Version 2 / 2006-03-23-02
[relies on: semi-formal text version 35a / 2004-09-24]
There are the two players Black and White.
For a player, the opponent is the other player.
Each player uses stones of his colour.
The board is a grid of 19 horizontal and 19 vertical lines forming 361 intersections.
Two intersections are adjacent if there is a line but no third intersection between them.
The string of a player's stone on an intersection consists of this stone and any this player's stones that are connected via lines and intersections with this player's stones on.
A black string is a string consisting of black stones. A white string is a string consisting of white stones.
A liberty of a string is an empty intersection that is adjacent by a line to at least one stone of the string.
A position is the distribution of black stones and white stones on the grid's specific intersections.
Motivation: The third move type ko-pass is used in hypothetical sequences because there the hypothetical ko rule is used.
A playputs one stone of a player on an empty intersection.
Rule of Capture: A play removes the stone or stones of any opposing string or strings without liberty.
Rule of No Suicide: A player's play may not leave his own string without liberty. If the play involves capture, this is executed before the without liberty condition is verified.
A pass does nothing but lets the opponent make the next move. The player speaks: "Pass."
A ko-pass does nothing but lets the opponent make the next move. The player speaks: "Ko-pass."
A move is either a play, a pass, or a ko-pass.
Motivation: The extra phase analysis is necessary to determine life and death on that the scoring depends. Under Traditional Territory Scoring, the score does not simply depend on the stone colours. Rather in the position at the end of the alternation, there are four types of stones: alive black stones, dead black stones, alive white stones, dead white stones. Since dead stones do not distinguish themselves from alive stones by blinking, the analysis phase does that determination.
The game consists of the following in the given order:
The alternation is a sequence of moves that starts by Black from the empty grid, lets the players alternate moves, and ends when a player's pass is succeeded by his opponent's pass.
Rule of Available Move Types during the Alternation: During the alternation, plays and passes are available as moves.
Ko Rules during the Alternation
Motivation: Since Japanese style rules circumvent superko, long cycles have to be treated by different means - the long cycle rule. - The direct ko rule, the related terms direct environment and direct ko stone, and the stage of their determination in the major analysis procedure are nothing but an exception to agree to professional Japanese tradition even in scarce positions. One should note that this direct ko rule differs from the precedential direct ko rules in the Japanese 1949 Rules or the World Amateur Go Championship 1979 Rules because the move type ko-pass, the rule of legal ko-pass, and the hypothetical ko rule treat also the other kos that had been called direct in the past. Also one should not confuse the term direct ko stone in the Japanese 2003 Rules with a ko stone in what is informally called a direct ko in traditional Go theory. The former is rare - the latter is frequent.
Basic Ko Rule: A play may not recreate the position just before the last opposing move.
A cycle is a part of the alternation
Long Cycle Rule: If a cycle occurs, then exceptionally and immediately the game ends with the result
Motivation: Since each string has its own life and death status, at least as many status assignments are necessary as there are strings in the position at the end of the alternation. Since a string might not have the status that is determined first, other possible statuses might have to be checked for the string. In particular one has to check for uncapturable, capturable of the type "under the string", and capturable of the type "local to the string" before one can assess a string as dead. All this is necessary to agree to Japanese rules tradition. Simpler Territory Scorings concepts are known but would not always agree to the tradition. However nasty the major and minor analysis procedures might appear at first, the constant 361*6 is an upper bound of the complexity because there are fewer than 361 strings on the board and at most 6 status types might have to be checked per string. This constant complexity of the basic structure of the analysis is uncomparably better than the literally infinite complexity within each status check because of infinite numbers of legally possible hypothetical sequences and strategies that might have to be considered for an application of the term force.
The analysis determines for each string in the position at the end of the alternation if it is either alive or dead.
The Major Analysis Procedure: The analysis does the following in order:
Rule of Single Type: A string is not capturable of the type "under the string" if the string is uncapturable. A string is not capturable of the type "local to the string" if the string is either uncapturable or capturable of the type "under the string".
Life and Death
Motivation: Naively one could think that the three types of alive might be replaced by the one type to force a two eye formation. However, then all strings in sekis would be dead. Therefore all the three types of alive are necessary. - The major applications of capturable of the type under the string are in nakade or snapbacks. Capturable of the type local to the string is applied in some rather minimal shapes where one cannot force both a two eye formation and capturable of the type under the string because the latter would fill one of the two eyes. This is scarce but essential for including all forced two eye formations. Besides professional Japanese intuition perceived capturable of the type local to the string also in some scarce sekis, even though the Japanese professionals failed to define capturable of the type local to the string formally in general. They were only able to describe their intuition by means of precedential examples. In retrospect, this is not particularly surprising because the local environment is an object that might enjoy a topologist.
Determination If a String Is Uncapturable
A player's string is uncapturable if the opponent starts in hypothetical sequences and cannot force capture of the string's stones.
Determination If a String Is Capturable of the Type "Under the String"
A player's string is capturable of the type "under the string" if the opponent starts in hypothetical sequences and cannot force both capture of the string's stones and no permanent stone of the player on an intersection of the string.
Determination If a String Is Capturable of the Type "Local to the String"
Firstly for a player's string its local environment is formed starting with all the string's intersections. Then as long as possible any further adjacent intersection is included without a stone of a string that is of the player and either uncapturable or capturable of the type "under the string".
Secondly a player's string is capturable of the type "local to the string" if the opponent starts in hypothetical sequences and cannot force both capture of the string's stones and no permanent stone of the player on an intersection of the string's local environment.
Determination If a String Is a Direct Ko Stone
Firstly for a string its direct environment is formed starting with all the string's intersections. Then as long as possible any further adjacent intersection is included without a stone of a string that is of either player and either uncapturable or capturable of the type "under the string".
Secondly, a string is a direct ko stone if the string is a ko stone, is capturable of the type "local to the string", and its local environment and direct environment are unequal.
Definitions of Alive and Dead
The alive strings are the strings that are either uncapturable, capturable of the type "under the string", or capturable of the type "local to the string".
The dead strings are the strings that are not alive.
Motivation: Since it is not mandatory to continue the alternation if the position contains long cycle shapes, the position at the end of the alternation might contain some. Since hypothetical sequences may represent moves that a wise player would call weak and other moves that he would call strong, long cycles can occur even regardless of shapes in the position at the end of the alternation. Professional Japanese tradition has chosen to treat long cycles in hypothetical sequences by simply allowing them to be of infinite length. The question is not whether this makes sense but how an infinite hypothetical sequence is to be interpreted. Since it contains some infinitely recurring cycle, it is enough to watch it once and to know that it does recur forever. E.g., if a string is not captured when the cycle is executed once, then it is also not captured during infinite recurring. Likewise one can detect if a permanent stone occurs due to an infinite hypothetical sequence.
A hypothetical sequence is an imagined sequence of moves that starts from the position at the end of the alternation and lets the players alternate moves.
Rule of Available Move Types during a Hypothetical Sequence: During a hypothetical sequence, plays, passes, and ko-passes are available as moves.
Rule of Length of a Hypothetical Sequence: A hypothetical sequence is of either finite or infinite length. If it is of finite length, then it ends when a player's pass is succeeded by his opponent's pass. If it is of infinite length, then a player's pass is never succeeded by his opponent's pass.
A permanent stone is a stone that is played during a hypothetical sequence and then not removed during the rest of the hypothetical sequence.
Motivation: While the basic ko rule can be written shortly without reference to the shape ko, the ko terms are really helpful for a reasonable wording of the ko rules during a hypothetical sequence.
A ko consists of two adjacent intersections so that a play on one of them succeeded by a play on the other one would recreate the position.
A ko stone is a string on one intersection of a ko.
A ko capture is a play that is in a ko and removes exactly one stone.
Ko Rules during a Hypothetical Sequence
Motivation: Japanese rules tradition in some rare shapes like a position with both a double ko death and a basic teire ko or a position with a triple ko with one eye and one external ko is the reason why the basic ko rule would not always create the desired scoring effect during the analysis. With the exceptional move type ko-pass and the ko rules during a hypothetical sequence, this becomes possible. - There is some freedom about the details of those ko rules because they are more precise than Japanese rules tradition has caused troublesome precedents. Nevertheless, rules design is not completely free here and the pass for a particular ko and by a particular player rule of the Japanese 1989 Rules would be a failure with respect to describing the professional Japanese traditional scores in some scarce or rare shapes.
Rule of Legal Ko-pass: A player may make a ko-pass only if a ko capture by the player in some ko is currently available but prohibited.
Hypothetical Ko Rule: A player may not make a ko capture on one intersection of a ko if since his opponent's last ko capture on the other intersection of the ko neither the player nor his opponent has made any ko-pass.
Rule of Application of Ko Rules during a Hypothetical Sequence: The rule of legal ko-pass and the hypothetical ko rule are applied only within each hypothetical sequence.
Motivation: Every strong kyu or dan player has an intuitive understanding of force because he knows what a forcing move is. However, defining force precisely is a demanding task because it depends on strategy for that a formal definition requires mathematical insight. This informal text of the Japanese 2003 Rules makes a compromise but avoids the cardinal mistake of the Japanese 1989 Rules that try to hide the infinite strategic complexity of the life and death analysis behind a word of grammar: "cannot". The Japanese 2003 Rules separate grammar from rules contents: "cannot force", which, e.g., is the usage in the definition of the term uncapturable. - For force, the opponent needs at least one strategy; it does not hurt if he has several strategies that achieve the aim, i.e. the something. The player, when answering the opponent's strategy, may consider every possible answer as a refutation; finding one refutation is enough but finding several refutations does not hurt. - Different equivalent definitions of strategy are possible. The text uses a short one. To understand it, one should recall that strategy is about making decisions for one's moves now or after some possible parts of hypothetical sequences. To represent when and in which position a move decision is made, simply the part of a hypothetical sequence is included in the collection that forms the strategy, that part that leads to the moment when and the position in that the move choice is made. The rules of one move choice then ensures that each such move choice provides only one move - the opponent has to choose exactly which move he makes after the considered part of a hypothetical sequence. - The rule of completeness ensures that the opponent behaves like an omniscient player that reads ahead all legally possible hypothetical sequences and makes a move choice for all theoretically possible parts of hypothetical sequences. This is unlike human Go players that make not more than maybe 1000 decisions of strategy at a time - it is like God solving Go completely at once. This is the way Japanese rules tradition works during the analysis, although it does not advertise with this feature and rather tries to hide it by showing only one hypothetical sequence in a solution diagram of a scoring example position. Also for that reason, the official commentary on the Japanese 1989 Rules contains strategic mistakes; too easily they occur unless all hypothetical sequences are considered. The latter is done by the Japanese 2003 Rules. - For the convenience of the reader of this informal text version, "opponent" is used consistently with the same function as it is applied in the Life and Death section. This is unlike the semi-formal version of the rules, where "player" and "opponent" are used locally within each term's definition. For the same reason, the starting player is shifted to the Life and Death section's definitions.
A player's opponent can force something if the opponent has at least one strategy so that that something is fulfilled regardless of the player's chosen hypothetical sequence.
An opponent's strategy is a collection of parts of hypothetical sequences that end with a move of his.
Rule of One Move Choice: An opponent's strategy may not contain two parts of hypothetical sequences so that they without their last move are equal.
Rule of Completeness: An opponent's strategy may not omit yet another part of a hypothetical sequence that ends with a move of his and follows the rule of one move choice.
Rule of Answer: The player may choose only such hypothetical sequences that answer the opponent's strategy.
Rule of Search: As long as a suitable strategy is not found but a further strategy is possible, that further strategy also has to be considered. As long as a suitable answer hypothetical sequence is not found but a further answer hypothetical sequence is possible, that further answer hypothetical sequence also has to be considered. Infinite numbers of strategies and hypothetical sequences might have to be considered.
Rule of Application for Force: For each application of force to something, possible strategies and hypothetical sequences are determined afresh.
Motivation: The terms black eye string and white eye string are necessary because dead stones are not removed miraculously but score twice, what is equivalent to the traditional Japanese counting method that removes them and then fills them or subtracts them if they cannot be filled. Before the traditional Japanese counting method could remove dead stones, one first has to determine that they may be removed because of being in territory. - The steps 3 - 10 and the terms therein are only necessary to create the traditional exception that sekis do not have territory. Otherwise those steps and terms could be omitted and black eye points and white eye points could simply be renamed as black territory and white territory.
The Scoring Procedure: For the position at the end of the alternation, the scoring does the following in order:
An intersection of a black eye string is a black eye point if the black eye string is only adjacent to intersections with stones of alive black strings. An intersection of a white eye string is a white eye point if the white eye string is only adjacent to intersections with stones of alive white strings.
An eye point is either a black eye point or a white eye point.
A dame is an empty intersection that is not an eye point.
A black region is formed starting from an intersection with a stone of an alive black string and then as far as possible by also including any adjacent intersection that has a stone of an alive black string or is a black eye point. A white region is formed starting from an intersection with a stone of an alive white string and then as far as possible by also including any adjacent intersection that has a stone of an alive white string or is a white eye point.
A black region or white region is in-seki if at least one of its intersections is adjacent to a dame.
An intersection is black territory if it is a black eye point that is not part of an in-seki black region. An intersection is white territory if it is a white eye point that is not part of an in-seki white region.
The prisoner difference is the number of white stones minus the number of black stones that are removed during the alternation.
The score is
The result is either a tie, a win of Black, or a win of White if the alternation ends and the score is either equal to, greater than, or smaller than zero, respectively. The long cycle rule creates an exception.