must capture this man with the man on 5 who jumps on to 14.

32 31 30 +---------------------------------------+ | | | | | | o | | | 29 |---------------------------------------| 28 | * | | | | o | | | | |---------------------------------------| | | | | o | | o | | * | 21 |---------------------------------------| 20 | | | | | | | | | |---------------------------------------| | | | | * | | o | | o | 13 |---------------------------------------| 12 | | | * | | | | | | |---------------------------------------| | | * | | * | | | | * | 5 |---------------------------------------| 4 | | | | | | | | | +---------------------------------------+

3 2 1

DIAGRAM 87.

White then sacrifices another man by 23-18 forcing Black to reply 14-23. Now White captures the three men on 23, 15 and 7 with his man on 26, and Black, before making his next move, must crown White's man who has just reached the King's row. He will naturally move his man 8, as otherwise White would capture him with the King on 3.

If a player overlooks the possibility of a capture his opponent has the right to remove the man who should have made the capture, from the board. This procedure is called "huffing" and does not constitute a play. Instead of huffing a player may ask the opponent to retract his move and to make the capture.

When neither player can force a win the game is considered a draw. When one side appears to be stronger and refuses to accept a draw offered the player of the weaker side can require the win to be demonstrated within 40 moves; otherwise the game is drawn.

II

ELEMENTARY TACTICS

The first thing a Checker player has to know is what superiority in material or position is required to FORCE a win in the ending. The most elementary case is the one shown in Diagram 88, in which White wins by playing 32-27. With this move White takes the opposition or as most Checker players call it, White has the "move." Whatever Black replies he is forced to the edge of the board and finally he is obliged to let White capture his King. Supposing Black plays (2) 26-22, in order to reach the double corner, where he would be safe as he could indefinitely move from 5 to 1 and from 1 to 5, then White continues with (2) ...,27-23, preventing (3) 22-18 which would gain the road to the double corner. After (3) 22-17, 23-l8; Black has to retreat to the edge by 17-13 or 17-21, and White, by playing 18-14, or 18-22 pins the black King so that he cannot move without being captured. If it had been Black's move in the position of the diagram, he would have gained the opposition by 26-31 and White would have been compelled to retire to the double corner and to draw by 32-28, 28-32, etc.

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

DIAGRAM 88.

With one King entrenched in the double corner it takes two Kings to force the win. In the position of Diagram 89 for instance White would win as follows:

Black White

(1) ... 19-24 (2) 32-28 23-19 (3) 28-32 24-28 (4) 32-27 28-32 (5) 27-31 19-15 (6) 31-26 15-18 (7) 26-31 18-22

In the ending THREE KINGS AGAINST TWO KINGS the most favorable spots for the weaker player are the two double corners; but the three Kings will always win when handled right.

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

DIAGRAM 89.

The method which has to be employed will be evident from the play in Diagram 90. In order to win Black must exchange one King; the position is then reduced to that of Diagram 89.

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

DIAGRAM 90.

If it were White's move, Black would easily win; for after (1) ..., 27-32; (2) 19-24, 9-5; (3) 10-6, White cannot avoid the exchange. For instance: (3) ..., 5-1; (4) 24-19. The problem reduces itself therefore to changing the move from Black to White. This is accomplished by:

Black White

(1) 15-18 27-32 (2) 19-24 9-5 (3) 10-14

Threatening 24-27. White can only reply

(3) ... 32-28 (4) 24-27 5-1 (5) 14-9, etc., as above.

If the weaker side does not control both double corners the exchange can be forced much more easily, as an experiment will quickly show.

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

DIAGRAM 91.

Sometimes the stronger side has an occasion to give up two Kings for one thereby forcing a position similar to that of Diagram 88. Diagram 91 offers an example:

Black on the move wins in 5 moves, thus:

(1) 16-19 27-31 (2) 20-24 32-27 (3) 28-32 27x20 (4) 19-24 20x27 (5) 32x23

and White is pinned.

With three Kings against four a player can sometimes offer prolonged resistance. But finally the stronger player will always be able to force an exchange which secures the victory. In the position of Diagram 92 for instance Black will proceed as follows:

(1) 18-15 19-24

It would not help to play 27-24, as Black would reply 14-17 and exchange on the next move by 10-14.

(2) 11-16

limiting White's mobility.

(2) ... 23-26

In answer to 24-20 Black would play 15-19.

(3) 16-19 24-28 (4) 14-18 26-30 (5) 19-23 28-32 (6) 15-19 27-31

32 31 30 +---------------------------------------+ | | | | | | | | | 29 |---------------------------------------| 28 | | | oo | | | | | | |---------------------------------------| | | | | oo | | | | | 21 |---------------------------------------| 20 | | | oo | | ** | | | | |---------------------------------------| | | | | | | ** | | | 13 |---------------------------------------| 12 | | | ** | | ** | | | | |---------------------------------------| | | | | | | | | | 5 |---------------------------------------| 4 | | | | | | | | | +---------------------------------------+

3 2 1

DIAGRAM 92.

Not 30-25 on account of 18-22.

(7) 10-14 31-26 (8) 14-17 26-31 (9) 17-22 31-27 (10) 19-16 27-24 (11) 16-19 and wins.

If, on the 10th move, White played 27-31 instead of 27-24, the game might proceed as follows:

(11) 18-15 32-28 (12) 15-19 28-32 (13) 22-26 31x22 (14) 23-27 32x23 (15) 19x17

These possibilities of exchanging "two for two" should always be looked for as they often occur, enabling a win within a few moves.

III

THE FIVE FUNDAMENTAL POSITIONS

While in the examples of elementary endings given in the previous chapter, the correct method of play was comparatively easy to find, positions with few men often occur which look very simple but which require considerable thought to be handled in the right way. The knowledge of these positions, of which there are five distinctly different types, is essential for any one who desires to become a fair player and they are, therefore, thoroughly explained in the following five characteristic examples.

THE FIRST POSITION

It does not make any difference in the method of play whether the Black man is located as shown in Diagram 93 or on 3, 4, 7, 8, 10, 11 16, 20 or 24. The essential point is that he must not be able to march to the King row without being intercepted by White.

The winning maneuver is this: White turns the Black King out of the double corner in the manner shown in the play from the position of Diagram 89 and thereby compels the Black man to advance, finally forcing an exchange which secures the opposition.

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

DIAGRAM 93.--White to Move and Win.

This maneuver, as will be evident from a careful study of the position, is possible only in case White has the move. If Black has the move the ending is a draw.

Black White

(1) ... 23-27 (2) 28-32 19-23 (3) 32-28

Black cannot play 12-16, as 27-24 would win a piece.

(3) ... 27-32 (4) 28-24

Again 12-16 is not possible on account of 32-27 winning a piece in three moves.

(4) ... 23-18

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

DIAGRAM 94.

White played 32-28 Black would exchange by five 24-19 and draw the game.

In the position of the Diagram Black has the choice between 24- 20, 12-16, 24-19 or 24-28, but he loses, no matter what move he makes as demonstrated below.

(A) (5) 24-20 32-27 (6) 20-16 18-15 (7) 16-20 15-18 (8) 12-16 18-15

(B) (5) 12-16 18-15

Now Black cannot play (6) 16-19 because of the exchange 32-27; (6) 16-20 would also lose quickly through 15-18, (7) 24-19, 32- 28, (8) 19-16, 18-23. The best try is (6) 24-28.

Against 15-18 Black would now draw by (7) 16-19, 32-27; (8) 19- 23.

The only way to win is

(6) ... 15-11

after which Black can do no better than

(7) 16-19 32-27 (8) 28-32 27-31 (9) 32-28 11-16 (10) 19-24 16-19, etc.

(C) (5) 24-19 32-28 (6) 12-16 28-32 (7) 19-24 18-15

and White continues as shown before.

(D) (5) 24-28 18-15 (6) 28-24 32-28 (7) 24-27 15-18 (8) 12-16 28-32 (9) 27-24 18-15

and wins as before by 15-18 in reply to (10) 16-20 or 15-11 in reply to 24-28.

THE SECOND POSITION (See Diagram 95)

White's advantage is that he can crown his two men while Black remains with only one King and two men. The reason why Black cannot use his two men to advantage is that they are pinned on the side of the board while White's men are located in the center where they have much more mobility. All the same White must have the move in order to win, just as in first position.

Black White

(1) ... 30-26 (2) 9-14 26-23 (3) 14-10 23-18

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

DIAGRAM 95.--White to Move and Win.

(4) 10-6 18-14 (5) 6-1 14-9 (6) 1-5 9-6 (7) 5-9 6-2 (8) 9-5 2-6 (9) 5-1 6-9 (10) 1-5 9-14 (11) 5-1 14-18 (12) 1-6 18-15 (13) 6-9 15-19 (14) 9-14 27-23 (15) 14-10 23-18 (16) 10-6 18-14 (17) 6-1 14-9 (18) 1-5 9-6 (19) 5-9 6-2 (20) 9-5 2-6 (21) 5-1 6-9 (22) 1-5 9-14 (23) 5-1 14-18 (24) 1-6 18-23 (25) 6-10 23-27 (26) 10-14 19-23 (27) 14-10 23-18 (28) 10-6 18-14 (29) 6-1 14-9 (30) 1-5 22-17

At last White has a position in which he can reduce the ending to one of the fundamental cases by exchange.

(31) 5-14 17-10 (32) 21-25

It will be noticed that through the exchange Black gained to move. White regains it by a second exchange.

(32) ... 10-15 (33) 25-30 15-19 (34) 30-26 27-32 (35) 26-22 19-24 (36) 20-27 32-23

and wins.

Second position as a rule results from a "Bridge position" like the following: Black men on 20, 21, 23, Black King on 26. White men on 30 and 32, White Kings on 15 and 19. Black to move:

(1) 26-31 19-26 (2) 31-22 32-27

and White wins by "second position."

THE CHANGE OF THE MOVE

By the exchanges of men in the foregoing example the move was altered in each case. However, exchanges of pieces often occur which do NOT change the move, and as win or loss in a great number of endings depends upon which player has the move, it is necessary for the beginner to obtain a clear insight into the questions involved. An exchange always alters the move if the capturing piece is recaptured in turn. If a different piece is recaptured, it depends upon the relative position of the captured pieces, whether the move has remained with the same player or gone over to his opponent. For the purpose of calculating the move and its changes it is useful to imagine the Checker board as being composed of two "systems of squares"--the Black system containing the ranks starting with the squares 1, 9, 17 and 25, and the White system containing the other four ranks. If each of the two systems contains an EVEN number of men, the player whose turn to play it is, loses the opposition, that is: his opponent has the move. If the number of men in each system is ODD, the player whose turn to play it is, gains the opposition, that is, he has the move. As the calculation of the move enters only into such positions in which both players have the same number of pieces, it is sufficient to correct the number of men in one of the systems to obtain the desired information. Diagram 96 furnishes an example.

Counting the men of a system, the Black one, for instance, shows their number to be odd. Therefore, the player whose turn it is to play, has the move, which in the present instance

32 31 30 +---------------------------------------+ | | | | o | | | | | 29 |---------------------------------------| 28 | | | | | | | | | |---------------------------------------| | | o | | | | | | | 21 |---------------------------------------| 20 | | | o | | | | | | |---------------------------------------| | | | | | | | | | 13 |---------------------------------------| 12 | * | | | | | | | | |---------------------------------------| | | * | | | | | | | 5 |---------------------------------------| 4 | | | | | * | | | | +---------------------------------------+

3 2 1

DIAGRAM 96.

secures the win for White and a draw for Black, thus

(A) Black to move

Black White

(1) 8-11

This is apparently Black's best move; if he plays 2-7, White replies 19-15, obtaining a very strong position.

(1) ... 31-26 (2) 2-6 26-22 (3) 6-10 22-18 (4) 11-16 18-15 Draw.

(B) White to move

Black White

(1) ... 31-26 (2) 2-6 26-22 (3) 8-11 24-20 (4) 6-10 22-19 Block.

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

DIAGRAM 97.

From the above explanation it is evident that in the case of an exchange the move remains unaltered if the captured pieces were located in the same system, and that the move changes if the captured pieces belonged to different systems.

Exceptions to the rule sometimes occur due to a piece having no mobility, as for instance in the position of Diagram 97 where Black, on the move, loses because his man on 28 is blocked.

THE THIRD POSITION

32 31 30 +---------------------------------------+ | | | | | | | | | 29 |---------------------------------------| 28 | o | | | | | | | | |---------------------------------------| | | | | | | | | | 21 |---------------------------------------| 20 | oo | | ** | | | | | | |---------------------------------------| | | | | | | | | | 13 |---------------------------------------| 12 | oo | | ** | | | | | | |---------------------------------------| | | | | | | | | | 5 |---------------------------------------| 4 | | | | | | | | | +---------------------------------------+

3 2 1

DIAGRAM 98.--White to Move and Win.

White being a man ahead appears to have an easy win; but owing to the difficulty of getting the man crowned he has a hard task before him.

If the Kings on 11 and 12 were removed White would not be able to win at all, as the Black King would go back and forth between 19 and 23. It is, therefore, clear that in forcing a win from the position of the diagram the King on 12 must cooperate.

Another point to be borne in mind is that the following position would be a draw with White to move.

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

DIAGRAM 99.

White is unable to make any headway because he cannot threaten an exchange. The method in which White threatens the exchange of the King on 19 in the example of third position given in Diagram 98 is the following:

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.