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Comments on Go

The game most commonly known as Go in the English-speaking world has simple rules and is more profound than Chess.

It originated in China thousands of years ago. While legends placing its origin at 2,000 B.C. may not be accurate, texts whose dates are known reliably prove it to have been known about 2,000 years ago.

The Chinese name for the game is Wei Ch'i (Weiqi); this translates to "The Game of Encirclement", or, in a more pedestrian fashion, to "Enclosing Chess".

The Basic Rules

The rules of play are simple enough:

A square grid is used as the board. The locations used for play are the intersections between lines, not the squares, and the board provides a 19 by 19 array of points.

Two players take alternating turns; the first player has a supply of 181 black stones, the second player has a supply of 180 white stones. Each move consists of placing one stone on one of the intersections or points on the board.

A group of stones that are the same color, each of which is immediately adjacent in an orthogonal direction to at least one other stone in that group, and every one of which is indirectly connected to every other stone in that group through a route consisting solely of steps from one stone to an orthogonally adjacent stone of the same color constitutes a unit.

A unit of this kind can only remain on the board as long as at least one of the stones in that unit is orthogonally adjacent to an empty point on the board. When this ceases to be true, because the opponent has played a stone of his color to the last remaining empty point orthogonally adjacent to a stone in the unit, all the stones of that unit are removed from the board.

It is not permitted to play a stone so that it causes one of one's own units of stones to be removed from the board. However, a play that causes both one of one's own units of stones (including a unit consisting only of the stone just played) and one (or possibly more) of the opponent's units of stones to no longer have any orthogonal adjacency to an empty square is legal, and the result is that only the opponent's unit or units of stones deprived of a connection to empty space are removed.

It is not permitted to make a move the effect of which is simply to reverse the effect of the opponent's immediately previous move.

A player can decline his turn; when both players decline consecutive turns, or when a player cannot play because he has run out of stones, the game is over.

This account of the rules of play may not be completely accurate; suicide moves may not be prohibited (and under rare circumstances, they might be useful) and in some forms of the game, players cannot decline a turn.

A consequence of these rules is that a single unit of stones, if it completely surrounds (in the four orthogonal directions, which are the ones significant in Go) two single vacant spaces, is immune from capture. In addition, two single vacant spaces, if only two units of stones belonging to one player completely surround them, and both units of stones are in contact with both single vacant spaces, so that neither unit can be captured by a move filling up one of those vacant spaces, give immunity from capture to both units of stones.

In fact, although it is not something that usually occurs in practice, two single vacant spaces could even give immunity to three connected groups of stones, but only if each one of those three connected groups were in contact with both of the vacant spaces; these cases, and an even more unusual case, in which there are four eyes and six disconnected groups of stones, but each group is in contact with two different eyes, are illustrated above.

Counting Up At The End

The objective of the game is to be the player who surrounds the most territory on the board. Unfortunately, the rules for determining who has won the game, at least according to the accounts of the game that I had read, appear to require one to be competent at playing the game to apply them, since territory surrounded by stones of one color is only counted if that player can be expected to be able to hold on to that territory.

While this somewhat put me off of suggesting this game as an alternative to Monopoly or Cribbage for a pastime at home to other members of my family, recently, I have learned some interesting facts about the game of which I had previously been unware.

A simple way to count the score of each player at the end of the game would be this: any empty spaces on the board which are (considering only orthogonal connections, not diagonal ones, of course) completely surrounded by stones of one color are to be filled with stones of that color. Other empty spaces are left alone. When that is finished, rearrange the stones on the board to make it easier to count them.

This method of counting is known as the Tromp-Taylor method. In can also be used as the basis for understanding the older methods of counting. In those methods, generally, since a group with empty space inside of it may still be subject to being captured, the space in such a group, as well as the stones around that space, are not counted, which makes counting more complicated.

Otherwise, except for including that consideration, the Chinese method is similar to the Tromp-Taylor method, but with what is termed a cutting penalty, or, in modern English-language discussions, a group tax. Since it takes two open holes to keep a group alive on the board, for each unit of connected stones, leave two empty spaces when filling up the empty space.

The ancient Chinese method, still used in Japan, instead involves counting all the empty space in units of stones, but only the empty space. This can still be done by re-arranging stones; simply remember which spaces were empty in each individual group, and fill them while taking off or using the other stones. But with this method, every stone captured is also added to a player's score, so this means one has to take the pieces of the opposite color one has captured, count off as many stones of one's own color, and add them to the board to be counted.

The Japanese method has been criticized because it leads to difficulties in a few unusual situations, one being bent four in the corner; a player ends up being penalized for playing the stones that need to be played to prove a group is not subject to attack.

In the traditional Korean game of Sunjang Baduk, the stones on the edge of an area are not counted, but stones not on the edge are counted along with vacant spaces. No credit is given for captured stones.

Although the Japanese rule seems to be the only one criticized for leading to strange situations, there seems to be no consensus that switching to the Chinese rule, or the old Korean one, would fully solve the problem. Or to a modified Chinese rule without the group tax, or even to the simple rule given above as a starting point (since, if there is no penalty for playing stones within one's areas to prove they belong to you, the game can continue until both players agree, so there is no need for an outside authority to determine that an area is subject to capture). Instead, new rules are proposed which involve additional complications; for example, a set of rules called the Ing rules, which are designed to fully address this issue, requires the players to keep their stones in racks so that they can be sure of the exact number of stones they have in their supply.

The Different Starting Arrays

The diagram below:

gives information about different forms of the game played in different times and places.

In the top row of the image:

The first diagram shows the form of the game that was played in Tibet and in Mongolia. It used a 17 by 17 board, and before play started, a fixed array of stones was placed on the board in the manner shown. These initial stones were larger than the stones used for playing the game on the rest of the points. One rule was slightly different: placing a stone on any square from which one's stones were removed on the previous move, not just so as to cause the position to repeat, was prohibited.

Each player has 6 large stones for the initial array, and 144 small stones for regular play. This is somewhat larger than the number of stones required to cover the board.

(Some sources give an additional rule, requiring stones to be placed within two squares of either one of the initial stones of one's color, or the last stone played, but I am inclined to agree with the one which considers this to be simply a mistaken conclusion from watching amateur play.)

Because there is evidence that Wei Ch'i was originally played on a 17 by 17 board in China, it is possible that this is the last survival of the original form, or at least an earlier form, of the game as played in China. This is not certain, however, because there have been extensive direct cultural contacts between Tibet and Mongolia; for example, at one time the Mongolian language was written using the Tibetan writing system, and so some modifications either of the old 17 by 17 Chinese game (or even a new 17 by 17 game which derived from the Chinese 19 by 19 game) which originated in Tibet could then have been the form transmitted to Mongolia.

The fact that a similar starting array is used with the old Korean game, which we will encounter shortly, gives, in my opinion, the strongest reason to think that at least some aspects of an early Chinese game are preserved in the Tibetan form.

The second diagram shows the starting position used in China for Wei Ch'i up to the 1930s.

This starting position is not that much different from common opening moves in the current form of the game without any setup stones, and thus it may well have served its apparent purpose of guiding beginning players towards the right style of play without changing the character of the game.

This is illustrated by the first nine moves of one of the most famous games of Go ever played in Japan:

The third and fourth diagrams deal with Sunjang Baduk; this was the traditional form of this game in Korea, and it, too, was actively played up to the 1930s. The first of these two diagrams, the third in that row, shows the normal starting position. The odd black stone in the center is not part of the initial array set up before play, but instead the player with the black stones is required to make his first move to the center point.

A weaker player can play the black stones with a handicap of from one to eight stones. In the case of a one stone handicap, the black stone in the center is now part of the initial array, and black has a first move of placing an additional black stone on any vacant intersection on the board.

In the case of a handicap of two through eight stones, a white stone is placed on the center point, and the stones to be added as the handicap increases are numbered in the next diagram.

In Go as played in Japan, once the handicap stones are placed, the next move is made by the player with the white stones. After the arrangements as shown for the Korean game, the next stone played is a black stone. But this does not really mean that the rule for Korean handicap games in this respect is the opposite of the Japanese rule, because the diagram shown includes the white stone in the center of the board. Since in a game without a handicap, black moves first, but that move must be made in the center of the board, this move now goes to white when the handicap is of two or more stones.

If one assumes the rule that the first move of the game, whether by Black, or, after a handicap, by White, is played to the center position in order to reduce the advantage of the first move, then an extension to the handicap scheme of Sunjang Baduk suggests itself that would permit handicaps to be given in units of one-half of a stone.

With a handicap of one-half of a stone, Black obtains the first move, but is free to place the first stone anywhere instead of in the center.

With a handicap of one and one-half stones, Black receives the handicap stones for a two-stone handicap, but White is then free to place the first stone anywhere instead of in the center, and the same principle applies to the larger handicaps to decrease the handicap by half a stone.

It may be the placing of the first stone in the center, and not the dense initial array, that accounts for the observed fact that in Sunjang Baduk, unlike conventional Go, it is better to begin play in the center than on the edge.

In modern Go, a practice has been adopted of adding a certain number of points, most often 6 1/2 points or 7 1/2 points at present, to White's score in order to determine who will win. These points, known as komidashi, compensate for the advantage of the first move that Black has. When first introduced, the number of points involved was 2 1/2 or 3 1/2, but this was gradually increased over the years. The odd half-point has the effect of rendering draws impossible. The main purpose of komi was to prevent the player with the Black stones from achieving a certain win, usually by a margin of three stones, through defensive play. Because this means both players, not just White, need to play agressively and take risks in order to win, it produces a more exciting game.

It should also be noted that while traditionally the first few stones were placed in positions near to those of the old starting position for Wei Ch'i in China, and a starting move in the center was considered inferior, this is no longer the case, thanks to the development of a new style of openings by Wu Ch'ing-Yuan, known in Japan as Go Seigen.

In the second row of the image:

In Go, the Japanese form of the game, no stones are placed on the board for players to start from, except when a handicap is in effect. The four diagrams in this row show where stones are placed to give increasing handicaps.

The first diagram shows how stones for handicaps from one to five stones are placed.

The fifth stone is then moved so that the arrangements for a handicap of six stones can be more symmetrical, and so the arrangements for six and seven stones are shown on the second diagram. Then the seventh stone is again moved so that the arrangement for eight stones can be symmetrical, and so the third diagram shows the arrangements for eight and nine stones. The fourth diagram shows how the next four handicap stones, called furin, are added for a larger handicap.

In the third row of the image:

The first diagram shows how an additional group of four stones, the nakayotsu, are placed for a handicap of 17 stones, and then shows the positions of still another group of four stones for a 21-stone handicap. Subsequent diagrams illustrate the 13 by 13 board, and the placement of handicap stones on that board, and the 9 by 9 board, and the placement of handicap stones on it.

One web site about go showed a scheme for larger handicaps in which the nakayotsu were used later than shown above; on the page, there was a comment that perhaps this was the Chinese scheme of handicaps. An account of the history of Weiqi noted that the four initial stones were not in some handicap games played by professional players, to which one group of game records referred, and there was also a reference to placing a single stone for a handicap in the center of the board.

Thus, I first attempted to combine the information from the two sources on the basis of placing the first handicap stone in the center while leaving the setup stones present, and then for larger handicaps switching to the system currently in use in Japan, except for the changes for the very large handicaps.

Further thought, however, inclines me to suspect that there might have been two systems of handicaps used in China. One could have begun with a stone in the center, and then continued to larger handicaps retaining the four setup stones, in a fashion similar to Sunjang Baduk, and the other might have corresponded to the Japanese system, except perhaps for changes for the larger handicaps.

The diagram below shows what I am now thinking of: the top two diagrams show a possible system of handicaps with the setup stones in place, which might have been used most of the time, and the bottom two show the higher handicaps as used in some professional play, which used, for the other handicaps, the system still retained in Japan.

If the handicap system for the old game of Sunjang Baduk is known, I doubt that the older system for China has been forgotten, even if so far it has not turned up in my web searches.

Finally, through further searching, I have found that in one of the oldest surviving books about Wei Ch'i, Carefree and Innocent Pastime, games are recorded which give examples of the two, three, and four stone handicap arrangements shown below:

The five stone handicap, the same as in the modern Japanese game, is also attested to in that source. Since the four stones on the star points were used in China until the 1930s, and given that the use of the Japanese system of handicaps apparently was not universal, although there are records of games showing that it, or a similar system, was used, I had expected that a system of handicaps building upon the initial array existed in China until recently. However, I have now found out that the general present-day practice in China with handicap stones is to allow the player receiving the handicap to place them freely on the board; if this had been the practice in China for a long time, it would explain the absence of what I was looking for.

Above, I showed how the first nine moves of the most famous game of Go ever played illustrated a point that I had made.

It seems unfair to show the first nine moves of such a game without making available the rest of the game, the part in which interesting things happen.

43, 49 = 33
46, 263 = 40
232, 240, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 311 = 180
237, 243, 249, 255, 261, 267, 273, 279, 285, 291, 297, 303, 309 = 229
274 = 104
313 = 238
321 = 29
322 = 107
323 = 36
324 = 203
325 = 253

This game represents the first game of a young challenger against the established champion. The challenger has the first move, with the black pieces.

In the early part of the game, in the lower right corner of the board, the challenger is placed at a disadvantage as a result of being caught by a prepared variation used by the champion.

Move 127 is considered to be the most impressive move, not only in this game, but perhaps in all the Go that has been played. This is because, with a single move, the challenger had strengthened his position materially on three, and perhaps all four, sides of the board. The audience, however, at the time, did not recognize the importance of this move, and believed that the challenger was still at a disadvantage. However, one member of the audience was a physician, and he noted that the champion's ears had become flushed as a result of that move, indicating that the advantage had shifted.

This is, of course, the famous "Ear-Reddening Game", with Honinbo Shusaku as Black, and Gennan Inseki as White.

When We Heard About It

In 1908, the book "The Game of Go, the National Game of Japan", written by Arthur Smith, was published in the English language, and the author stated that to his knowledge, there was not another book about this game available in English at the time. However, he did note that there was a short description of the game in a book about Korean games by Stewart Culin, and an extensive description available to the West in German, from the year 1880, by Otto Korscheldt.

As well, the book "Historic China: and Other Sketches" by Herbert Allen Giles, published in 1882, included an account of the game Wei Ch'i as played in China.

Other books on Go soon followed, such as the book "Go and Go-Moku" by noted American chessplayer Edward Lasker in 1934, and "The ABC of Go, the National War Game of Japan" by Walter Augustus de Havilland (father of Olivia de Havilland and Joan Fontaine!) in 1910.

Even before 1880, however, the game of Wei Ch'i was not unknown in the West. A book about the history of Chess and Backgammon was published in England in 1694; this book was De Ludis Orientalibus, which consisted of two parts, De Historia Shahiludii and De Historia Nerdiludii. Wei Ch'i was discussed for six pages in the second part. This book, written by Thomas Hyde, was in Latin, however, not in English, and it is noted for its extensive use of quotations in Greek, Hebrew, and Arabic.

The description of Wei C'hi, given as Hoy Kî, is titled De Circumvienendi Ludo Chinesium, and begins on page 195 of the version of this book currently available from Google Books. It begins by noting that prior to the Jesuits arriving in China, previous descriptions of this game were imperfect and had discrepancies.

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