Checkers - The Five Fundamental Positions (Part I)

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 1 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 1 and thereby compels the Black man to advance, finally forcing an exchange which secures the opposition.

DIAGRAM 1.--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

DIAGRAM 2.

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 3)

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.

DIAGRAM 3.--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 4 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

DIAGRAM 4.

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.

DIAGRAM 5.

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 5 where Black, on the move, loses because his man on 28 is blocked.

Beginning Checkers (English: Draughts)

The game of Checkers (English: Draughts)

Draughts is a duel, a battle of ideas. You win your game because your ideas are better, stronger, than of those of him whom you play. This does not mean that you have to be related to Einstein to be a draughts champion. If you have an imagination, know the truth when you see it, and can keep a straight face, then you are half-way there.
Now, ideas about draughts and probably almost anything else come from knowledge, which you can get in two ways. By experience, or by thinking it out for yourself. Many players will tell you experience is the only teacher; and they will point with pride to the fact that they have put in some thirty or forty years, amassing draughts lore. By the time I was in my late 'teens I could usually take these experienced woodpushers and trim them down to size in about half an hour. Even now, it is the really original player, the one who has his own ideas about the game, who gives me the most trouble.
When you go into a fight, of any sort, a main concern must be the battlefield, so to speak. It may be there are danger zones which you must shun, into which you must seek to impel the foe: these should be known. It may be there are key points which, seized, will control the whole sphere of action and will let the course of events be dictated - by you, or by the other player? If we take a look at the board se may get some ideas of this.
You may think that looking only at an empty board will not tell you much about the game -beyond the bare fact that, as draughts is played on all squares of the same hue, all the moves and jumps are done in an oblique direction.

DIAGRAM 1

Look again, and note first that the squares are not all the same - those in the centre of the board are very unlike those around the perimeter. From the centre, it uses only a few moves to get to any square on the board; a few steps and you are at the scene. It is a long way from one side of the board to the other; by the time you get there it may be too late. Apart from speed, the central squares offer a wider scope: from them you can assail or uphold either flank, wherever there is the more profit. In some cases you will switch your attack, or defence, from this flank to that; and usually you will need to pass through the central squares. If these are in your control you can carry out your plan; while if they are ruled by the foe your communications are cut and your men may have to slink around the side-lines, lurking in the shadows until in the end, alone, they are made away with. Control of the centre can mean control of the board.
If the outer squares are less desirable, then of these the squares in the very corners of the board will be even less so and in many cases they are really unsafe. A boxer will not be pinned on the ropes if he can help it - if he is held fast in a corner then he is in dire trouble.
The four corners of a draughts board are not identical. Two of them consist of only one square with one exit from that square: these single corners will as a rule be good places to stay away from. The double corner squares protect each other, and with twin exits will be safe in contrast to the single corners.
Now, all these remarks may give you the idea that by playing towards the centre all the time you can step out along the winning path; but go not so fast. That is the way to ruin. If you move all your men to the centre they will only get in the way of each other and give rise to a jam. A tightly packed group calls forth a pincer movement from the foe. Control is the essential; you occupy the centre by as many men as will gain control, but no more. You get control when your opponent is unable to move on to any of the centre squares and so is forced into the less favoured areas of the board. This is in fact your ultimate goal: to drive the enemy into the wilderness where he shall perish. Central control is a means to this end.
We can stress this view of the board, by contrasting the action of a king to that of a man. A king surveys the board in all directions, and the power of a king may be felt near and far. Not so a man, which from the first sees a vista rapidly waning in size and scope; at each step the range narrows, the danger grows, and so often the short life is put out long ere there is any chance to be a king. This is why it is not wise to let a man that is well advanced come to be fixed on the side of the board; there it will be cut off from comrades and be of no use, perhaps for the rest of
the game, and the time and effort spent in advancing it will have been wasted.
A chain of squares across the board forms an oblique line. Perhaps we ca call such lines diagonals - after all, that is what they are. As you will soon see, there are seven diagonals. However, only one of them is quite straight from end to end; that is the diagonal which extends from single corner to single corner, thus:

DIAGRAM 2

It may be as well to estimate the nature of a diagonal you intend to occupy or control. A diagonal may affect the power of a piece just as we find a square to do. The most obvious effect that the single corner diagonal has is that it cuts the board into halves, as it were. It divides your forces from those of the foe. Seen from this angle, at the start of a game only one of your twelve men is already in the enemy area; three are on neutral ground. In playing an attacking game these men will be brought into action with little delay, you may guess, and you will be right.
The single corner diagonal is the line of defence (we can call it the D-line) that separates the two armies: to gain control of this line is to take the initiative; to cross it is to begin the attack.
In the following set-up neither side takes any risks and control i shared.

DIAGRAM 3

The D-line

If the single corner diagonal is defensive in character, then a line which cuts across it and through the centre of the board must clearly be termed a line of attack: any activity along this line signifies aggression. This is the A-line.
In Diagram 5, the Blacks occup their own A-line and in that way control it. Whether they also control White's A-line will depend on the placing of the White men, which I do not show.Wherever they are,

DIAGRAM 4

The A-line

DIAGRAM 5
A-line control

one thing is plain - they cannot be on the like squares on White’s side of the the board, as both armies cannot be attacking at the same time along their own A-line. In other words, the player who first engages in an A-line attack takes the lead. The opponent must reply in some other way.
In both Diagrams 3 and 5, did you notice the extra man at the base? Though this man takes no active part in commanding the diagonal yet the added strength is desirable, for it is the base which the opponent will attack.
If the base can be destroyed the whole structure may break up.
It is here that we have the case for the squares at the outer edges of the board. A man on such a square is immune from direct 'capture' (the word often used by draughts players to denote a jump; yet the act of leaping over an enemy piece surely symbolizes 'over thy dead body' - but this is by the way). A man at the edge of the board is in a position to support other men which may form a chain of some power. A strong player will in this way transform into a weapon what might have been a defect.

I clarify this point because it is one about which most tyros are haz and very few self-styled experts are able to enlighten them on it.
The A and D diagonals are the major lines of attack and defence. You expand the power and scope of your men when you fill and control vital lines with them, so it is, of course, this you will try to do.
The diagonal which runs this side of the A-line has by contrast much less import; for the greater part of its length points to the side of the board.
It’s best squares are those at the edges, which may be used to support more active pieces. The B-line (the name comes easily to it) is a diagonal with weaknesses, which a clever opponent will often make use of for his own ends.
One of the more potent ways is for the foe to place a man on the square which intersects your D- and B-lines, dominating both and undermining your A-line also. Beware of danger at the spot marked X!
Most of the C-lin runs towards the centre and so it is stronger than the nearby B-line, and as also this part of the C-line intersects the attacking A-line it can be termed an important diagonal. I need hardly say that the square at which the A- and C-lines meet and cross is of great value in formational play, both in attack and in counter-attack. It is a key square, and now you know why.

DIAGRAM 6

The weak B-line

DIAGRAM 7

The C-Line

The lines E and F are for the most part defensive, supporting as they do activity along the D-line. This is their main utility

DIAGRAM 8

The E-line

DIAGRAM 9

The F-line

If you look at Diagram 3, you will see that both sides occupy their E-lines, and this is a typical set-up.Ending our alphabetical trip along the diagonals, we arrive at G:

DIAGRAM 10

The fact that the G-line has almost all the features of the A-line tempts one to regard it as a line of attack, until we realise that what is our G-line is also the opponent's A-line. Any attacks along this line may be expected to stem from the opposite side of the board rather than from our side. However, if we first set up a strong formation along our A-line then an attack along the G-line can be effectual, thus:

DIAGRAM 11

Here, Black advances two men along the G-diagonal with the powerful support of the formation shown before, at Diagram 5. This is about the best way to conduct a G-line attack.
In general, an advance early in the game along the G-line serves only to forestall enemy activity and is a defensive measure. In Diagram 12 below, Black has thrown away the natural advantages of having the right to move first and so make the first threat, and here plays for safe defence.

DIAGRAM 12

Around the early nineteenth century, most of the leading Masters thought that starting off a game in such a way as this would give Black a weak formation. Most of the moderns consider it a good method of opening. This may seem just another case of the light of present-day knowledge illumin- ating the dark ages. Not so. The truth is that the old-timers held a view of the word 'weak' not at all like that of the modern players. To them, a weak opening was one which promised few chances of getting a win, though it might be safe enough merely to get a draw - weakness denoted lack of opport- unity rather than danger - the nineteenth-century players thought the proper aim in playing draughts was to win the game. Nowadays, the view is that the player should first and foremost play to avoid defeat, that is to say, play for a drawn result. Of course, if an opportunity to win should appear (and it IS by chance) then go for it, but keep the draw in sight at all times.
To the modernist then, an opening is not weak if it is safe for a draw, even though it may offer virtually no chances to win.
My money is on the old-timers in this. I play the game to win. I make the chances. I win all the games I can, and I do not wait for chances to win. I make the chances. Maybe that is why I am Champion. However, I have the perfect system for anybody who wants to become unbeatable at the game, and it is this. Do not play. Then you can't lose.
If we now sum up our survey of the squares and diagonals, we must come to see very clearly that as the squares often determine the value of the pieces, so the action of the pieces as a whole may determine the character and strength of the diagonals - a diagonal is strong because it allows the build-up of telling formational patterns. It might be useful to state generally that, early in the game, when we have available numbers of men to form chains of attack or defence, then the diagonals are of paramount importance. Late in the game, when forces are dwindling to a few scattered units, then the individual squares come into their own.
To master these features of the board is a basic ‘must’ in pursuing a grasp of the mysteries of the game. You can hardly overdo this, you cannot know your board too well. Whatever plans you may conceive, however grand the scale, if they do not take into account the contours of the field of battle then they will not work out. The successful boxer knows how to use the ring.
You must know how to use the board.
Here is a composite picture of the seven diagonals, see from the point of view of each player. Study this well.

THE GAME OF CHECKERS

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 1. 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.

Diagram 1

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.

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 2 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.

Diagram 2

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.

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 3, 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.

Diagram 3

With one King entrenched in the double corner it takes two Kings to force the win. In the position of Diagram 4 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.

Diagram 4

The method which has to be employed will be evident from the play in Diagram 5. In order to win Black must exchange one King; the position is then reduced to that of Diagram 4.

Diagram 5

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.

Diagram 6

Sometimes the stronger side has an occasion to give up two Kings for one thereby forcing a position similar to that of Diagram 3. Diagram 6 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 7 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

Diagram 7

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 awin within a few moves.