Chess and Checkers: The Way to Mastership, Edward Lasker [psychology books to read txt] 📗

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

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| | | | | | | | | 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