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Go and Go-Moku
The Original Board Games
By Edward Lasker
Dover Publications, Inc.Copyright © 1960 Edward Lasker
All rights reserved.
Board and men
THE Go BOARDS USED IN THE ORIENT are made of wood, usually between four and five inches thick, and supported by four feet, which make the whole board about eight inches high, convenient for players who squat on mats. More modern boards, intended to be placed on tables, are only about an inch or an inch and a half thick.
On the board 19 x 19 lines are drawn, parallel to the edges. The board does not form exactly a square, but is slightly oblong, the narrower sides facing the players. The horizontal lines are 29/32" apart from each other and the vertical lines 27/32".
The stones are not placed on the squares, as in Chess or Checkers, but on the points of intersection of the lines. There are 361 of these points all together, and each player has 181 stones, though rarely more than 125 to 150 are used in a game. The stones have the form of a convex lens about 7/8" in diameter and 3/32" to 3/8 thick in the centre. In Japan the black stones are usually made of slate, and the white stones of shells, the latter a shade larger than the former, and both a little too large for the space on the board, so that during the play they overlap here and there and lend a feeling of irregularity to the whole board which is enhanced still further by the careless manner in which the players place the stones on the points.
All this has perhaps grown out of the innate artistic sense of the Oriental, who is opposed to the monotony entailed in excessive regularity.
Cardboard is not a suitable material for Go boards. When a stone is grasped between the nail of the second finger and the tip of the third finger, as the Japanese do, and placed on the board with decision, a cheerful sound results on wood, but only a dull thud on cardboard.
In order to describe the points on the board in discussing moves and positions the algebraic method which is used in Chess is best suited. The vertical lines from the left to the right of the player of the black stones are named a, b, c, etc., to t, omitting the j, and the horizontal lines are numbered 1, 2, 3, etc., to 19, beginning from the side on which the player of the black stones sits.
The 4th, 10th, and 16th lines, as well as lines d, k, and q, are drawn somewhat heavier than the rest of the lines to facilitate orientation. The nine intersections of these lines, which according to the system of notation just explained would be d4, k4, q4, d10, kio, qio, d16, k16, and q16, are distinguished by small dots or circles, which the Japanese call stars, and which serve as handicap points.
The rules of the game
The game starts on the vacant board. With Black beginning, the players alternately place one stone on any unoccupied point they choose. An exception is a case, discussed later on, which occurs a number of times in almost every game, and in which there is one point a player can occupy only under certain specified conditions.
Once placed, a man is never moved. On the Go board, motion takes the form of extending a man's position in one direction or another by placing additional men on points located in that direction.
The main objective of the players is to join their men gradually into groups surrounding as many vacant points as possible, and to do this in such a manner that, with proper play on both sides, hostile men placed in the surrounded territory cannot escape capture. A stone or a group of stones is captured and removed from the board by the opponent when the latter occupies the last vacant point directly adjoining that stone or group on a line.
A second objective of a player is the capture of as many hostile men as possible. In games between reasonably good players the number of men captured only very rarely comes anywhere near the number of vacant points surrounded.
The game is over when neither player can make a move that increases the size of this territory or the number of his prisoners. Each player then scores the number of vacant points he has surrounded, less the number of his men captured by the opponent. The larger score wins, though in master games it is sometimes agreed that Black, to offset the advantage the first move gives him, must score at least 5 points more than White to be considered the winner.
The weaker player always takes the Black stones. When receiving a handicap, he starts by placing the agreed number of stones on the handicap points in accordance with the convention described on page 79, and then White makes his first move.
Beginners often misinterpret the rules of play cited without an actual demonstration on the board. Their most frequent error is to consider stones firmly connected which are not adjoining on a line. Let us look at the position in Diagram 1 between the lines e and m and the lines 2 and 6. We see here a Black and a White army, the former being partly surrounded by the latter. Neither the Black nor the White men are completely united to chains. Black's group still lacks a stone at either f4 or g3 and a stone at k3 or i2. White's army still lacks connection at e4, at e6 or f5, at g5 or h6, and at k5. Let us assume that both Black and White will be able to carry out these connections in due course. Then the question still remains: are the unoccupied points which are surrounded by Black really Black's territory or are the Black stones lost, thus making the points they enclose as well as the points on which they themselves are located White's territory
How men are captured
To decide this question we have to establish under what conditions a group of stones is permanently safe from capture. This definition does not form part of the rules of the game but follows automatically from their application, as some of the examples discussed later on will elucidate.
The Diagram illustrates eight cases in which White on the move could immediately effect a capture. In the lower left corner he could remove Black's man by playing a2. On the left edge he would capture the Black stone with a11, and with e17 he would kill the man on e16. Likewise, the Black stones extending from p10 to m12 would be removed when White occupies n12, their last "breathing space" or "liberty," as such vacant points adjoining a group are called. g12 is the only liberty the 8 men around that point have left. Therefore, g12 does not represent Black territory. It is in White's hands, together with the 8 points which will be vacant after Black's men are removed from the board. White can play g12, although his man is completely surrounded on that spot, only because in occupying it he is killing the surrounding group. The move would be illegal if Black still had another breathing space.
The positions around m7 and s5 illustrate the one exception to the rule that a player may place a man on any vacant point of his choice. After White plays 17, capturing Black's man on m7, Black is not permitted to recapture White's stone immediately by playing back into m7. He must make a move at another part of the board before he returns to m7. A position of this type is called "Ko" and brings about the most interesting situations.
It is evident that unless Black makes a threat which White must answer in order not to lose more than he would gain by filling in the Ko at m7, his intervening move would not affect the Ko situation. If that move forces a reply on the part of White, however, Black will be able to recapture at m7 on the following move. White, again, will have to invent a threat which Black must answer before he can capture Black's man on m7 for the second time, and so on. Sometimes these Ko fights extend through a series of twenty or thirty moves and decide the outcome of the game.
Though this statement will not be clear until it is illustrated later on by an actual game, an inkling of the possibilities entailed in Ko situations will be conveyed by the position on the right side of Diagram 1. It is Black's move. White threatens to play r4, capturing seven Black men. Black cannot save these men by playing himself into r4, because White would reply q8, killing twelve men. Black will therefore play s6 and take White's man s5, at the same time attacking the five White men around s6. White cannot save these by playing t8, because Black would capture the group with t9. Thus White must invent a threat at another part of the board, important enough for Black to answer, and then he can recapture on s5, again attacking the seven Black men. Whether White wins these seven men or Black wins the six White men will depend upon who has more threats available to him elsewhere.
In the position shown in the upper part of Diagram 1 White threatens to play 019, which would not merely capture two men, but would separate Black's army into two groups. As we will see later, these groups could avoid getting captured only when connected with each other. Black can ensure that connection by playing 1.n19, because after White replies 2.019, taking two prisoners, Black recaptures with 3.018, taking one, and if at any time White attacks the stone on 018 with 017, Black can fill at 010, linking his groups solidly.
After White has played 019, Black is permitted to recapture immediately, because this is not a case of Ko, inasmuch as White has captured more than one stone. If a White man were located on 017 instead of a Black one, so that White would take only one man by playing at 019, Black could not recapture until he had played a move elsewhere. In other words, the life of his army would then depend upon the outcome of a Ko fight.
In such a fight the players must carefully calculate how many points are at stake. Only then are they in a position to decide whether it is better to fill the Ko or to answer the opponent's threat. In the present case Black would lose fifteen men if White filled the Ko, and White would increase his territory by the fifteen points vacated by the captured stones, plus the four vacant points within Black's group. The total number of points involved is therefore thirty-four, less the number White would lose by ignoring Black's threat and filling the Ko instead. Let us assume, for argument's sake, that his net gain would be eighteen points. Before making his decision he would scan the positions on the board to see whether he has a threat of comparable size available to him. If so, he will defend himself against Black's threat and let him recapture in the Ko, whereupon Black will be guided by similar considerations on his next turn.
The beginner rarely realizes that a Ko threat need not necessarily involve the capture of a hostile group. It may instead merely prepare an invasion of territory which must be warded off to avoid a greater loss than at stake in the Ko. Diagram 2 will illustrate this point. Black has just captured in the Ko at d16. The stake is rather sizeable; for if Black could fill the Ko at c16, he would seal off about ten points in the corner, with good prospects of increasing this territory considerably by expansion toward line k. If White wins the Ko, however, he will be able either to ruin Black's corner by playing b18 and capturing the men on c17 and c18, or to break into the territory on the side with c14, which would attack the man on c15.
White has excellent Ko threats of the territorial type at his disposal. He could invade Black's prospective territory on the upper right, for example, by playing r17. This would threaten q17 and incidentally promise a good chance of surrounding Black's men on line q completely. Or he could play p2, threatening to continue with 02 and n2 or m3, thus forming a chain connecting his three men on the third line and taking a territory of a good many points away from Black.
Let us now discuss a number of typical situations with which every beginner must be familiar to avoid sudden fatal losses.
In Diagram 3 the Black men on d3, d4, c5, and b6 partly surround the corner territory, while the White men on e3, e4, g5, h3, and h4 partly surround territory between the lines e and h. If Black plays 1.e2 and White replies 2.f2, the life of the Black man on e2 is threatened. For if Black makes a move on some other part of the board to which White need not answer immediately, White could continue with 4.d2, attacking e2 directly, and 5.e1 will not save Black because after 6.d1 and 7.f1 White captures the three Black men by 8.g1.
This is a very important play to remember, as it recurs many times in every game, owing to the fact that the opposing armies, in their desire to wall off territory within their lines, almost always extend these lines toward the edge of the board as far as the third line and frequently attempt to encroach upon the territory of the adversary by an advance in the second lines as just illustrated.
The danger of capture by the method shown in this example always exists when a group of men has only two adjoining vacant points connected to it. In Diagram 3 the White group l13, l14, m13, for instance, would be lost if Black played 1.n13, occupying one of the two vacant points adjacent to the White group and threatening to kill the group with m12. For if White tries to save himself by 2.m12, Black plays 3.m11, again leaving only one point of escape for White. After 4.n12 and 5.012, 6.n11; 7.n10, 8.011; 9.p11, etc., as indicated in the diagram, the White chain finally reaches the edge of the board, from where there is no further escape. After 26.s6, 27.s5, and 28.t6 Black kills the whole White army with 29.t5.
The play illustrated in the last two examples is called Sh'cho (the ladder). This method of attack must never be used if the ladder of the defending player zigzags toward a stone of his own. If a White man had been standing on q9, for instance, Black's move 15.p8 would leave White two open points in his chain instead of only one, so that he would have time to play 16.n14 or 013 or any one of several other moves available which attack two of Black's men simultaneously, winning one of them and providing an avenue of escape for the whole White army.
Another type of constellation in which the ladder attack cannot be employed is illustrated on the lower left of Diagram 4. If Black attacks with 1.f7, 2.e7; 3.e8, White escapes with 4.d7, because this move attacks Black's man d6. If no White stone had been standing on d5, Black would have won the White group if we disregard the men on lines 9, 10, and 11.
Similarly, Black cannot succeed by attacking with 1.e7, 2.f7; 3.f8, 4.97; 5.h7, 6.g8; 7.g9, because White escapes with 8.h8 through attack on the Black man h7, who is threatened through co-operation with the White man on h6.
If Black played 1.d7, which does not directly attack the White group, White would have to make a defensive move all the same, because Black threatens 3.f7, and after 4.e7 Black would capture the White men by e8.
Along the edge of the Diagram 4 a number of errors are illustrated which every beginner makes frequently. Instead of playing aio in answer to White's c10 Black should have connected at b11, or he should have played a11 or b12 in order to prevent White's b11 which, in the position of the diagram, wins two Black men. To play a16 instead of a15 or b15 is a very similar mistake. White does not protect the man on a17 which is attacked, but continues with b15 and wins the three Black men. Black's man i18 is lost through White's k18, and the man on m19 is lost through White's n19 or l19. Again, White need not protect his man on t15 when Black attacks with t16, but he can win Black's man through s16, because if Black takes White's man with t14, White continues with r16; and connecting at t15 does not save Black's men, since White would win them all through t13. Similarly Black should not have answered White's s5 with t4, but he should have connected at r5, for White can now win the three Black men through r5.
Around 09 a white group is shown which cannot escape capture. The method of capturing it should be studied carefully.
It is evident that White can neither escape with n10 nor 010 nor p10, because Black would place a man correspondingly on the eleventh line and enclose White from the top.
It is also easily seen that neither n11 nor p11 will help White, because Black answers n10 or p10 respectively and completes the enclosure from the top.
However, White can apparently save himself by starting with o11, threatening to connect on the next move with 010 and to run away into the open. This plan can only be met by Black's playing a man on 010 himself. White can attack this man by 3.n10, and if Black defended him with p10, White would indeed be safe through connection at n11. But Black plays 4.n11 himself, sacrificing the stone at 010, and after White takes him with 5.p10, Black continues 6.p11, threatening to take seven men by playing again into 010; and 7.010 does not save White, because Black replies 8.012, capturing the whole group of nine men.
Not infrequently positions occur in which an army is safe although it has only two vacant points adjacent to its men, because the opposing army which surrounds it depends upon the same vacant points for its own life.
The position in the lower left of Diagram 5 is an example. The eleven White men which are surrounded by Black have only the points a2 and b2 open, but Black cannot attack the group by occupying either one of these two points because White would occupy the other, killing the six Black men by taking the last adjoining vacant point away from them. Neither can White attack the Black men by playing either a2, or b2, because Black would occupy the last vacant point and kill the twelve White stones.
Excerpted from Go and Go-Moku by Edward Lasker. Copyright © 1960 Edward Lasker. Excerpted by permission of Dover Publications, Inc..
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