2004-09-02-02 newest contents, 2006-03-23 last update, 2004-06-25 first day, Robert Jasiek

INDEX | GO | RULES |
JAPANESE 2003 rules - COMMENTARY - INFORMAL
NEW AMATEUR-JAPANESE rules - COMMENTARY

Commentary on the New Amateur-Japanese Rules

[Copyright: Optional tournament rules: like for the Japanese 2003 Rules. Rest of this page: Robert Jasiek]

Optional Tournament Rules Modules
Concept of the New Amateur-Japanese Rules +++NEW+++
Acknowledgements
Remarks on the Rules of Play
Remarks on the Optional Tournament Rules Modules
Abbreviations
Success
No Further Simplification
No Unnecessary Complication
Legend
Basic Commentary on Particular Rules +++NEW+++
Advanced Commentary on Some Rules Details +++NEW+++
Easy Examples for Control
Examples for NAJ or NAJN with Unexpected Scores
Examples for NAJ or NAJN with Long-cycle-tie under NAJN
1000-year Kos+++NEW+++

Optional Tournament Rules Modules

No-result

During the alternation, the fixed-ko rule does not apply. During the alternation, if a play recreates an earlier position and if the players agree, then the game ends exceptionally and immediately with the result tie. This is also called "no-result". If the same cycle recurs very many times, then the players have to agree as mentioned before.

Agreement versus Disagreement

If the players agree during the black-analysis, the white-analysis, and the result, then

1) the black-analysis and the white-analysis are hypothetical only,
2) the players count the score,
3) the players determine the result,
4) the players make the result-agreement.

If the players disagree until the result-agreement, then they

1) interrupt the normal procedure,
2) restore the final-position and the prisoners at it,
3) copy the final-position to two extra boards,
4) use one of the extra boards to perform the black-analysis,
5) use the other extra board to perform the white-analysis,
6) determine the intersections that Black controls,
7) determine the intersections that White controls,
8) determine the score,
9) determine the result,
10) make the result-agreement due to the determined result.

Resumption

If the players disagree until the result-agreement, then they enhance the disagreement procedure by inserting the following procedure in between (2) and (3):

A) The two successive passes at the end of the alternation are cancelled.
B) The alternation continues with the opponent of the last play's player. For ko restrictions, the alternation and the resumed alternation are treated together as one move-sequence.

Concept of the New Amateur-Japanese Rules

Purposes of the New Amateur-Japanese Rules

The New Amateur-Japanese Rules serve the following purposes:

The rules are logical: They are complete, can always be applied, and do not have any contradiction.
The rules can be applied as rules: Executing the rules' application requires sufficiently little time so that execution is possible in the practice of tournament games.
The rules can be understood: Players and referees can understand them if only they read them carefully. The rules are not so difficult that the average player or referee would fail because of the rule text's complexity.
The rules are Japanese style rules: Generally strategy under the rules behaves as one would expect from Japanese rules tradition.
The rules are suitable for amateurs: Simplicity of the rules is considered more important than precedental exceptions, which virtually no one would remember anyway.

Comparison with Other Rulesets

The Japanese 1989 Rules: Currently they are the rules used by the Japanese professionals, however, they are illogical, cannot be applied as rules, cannot be understood, and are not suitable for amateurs.
The World Amateur Go Championship Rules: They are illogical, cannot be applied as rules, cannot be understood, and are not suitable for amateurs.
The Japanese 2003 Rules: They describe professional Japanese rules tradition as well as anyhow possible, however, they cannot be applied as rules, cannot be understood by the average player or referee, and are not suitable for amateurs.
The New Amateur-Japanese Rules modified to approach tradition more closely: They could hardly be applied as rules and cannot be understood by the average player or referee.
Area Scoring rulesets: One of the great advantages (other advantages shall not be discussed here) of Area Scoring rulesets is that there is a direct correlation between the visual appearance of the (played-out) final-position and the score. This can never be achieved by Territory Scoring rulesets like Japanese style rulesets, regardless of how or how far they might be simplified. Hence one cannot set the aforementioned correlation as a purpose of the New Amateur-Japanese Rules; it could not be fulfilled.

Control Replaces Life and Death

Traditionally Japanese style rules used concepts of "life and death" to specify scoring intersections. In rules, life and death has a very severe disadvantage: Its definition and hence its practical determination are the most complex.

The New Amateur-Japanese Rules use the concept of "control" to specify scoring intersections. Control relies on a player's ability to establish "immortal" stones, i.e. to fill parts of the board with two-eye-formations. This is simple.

Why is life and death complex while control is simple? Life and death can be determined hypothetically only; otherwise filling stones in one's territories would cost points. Hypothetical means that each theoretically possible move-sequence must be considered. - Control can be determined practically because each of Black's control and White's control is determined by only one considered move-sequence. The practically executed performance allows the players to understand why intersections are controlled or not controlled.

Acknowledgements

Ikeda Toshio: used the word "immortal" first
Robert Jasiek: designed and tested the rules and invented the "fixed-ko" rule
Robert Pauli: invented a concept of the kind "control" first
Winfried Borchardt: invented the concept of analysis that can be played out as one move-sequence by the players and does not use pass stones

Remarks on the Rules of Play

Ko rules: Amateur-Japanese rules tradition wants to avoid superko by all means. Therefore the basic-ko rule is used. Analysis play must be finite so that it can be performed in practice. The fixed-ko rule ensures this very well. For consistency, it is natural to apply it during the alternation, too. It allows beginners to test sending-2-returning-1 once.
Two passes end alternation: Amateurs are more used to two than to three passes ending the alternation. (Besides two passes ending the alternation have the advantage that, if the optional tournament rule No-result is used, in a double-ko-seki neither player can force a long cycle tie but it would occur only if both players cooperate. This agrees to tradition, although most amateurs would not even be aware of that. That position is so rare that this fine difference does not really matter; it is just a nice side-effect.)
Three passes end an analysis: This allows dissolution of some so called direct-kos and dead-kos and avoids ko-passes as a third move type and rules for them.
Control: The combination of three ending passes in an analysis, the basic-ko rule, the fixed-ko rule, the two analyses, and the concept "controls" models traditionally expected outcomes very well. This has been verified for a broad variety of test examples. E.g., neither player controls anything in so called sekis.
One move-sequence per analysis: The combination of "controls", "immortal", and one move-sequence per analysis models life and death as simply as anyhow possible. One could make the rules more or even arbitrarily complicated but the effect could hardly be measured at all. E.g., adding a concept of "surrounded" would make the rules considerably longer and does not even improve them if the players play dame, teire, dame kos, and points of value during the alternation or - due to a tournament rule - during the resumed alternation.
Two analyses: Using two analyses instead of one analysis is fair because always the opponent starts. If all dame, teire, dame kos, and points of value are played during the alternation, then two versus one analyses makes a difference only in rare positions. However, it fits the thinking of those amateurs used to Japanese style rules better.
Control by both players: If all dame, teire, dame kos, and points of value are played during the alternation, then intersections controlled by both players are rare in playing practice. It is hard to construct some and none has been discovered so far where the score would differ and the players should have ended the alternation.

Remarks on the Optional Tournament Rules Modules

No-result: Beginners may make the strategic mistake to play the sending-2-returning-1 cycle. Otherwise on average the rule becomes relevant at most once during an amateur player's lifetime. The following positions are accordingly rare: double-ko-seki + fighting-ko, triple-ko, n-tuple-ko, eternal-life, round-robin-ko, other shapes with a long cycle with the captures difference zero. Probably most players weaker than 3 kyu would neither know the rule nor have seen one of those positions in literature. A rule that is applied so rarely creates more disputes than it solves. Celebration of those positions does not need the rule. Its purpose is tradition for the sake of tradition.
Agreement versus Disagreement: This rule is recommended. In almost all practical games, the players have agreement. In the rare games with disagreement, the procedure is precise and its restriction to one move-sequence in each of the black-analysis and the white-analysis makes it very practical and useful. Thereby analyses of complete, hypothetical game trees is avoided.
Resumption: This rule allows disagreeing players to play still unplayed dame, teire, dame kos, or forgotten points of value. Since disciplined players can fill such during the alternation, resumption is useful only for maintaining a tradition of allowing a player to fill dame and teire somehow during the counting instead of alternately during the alternation. Resumption is not recommended for international tournament rules because there the trend goes towards alternate filling.

Abbreviations

NAJ = the New Amateur-Japanese Rules
NAJN = NAJ + the tournament rules module No-result
NAJD = NAJ + the tournament rules module Agreement versus Disagreement
NAJR = NAJ + the tournament rules module Resumption.
AJT = post-1949 amateur-Japanese go rules tradition
J2003 = the Japanese 2003 Rules (in their latest version)

Success

There have been the following proposals as models for amateur-Japanese go rules and they have the listed major weaknesses (possibly from the view of AJT):

American Go Association 1991 Rules with territory scoring and without the rule that White makes an extra last pass: The rules have not been studied with a broad variety of test examples. Usage of pass stones leads to too many pass fights. Superko is used.
Ikeda Territory Rules II: The rules have not been studied with a broad variety of test examples. Usage of pass stones might lead to too many pass fights. Superko is used.
Lasker-Maas Rules: The rules have not been studied with a broad variety of test examples. Usage of pass stones leads to too many pass fights. Superko is used.
Spight Territory Rules: The rules have not been studied with a broad variety of test examples. Usage of pass stones might lead to too many pass fights. Superko is used.
Logical Japanese Rules of Go: The rules have not been studied with a broad variety of test examples. Practical application of the rules is too complex. The ko rules are too strange even though they work. Undesired behaviour in some positions is considerably more frequent than being rare.
Various descriptions for beginners: The rules have been very incomplete. They have not been studied with a broad variety of test examples. Their practical application would be too complex if they were made complete.

In comparison, NAJ and NAJN have the following features:

On a level of semi-formality, the rules are complete.
The rules have been studied with a broad variety of test examples.
The rules have unexpected behaviour only in rare or very rare positions.
Practical application of the rules is possible very well.
Pass stones are not used and so there are not too many pass fights.
The ko rules are only slightly unfamiliar.

NAJ and NAJN are the first complete rulesets ever that are both applicable and strategically close enough to AJT so that they can be used honestly as the amateur-Japanese rules!

No Further Simplification

Some aspects of NAJ are not simplified further for the following reasons:

Ko rules: Superko does not replace the combination of the basic-ko rule and the fixed-ko rule because the majority opinion among AJT does not like superko.
Analysis: The two analyses (black-analysis and white-analysis) are not unified as one analysis because then some positions that are not rare but already scarce would have unexpected behaviour. The most prominent example is a position with a bent-4-in-the-corner and a big seki, which would serve for at least one ko threat, elsewhere on the board; an exchange would take place during the analysis. (For reference, under Area Scoring rules such an exchange occurs.)
Passes: Three and not just two passes end the move-sequence of an analysis so that, e.g, so called dead-kos can be removed without filling one's own eye as the possibly only available type of ko threats.

No Unnecessary Complication

NAJ does not include any unncessary concepts.

Strategic concepts like "life and death" are not included. Otherwise the rules and especially their application would be extremely more complicated. It is the right of the players to develop strategy and not the task of the rules to prescribe it.
Precedents: Like it was done for the Japanese 1949 Rules, the World Amateur Go Championship Rules, etc., some might be tempted to treat the few, rare positions with unexpected behaviour under both NAJ and NAJN (and although AJT fails to score most of them anyway) by special rulings or by making the rules much more complicated. For which purpose? The effect would just be new side-effects of every "treatment" in other positions, which then would require yet further exceptional rules. It is overdue to end vicious circles in rules design. Everybody admires tesujis. Why not admire the strategic excitement in those positions with unexpected behaviour, too?

Legend

General

Positive scores are favourable for Black. Negative scores are favourable for White.
For a final-position and unless stated otherwise, the prisoner-difference zero is assumed.

Diagrams

# = intersection with black stone
O = intersection with white stone
. = empty intersection
A blank space separates horizontally adjacent intersections.
A line break separates adjacent grid lines vertically.
a,b,c... = denoted intersections

`Sequences`

[] = move-sequence (or a part of it) of alternating moves of both players
#[] = Black moves first
O[] = White moves first
x = move on intersection x
p = pass
t = tenuki (possibly on an imagined bigger board) or intersection t
[xy..] = obvious part omitted
[]* = repeated infinitely
[][] = move-sequence followed by another move-sequence
[]*[] = the first part is repeated several times
[..xy] = beginning of the alternating-sequence omitted; however, the obvious ".." is often omitted.
#[abcppp] = Black plays at a, then White plays at b, then Black plays at c, then White passes, then Black passes, then White passes.

Basic Commentary on Particular Rules

This section provides a basic commentary on the New Amateur-Japanese Rules. Trivial aspects, which every go player should know or understand immediately, are not treated.

Ko Restrictions

Japanese style rules reject the superko rule in practice. Therefore the superko rule is not used as the one and only ko rule. Instead the next simplest complete ko restrictions are used: the combination of the basic-ko rule and the fixed-ko rule. This combination is not as simple as the superko rule would be as a rule. On the other hand, in complex kos strategy is simpler under this combination because generally superko-like strategy does not occur. Instead generally the fixed-ko rule makes all strategy in complex kos trivial: Not fighting a complex ko is correct in most practical cases.

The Basic-ko Rule

"A play may not recreate the position just before the last opposing move."

The only shape in that this rule needs to be applied is the basic ko shape, which is a ko that consists of two adjacent intersections. A position might contain several basic kos but the rule becomes relevant only if in the same basic ko a play captures a stone and then immediately the next play would recapture that stone.

(1)

position with Black to move

. . . . . .
. . # O . .
. # O . O .
. . # O . .
. . . . . .

position after Black play 1

. . . . . .
. . # O . .
. # . # O .
. . # O . .
. . . . . .

position after prohibited White play 2

. . . . . .
. . # O . .
. # O . O .
. . # O . .
. . . . . .

The White play 2, which would capture a stone in the basic ko, is prohibited. It would recreate the position just before the last opposing (black) move 1; this is prohibited by the basic-ko rule. Currently White has to make a different move.

(2)

position with Black to move

# # # # #
. # O # O
# O . O .
O O O O O

position after Black play 1

# # # # #
. # . # O
# O # O .
O O O O O

prohibited play P for White

# # # # #
. # P # O
# O # O .
O O O O O

Currently the basic-ko rule prohibits White to play at the intersection P. Instead White might play in the left basic ko or pass.

The Fixed-ko Rule

"A play is prohibited if the positions just before and just after it are the same and in the same order as the positions just before and just after an earlier play of the same move-sequence. "

For the rule to apply, some positions must be recreated. Otherwise there is no possibility that the rule might apply usefully. Recreated positions are rare; therefore almost always one can ignore the rule entirely. The following examples show some rare shapes with repetition nevertheless.

(1)

position with Black to move

. # # . O
# O O O O
. O # # #
O O # . #
# # # # .

position after Black play 1

. # # . O
# O O O O
# O # # #
O O # . #
# # # # .

position after White play 2

O # # . O
. O O O O
. O # # #
O O # . #
# # # # .

position after Black play 3

. # # . O
# O O O O
. O # # #
O O # . #
# # # # .

The fixed-ko rule does not prohibit Black's play 3: The position before the play 3 and the position before the play 1 are not the same. The rule does not prohibit that the position after the play 3 and the position before the play 1 are the same.

position after White pass 4

. # # . O
# O O O O
. O # # #
O O # . #
# # # # .

The fixed-ko rule applies only to plays, not to passes. Therefore White is not prevented from passing.

position after prohibited Black play 5

. # # . O
# O O O O
# O # # #
O O # . #
# # # # .

The fixed-ko rule prohibits Black's play 5: The position before the play 5 and the position before the play 1 are the same. Furthermore the position after the play 5 and the position after the play 1 are the same. The fixed-ko rule prohibits that both the positions before two plays and the positions after these are the same. In other words, as soon as a position recurs, the next play may not start recycling on the same intersection again.

In practice in the alternation, during the played cycle Black has lost more captured stones than White. Therefore it was a strategic mistake of Black to start the cycle. He might have passed immediately.

(2)

position with Black to move

# # # # #
. # O # O
# O . O .
O O O O O

position after Black play 1

# # # # #
. # . # O
# O # O .
O O O O O

position after White play 2

# # # # #
O # . # O
. O # O .
O O O O O

position after Black play 3

# # # # #
O # . # .
. O # O #
O O O O O

position after White play 4

# # # # #
O # O # .
. O . O #
O O O O O

position after Black play 5

# # # # #
. # O # .
# O . O #
O O O O O

position after White play 6

# # # # #
. # O # O
# O . O .
O O O O O

prohibited plays for Black

# # # # #
. # O # B
# O P O #
O O O O O

Black may not play at B because of the basic-ko rule.

The fixed-ko rule prohibits P because otherwise the positions before the play 1 and before the play 7 at P would be the same and the positions after the play 1 and after the play 7 at P would be the same.

Hence Black passes:

position after Black pass 7

# # # # #
. # O # O
# O . O .
O O O O O

position after White pass 8

# # # # #
. # O # O
# O . O .
O O O O O

Note: Strategically, the fixed-ko rule lets many complex ko shapes be fixed. Playing a cycle is legal but futile. Black might have passed with his move 1 and the result would be the same. In a triple ko, generally the player with initially more ko liberties wins the triple ko.

The Game

A Naive Approach

A player not caring for rules might think: First there is the alternation, then we have the result. Let us consider an example and see how this would work:

Example on a 5x5 board:

empty grid

. . . . .
. . . . .
. . . . .
. . . . .
. . . . .

alternation with Black moving first

. . . . .
7 3 1 5 11
8 6 2 4 12
. . 10 . 9
. . . . .

13 = pass, 14 = pass

position at the end of alternation

. . . . .
# # # # #
O O O O O
. . O . #
. . . . .

Result: White wins by 5 points.

Such a naive approach looks simple. Actually it is too simplistic. Why? It is entirely unclear how the result is determined from the position at the end of the alternation. The rules must specify such.

Naive Scoring

Let us be a little less naive: Now we identify the scoring intersections before we state a result.

position at the end of alternation

. . . . .
# # # # #
O O O O O
. . O . #
. . . . .

intersections scoring for Black B

B B B B B
# # # # #
O O O O O
. . O . #
. . . . .

points per scoring intersection for Black

1 1 1 1 1
# # # # #
O O O O O
. . O . #
. . . . .

Black has 5 points.

intersections scoring for White W

. . . . .
# # # # #
O O O O O
W W O W W
W W W W W

points per scoring intersection for White

. . . . .
# # # # #
O O O O O
1 1 O 1 2
1 1 1 1 1

White has 10 points. The intersection that scores for White and has a black stone on scores 2 points for White.

Score: The score is 5 - 10 = -5, i.e. 5 points for White.

Result: White wins.

The calculation has already been pretty convincing, has it? As far as the numerical calculation for itself is concerned - yes. However, how could we know which intersections do score for Black or White? We have guessed only. Rules must be more objective than such.

The Purpose of Control, Black-analysis, and White-analysis

The term "controls" has a clear purpose: It specifies those intersections that might contribute to a player's score.

The "black-analysis" determines the intersections Black controls. The "white-analysis" determines the intersections White controls.

Now we understand why the process of the game contains the "black-analysis" and the "white-analysis" and why these are in between the alternation and the result. Accordingly the rules define the term "game":

"The game consists of the following in the given order:

1. the alternation
2. the black-analysis
3. the white-analysis
4. the result "

Immortal

"In a position, those stones of a player are immortal that are not removed in a move-sequence that starts by the opponent and in that the player always passes."

In other words, stones of a player are "immortal" if they cannot be removed even if the opponent makes as many successive legal plays as he likes.

(1)

. # . # O . O # O . # .
# # # # O . O # # # # #
O O O O O . . . . O . .

All black stones are immortal. White, who starts, might try to remove some of them but would fail:

. # . # O . O # O . # .
# # # # O . O # # # # #
O O O O O . . 1 3 O 5 7

The moves 2, 4, 6 are passes. Due to the no-suicide rule White cannot occupy the last liberties of the black stones.

(2)

. . O .
. O O O

The white stones are not immortal. Black, who starts and chooses well, can remove them as follows:

. 1 O 5
3 O O O

The moves 2 and 4 are passes. By the definition of "immortal", White is obliged to pass. Black succeeds in removing the white stones. Therefore they are not immortal.

Control

There are two types of control: 1) Black control, 2) White control.

The final-position, i.e. the position at the end of the alternation, is the one and only position in that the players can control intersections. It is necessary only in the final-position since that position defines the score of the game.

Black Control

"In the final-position, Black controls an intersection if the black-analysis ends with immortal stones of Black on the intersection or on all its adjacent intersections."

The black-analysis determines which intersections are controlled by Black.

During the black-analysis, the players decide their strategy. However, naturally Black wants to maximize his score on the board while White wants to minimize Black's score.

(1)

In this example, passive strategies are used during the black-analysis.

final-position

. . . . .
# # # # #
O O O O O
. . O . #
. . . . .

black-analysis

4 . 2 . 6
# # # # #
O O O O O
. . O . #
. . . . .

The moves 1, 3, 5, 7, 8, 9 are passes.

position at the end of the black-analysis

# . # . #
# # # # #
O O O O O
. . O . #
. . . . .

Black control B

B B B B B
B B B B B
O O O O O
. . O . #
. . . . .

For Black to control some intersection, Black must have occupied the intersection with an immortal stone or must have immortal stones on each of its adjacent intersections. In other words, to control a region of the board, Black must have filled it with his stones or ponnukis.

application of the Black control for the Black score

1 1 1 1 1
# # # # #
O O O O O
. . O . #
. . . . .

In the position at the end of the black-analysis one sees which intersections Black controls in the final-position. Accordingly such intersections can score for Black in the final-position: 1 point if they are empty, 2 points if they are occupied by white stones.

(2)

In this example, aggressive strategies are used during the black-analysis.

final-position

. . . . .
# # # # #
O O O O O
. . O . #
. . . . .

black-analysis

8 3 1 4 .
# # # # #
O O O O O
7 6 O . #
. 5 2 . .

10 is played at 1. The moves 9, 11, 12, 13 are passes.

position at the end of the black-analysis

# . # # .
# # # # #
O O O O O
O . O . #
. O # . .

Black control B

B B B B B
B B B B B
O O O O O
. . O . #
. . . . .

Black controls the same intersections of the final-position as in example (1).

For the final-position, only one black-analysis is performed. It depends on the players which strategies they choose. The Black control is determined at the end of that black-analysis that they play.

White Control

"In the final-position, White controls an intersection if the white-analysis ends with immortal stones of White on the intersection or on all its adjacent intersections."

The white-analysis determines which intersections are controlled by White.

During the white-analysis, the players decide their strategy. However, naturally White wants to maximize his score on the board while Black wants to minimize White's score.

(1)

In this example, passive strategies are used during the white-analysis.

final-position

. . . . .
# # # # #
O O O O O
. . O . #
. . . . .

white-analysis

. . . . .
# # # # #
O O O O O
4 . O 8 #
. 6 2 . 10

The moves 1, 3, 5, 7, 9, 11, 12, 13 are passes.

position at the end of the white-analysis

. . . . .
# # # # #
O O O O O
O . O O .
. O O . O

White control W

. . . . .
# # # # #
W W W W W
W W W W W
W W W W W

For White to control some intersection, White must have occupied the intersection with an immortal stone or must have immortal stones on each of its adjacent intersections. In other words, to control a region of the board, White must have filled it with his stones or ponnukis.

application of the White control for the White score

. . . . .
# # # # #
O O O O O
1 1 O 1 2
1 1 1 1 1

In the position at the end of the white-analysis one sees which intersections White controls in the final-position. Accordingly such intersections can score for White in the final-position: 1 point if they are empty, 2 points if they are occupied by black stones.

(2)

In this example, aggressive strategies are used during the white-analysis.

final-position

. . . . .
# # # # #
O O O O O
. . O . #
. . . . .

white-analysis

. . 2 . .
# # # # #
O O O O O
5 6 O 7 #
. 4 1 3 8

intermediate position during the white-analysis

. . O . .
# # # # #
O O O O O
# O O . .
. O . . O

continued white-analysis

. 12O 13.
# # # # #
O O O O O
# O O 1810
14O 169 O

The moves 11, 15, 17, 19, 20, 21 are passes.

position at the end of the white-analysis

. O O # .
# # # # #
O O O O O
. O O O O
O O O . O

White control W

. . . . .
# # # # #
W W W W W
W W W W W
W W W W W

Despite aggressive play by both players, White controls the same intersections of the final-position as in example (1).

For the final-position, only one white-analysis is performed. It depends on the players which strategies they choose. The White control is determined at the end of that white-analysis that they play.

Agreement versus Disagreement

Now that we have some idea how the "game" proceeds and what "immortal" and "control" are, we can learn how the "black-analysis" and the "white-analysis" are performed in an actual game. Strictly following the New Amateur-Japanese Rules, one would perform the black-analysis and the white-analysis in each game. However, there are useful tournament rules that distinguish between agreement and disagreement. In most practical games, the players would agree and can follow the procedure for agreement. Only in games with, say, difficult positions on the board, the players would disagree and follow the procedure for disagreement.

Agreement

"If the players agree during the black-analysis, the white-analysis, and the result, then

1) the black-analysis and the white-analysis are hypothetical only,
2) the players count the score,
3) the players determine the result,
4) the players make the result-agreement."

The especially noteworthy aspect here is that the black-analysis and the white-analysis are not performed in practice. Instead as soon as the alternation reaches its final-position, the players count the score and determine the result immediately.

Example without prisoners during the alternation:

final-position

. . . . .
# # # # #
O O O O O
. . O . #
. . . . .

intersections scoring for Black

1 1 1 1 1
# # # # #
O O O O O
. . O . #
. . . . .

intersections scoring for White

. . . . .
# # # # #
O O O O O
1 1 O 1 2
1 1 1 1 1

Score = 5 - 10 = -5. White has 5 points more than Black.

Result: White wins.

Typically, the players would use some mechanical counting procedure for determination of the score. E.g. they might use the Japanese counting, which removes opposing stones from scoring intersections, fills in all prisoners, and rearranges scoring territories in multiples of 10 or 5.

Disagreement

"If the players disagree until the result-agreement, then they

1) interrupt the normal procedure,
2) restore the final-position and the prisoners at it,
3) copy the final-position to two extra boards,
4) use one of the extra boards to perform the black-analysis,
5) use the other extra board to perform the white-analysis,
6) determine the intersections that Black controls,
7) determine the intersections that White controls,
8) determine the score,
9) determine the result,
10) make the result-agreement due to the determined result."

Whatever the players might already have done before they find out about their disagreement, they restore the alternation's final-position and start from there. The essential aspects of the disagreement procedure are the performance of the black-analysis and the white-analysis. The are performed to see which intersections Black controls and which intersections White controls, respectively. The final-position is kept on the regular playing board and two extra boards are used to duplicate the final-position. The black-analysis is then performed on one of the extra boards and the white-analysis is performed in the second extra board.

Example without prisoners during the alternation:

final-position

. . . . .
# # # # #
O O O O O
. . O . #
. . . . .

Suppose that the players start counting using the Japanese counting procedure. They might rearrange the stones as follows:

Japanese counting with some mistake

. . . . .
# # # # #
O O O O O
O . . . .
. . . . .

Now we assume that the players make the mistake of not recalling whether they have already filled in the one black prisoner stone. They disagree. This invokes the disagreement procedure.

Step 1) The normal procedure is interrupted.

The players do not continue with the normal procedure. Instead they start the disagreement procedure.

Step 2) The players restore the final-position and the prisoners at it.

final-position

. . . . .
# # # # #
O O O O O
. . O . #
. . . . .

The players restore the final-position as it arose at the end of the alternation. The players also restore the prisoners, but in this case there have been none that were made during the alternation.

Step 3) The players copy the final-position to two extra boards.

final-position copy 1 copy 2

. . . . .        . . . . .        . . . . .
# # # # #        # # # # #        # # # # #
O O O O O        O O O O O        O O O O O
. . O . #        . . O . #        . . O . #
. . . . .        . . . . .        . . . . .

Step 4) The players use copy 1 of the final-position to perform the black-analysis.

black-analysis performed on copy 1 of the final-position

. . . . .        4 . 2 . 6        . . . . .
# # # # #        # # # # #        # # # # #
O O O O O        O O O O O        O O O O O
. . O . #        . . O . #        . . O . #
. . . . .        . . . . .        . . . . .

The moves 1, 3, 5, 7, 8, 9 are passes.

position at the end of the black-analysis on the copy 1 board

. . . . .        # . # . #        . . . . .
# # # # #        # # # # #        # # # # #
O O O O O        O O O O O        O O O O O
. . O . #        . . O . #        . . O . #
. . . . .        . . . . .        . . . . .

Step 5) The players use copy 2 of the final-position to perform the white-analysis.

white-analysis performed on copy 2 of the final-position

. . . . .        # . # . #        . . . . .
# # # # #        # # # # #        # # # # #
O O O O O        O O O O O        O O O O O
. . O . #        . . O . #        4 . O 8 #
. . . . .        . . . . .        . 6 2 . 10

The moves 1, 3, 5, 7, 9, 11, 12, 13 are passes.

position at the end of the white-analysis on the copy 2 board

. . . . .        # . # . #        . . . . .
# # # # #        # # # # #        # # # # #
O O O O O        O O O O O        O O O O O
. . O . #        . . O . #        O . O O .
. . . . .        . . . . .        . O O . O

Step 6) The players determine the intersections that Black controls in the final-position.

B B B B B        # . # . #        . . . . .
B B B B B        # # # # #        # # # # #
O O O O O        O O O O O        O O O O O
. . O . #        . . O . #        O . O O .
. . . . .        . . . . .        . O O . O

The intersections B are the intersections that Black controls in the final-position: These are the intersections on or around that Black has got immortal stones in the black-analysis.

Step 7) The players determine the intersections that White controls in the final-position.

. . . . .        # . # . #        . . . . .
# # # # #        # # # # #        # # # # #
W W W W W        O O O O O        O O O O O
W W W W W        . . O . #        O . O O .
W W W W W        . . . . .        . O O . O

The intersections W are the intersections that White controls in the final-position: These are the intersections on or around that White has got immortal stones in the white-analysis.

Step 8) The players determine the score.

intersections scoring for Black

1 1 1 1 1        # . # . #        . . . . .
# # # # #        # # # # #        # # # # #
O O O O O        O O O O O        O O O O O
. . O . #        . . O . #        O . O O .
. . . . .        . . . . .        . O O . O

intersections scoring for White

. . . . .        # . # . #        . . . . .
# # # # #        # # # # #        # # # # #
O O O O O        O O O O O        O O O O O
1 1 O 1 2        . . O . #        O . O O .
1 1 1 1 1        . . . . .        . O O . O

Score = 5 - 10 = -5. White has 5 points more than Black.

Step 9) The players determine the result.

Result: White wins.

Step 10) The players make the result agreement due to the determined result.

The players sign the result form so that White wins the game. (In some tournaments, the players would mark the correct result on some walllist rather than signing a result form.)

Advanced Commentary on Some Rules Details

Position

"The position is the distribution of black, white, and no stones on all the specific intersections of the grid. For a play, this is given after all its removals."

An often posed question about definitions of the term "position" is whether rotating or mirroring the board with otherwise the same distribution of stones creates a different position. The answer is: yes. The reason is that the rule speaks of "specific" intersections. Each of the 361 intersections of the grid is unique. (Of course, the rule text might be more precise and explicit, however, a semi-formal text is always a compromise between accessibility by the average reader and a mathematician's desire for ultimate precision.)

The Basic-ko Rule at the End of the Alternation

Since the basic-ko rule refers to "just before the last opposing move", it does not carry prohibitions from the alternation to the black-analysis or the white-analysis. The last opposing move of the alternation is either of the two successive passes that end the alternation.

The basic-ko rule might have been more explicit about this like the fixed-ko rule's mentioning of "of the same move-sequence". However, because of the aforementioned reason in a semi-formal rule text this is not really necessary.

Triple Ko

In the section about the fixed-ko rule, you have seen a position with a triple ko during the alternation. Surely you have wondered what happens during the black-analysis and the white-analysis.

position with Black to move during the alternation

# # # # #
. # O # O
# O . O .
O O O O O

As we have seen earlier, this will also be the final-position. But why does White not need to remove the black stones during the alternation? This is answered by looking at the black-analysis and the white-analysis: Playing a stone during the alternation would cost 1 point for the score.

black-analysis: White moves first

# # # # #
1 # O # O
# O . O .
O O O O O

The moves 2, 3, 4 are passes.

position at the end of the black-analysis

. . . . .
O . O . O
. O . O .
O O O O O

Therefore Black controls nothing in the final-position.

white-analysis: Black moves first.

Let us suppose strong Black attacks:

position after Black play 1

# # # # #
. # . # O
# O # O .
O O O O O

position after White play 2

# # # # #
O # . # O
. O # O .
O O O O O

position after Black play 3

# # # # #
O # . # .
. O # O #
O O O O O

position after White play 4

# # # # #
O # O # .
. O . O #
O O O O O

position after Black play 5

# # # # #
. # O # .
# O . O #
O O O O O

position after White play 6

# # # # #
. # O # O
# O . O .
O O O O O

position after Black pass 7

# # # # #
. # O # O
# O . O .
O O O O O

Due to the fixed-ko rule, Black may not capture the middle white ko stone. Due to the basic-ko rule, Black may not capture the right white ko stone.

So far the move-sequence is familiar to us; it agrees to that one that might have occurred during the alternation. Note that move-sequences during the alternation and the white-analysis are considered separately, i.e. prohibitions during the alternation are not considered for the white-analysis.

position after White play 8

. . . . .
O . O . O
. O . O .
O O O O O

position after Black pass 9

. . . . .
O . O . O
. O . O .
O O O O O

position after White play 10

. O . . .
O . O . O
. O . O .
O O O O O

position after Black pass 11

. O . . .
O . O . O
. O . O .
O O O O O

position after White play 12

. O . O .
O . O . O
. O . O .
O O O O O

position after Black pass 13

. O . O .
O . O . O
. O . O .
O O O O O

position after White pass 14

. O . O .
O . O . O
. O . O .
O O O O O

position after Black pass 15

. O . O .
O . O . O
. O . O .
O O O O O

Therefore White controls all intersections in the final-position.

The score is 19 points for White. (Look at the final-position to calculate the score and recall that Black controls none of the intersections.)

Now you have seen a typical example of how a position with some rare, complex ko is scored. Traditional Japanese rules would have produced the result "No Result". The New Amateur-Japanese Rules always produce a score. This differs from tradition but who cares? Rare kos occur zero or one times during an amateur's lifetime. Such does not justify an exceptional no-result rule that would have to be applied during each move of each game. Note that the fixed-ko rule is not such an exceptional rule since it is necessary during the black-analysis and the white-analysis to make these move-sequences finite so that they can always be actually performed by the players. Since the fixed-ko rule is used during the analyses, it can be used during the alternation as well. There is no need to replace it by a no-result rule during the alternation only.

Two and Three Successive Passes

The alternation ends with two successive passes because that expresses sufficiently well that neither player wants to play another stone during the alternation. Each of the black-analysis and the white-analysis ends with three successive passes so that a pass serves as a ko threat; thereby dead kos can be dissolved even if a pass is the only reasonable ko threat.

For consistency also the alternation might have got an end with three successive passes, however, this is not necessary since dead kos are dissolved during analysis and not already during the alternation; dissolving dead kos during the alternation would cost points while it is free during analysis. Besides, if the optional tournament rule "no-result" should be used, in an alternation ending with three sucessive passes a double ko could be a cause for a no-result, what does not agree to tradition.

(1)

Example with two successive passes ending each analysis (this does not agree with the New Amateur-Japanese Rules):

final-position

. # O . O O
# # # O O .
O O O O . O

white-analysis: Black moves first

. # O 1 O O
# # # O O .
O O O O . O

The moves 2 and 3 are passes. This ends the white-analysis and White cannot control the intersections of the so called dead ko.

(2)

Example with three successive passes ending each analysis (this agrees with the New Amateur-Japanese Rules):

final-position

. # O . O O
# # # O O .
O O O O . O

white-analysis: Black moves first: position after Black play 1

. # . # O O
# # # O O .
O O O O . O

position after White pass 2

. # . # O O
# # # O O .
O O O O . O

The basic-ko rule prohibits White to recapture now. Also White does not want to play as a ko threat.

position after Black pass 3

. # . # O O
# # # O O .
O O O O . O

position after White play 4

. # O . O O
# # # O O .
O O O O . O

The basic-ko rule does not prohibit White to recapture now since the position just before the last opposing move (Black's pass 3) was different.

position after Black pass 5

. # O . O O
# # # O O .
O O O O . O

position after White play 6

O . O . O O
. . . O O .
O O O O . O

position after Black pass 7

O . O . O O
. . . O O .
O O O O . O

position after White play 8

O . O . O O
. O . O O .
O O O O . O

The moves 9, 10, 11 are passes.

In the final-position, White controls also the intersections of the dead ko. This is possible due to the necessary three successive passes that end the white-analysis.

Two instead of One Analysis

The rules would also work if they had only one analysis ("the analysis") instead of two analyses ("the black-analysis" and "the white-analysis"). However, with only one analysis strategy would differ from traditional strategy occasionally and not only (very) scarcely. Probably many players would consider the differences to be too frequent for their tastes. Letting the rules use the two analyses is a compromise. In practice one versus two analyses can make a strategic difference in positions with a bent-4-in-the-corner and ko threats elsewhere on the board.

It might be tolerated and seen as part of komi that with only one analysis Black would always start and in some final-positions possibly get an advantage from moving first.

Usage of only one analysis has an aesthetic disadvantage: the score of a position and the negative score of its colour-inverse position need not be the same for some scarce positions.

(1)

Example with only one analysis (this does not agree with the New Amateur-Japanese Rules):

final-position

# # # . O # O O . #
. O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

analysis: Black moves first (always Black starts the analysis)

moves 1 to 4

4 3 # 2 O # O O . #
1 O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

position after Black move 5 (ko capture at 1)

. # . O O # O O . #
# O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

moves 6 to 8

. # 7 O O # O O 6 #
# O O O O # O O 8 #
O O # # # # # O # #
# # # . # . # O # #

position after move 8

. # # . . # O O O .
# . . . . # O O O .
. . # # # # # O . .
# # # . # . # O . .

moves 9 to 18

. # # 13. # O O O .
# . 11. 15# O O O 10
. 9 # # # # # O 12.
# # # . # . # O . 14

The moves 16, 17, 18 are passes.

position at the end of the analysis

. # # # . # O O O .
# . # . # # O O O O
. # # # # # # O O .
# # # . # . # O . O

Black control B and White control W

B B B B B B W W W W
B B B B B B W W W W
B B B B B B B W W W
B B B B B B B W W W

In the final-position, Black controls the intersections of the bent-4-in-the-corner and of his centre group while White controls the intersections of the seki. During the analysis, an exchange takes place. The score is 4 favouring Black. (Recall that the score is calculated in the final-position and that removals during the analysis do not contribute to the score. The analysis is done on a separate board.)

(2)

Like example (1) but the players play a different analysis from move 7:

position after move 6 of the analysis

. # . O O # O O O #
# O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

moves 7 to 10

8 # 10O O # O O O #
# O O O O # O O 7 #
O O # # # # # 9 # #
# # # . # . # O # #

position after move 10

O . O O O # . . . #
. O O O O # . . # #
O O # # # # # # # #
# # # . # . # . # #

moves 11 to 16

O . O O O # . 11. #
. O O O O # 13. # #
O O # # # # # # # #
# # # . # . # . # #

The moves 12, 14, 15, 16 are passes.

Black control B and White control W

W W W W W B B B B B
W W W W W B B B B B
W W B B B B B B B B
B B B B B B B B B B

In the final-position, the score is 8 favouring Black.

So that the reader is not confused, we shall calculate the score in greater detail. To recall, the final-position is:

# # # . O # O O . #
. O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

Black controls 4 empty intersections (making 4 points) and controls 6 white intersections (making 12 points). Altogether Black has 16 points. - White controls 2 empty intersections (making 2 points) and controls 3 black intersections (making 6 points). Altogether White has 8 points. - The difference between both players' scores is 16 - 8 = 8. Black wins by 8 points.

(3)

Like example (1) but the players play a different analysis from move 1:

Black 1, White 2, Black 3 are passes.

position at the end of the analysis

# # # . O # O O . #
. O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

Black control B and White control W

# # # . O B O O . #
. O O O O B O O . #
O O B B B B B O # #
B B B B B B B O # #

White controls nothing. Neither player controls anything in the seki or in the bent-4-in-the-corner since neither player has any immortal stones there.

The score is 2 favouring Black.

Conclusion: Black would force White to play like in example (2) and hence win the game by 8 points.

Alternation: If Black starts the ko, gets the left side, and White gets the right side, then the score will be 4. If Black starts the ko, gets the right side, and White gets the left side, then the score will be 9. If both players pass, then the score will be 8 (see (2)). The second of these three options is perfect play. Hence alternation should result in the score 9; in this example, the bent-4-in-the-corner should be dissolved during the alternation.

(4)

Example with two analyses (this agrees with the New Amateur-Japanese Rules):

final-position

# # # . O # O O . #
. O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

black-analysis: White moves first:

moves 1 to 6

5 4 # 3 O # O O . #
2 O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

The move 1 is a pass. The move 6 captures at 2.

position after move 6

. # . O O # O O . #
# O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

moves 7 to 9

. # 8 O O # O O 7 #
# O O O O # O O 9 #
O O # # # # # O # #
# # # . # . # O # #

position after move 9

. # # . . # O O O .
# . . . . # O O O .
. . # # # # # O . .
# # # . # . # O . .

moves 10 to 19

. # # 14. # O O O .
# . 12. 16# O O O .
. 10# # # # # O . .
# # # . # . # O . .

The moves 11, 13, 15, 17, 18, 19 are passes.

Why does White pass so early? The purpose of the black-analysis is to determine what Black controls and only what Black controls. In the black-analysis, White cannot prove to control anything. White proves his control in the white-analysis.

position at the end of the black-analysis

. # # # . # O O O .
# . # . # # O O O .
. # # # # # # O . .
# # # . # . # O . .

Black controls B

B B B B B B O O . #
B B B B B B O O . #
B B B B B B B O # #
B B B B B B B O # #

(Black might have used a different strategy during the black-analysis: passing all the time. This would have been a bad strategy for Black would have controlled only his centre group with its two empty intersections.)

white-analysis: Black moves first

moves 1 to 3

# # # . O # O O . #
. O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

The moves 1, 2, 3 are passes.

position at the end of the white-analysis

# # # . O # O O . #
. O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

White controls W

# # # . O # O O . #
. O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

White controls nothing in the final-position.

(White might have played more aggressively by giving atari everywhere only to be removed everywhere. This strategy during the white-analysis would not have been more successful than passing.)

The score is 18 favouring Black. (In the final-position, Black controls 4 empty intersections and 7 white intersections, which score twice. White controls neither empty intersections nor black intersections.)

With the two analyses (black-analysis and white-analysis, the score agrees to tradition.

(5)

Like example (4) but the players play a different black-analysis:

black-analysis: White moves first:

moves 1 to 9

5 4 8 3 O # O O . #
2 O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

The moves 1, 7, 9 are passes. The move 6 captures at 2.

position after move 11

. # # . . # O O . #
# . . . . # O O . #
. . # # # # # O # #
# # # . # . # O # #

moves 10 to 19

. # # 14. # O O . #
# . 12. 16# O O . #
. 10# # # # # O # #
# # # . # . # O # #

The moves 11, 13, 15, 17, 18, 19 are passes.

position at the end of the black-analysis

. # # # . # O O . #
# . # . # # O O . #
. # # # # # # O # #
# # # . # . # O # #

Black control B

B B B B B B O O . #
B B B B B B O O . #
B B B B B B B O # #
B B B B B B B O # #

Black-score = 18.

(6)

Like example (4) but the players play a different black-analysis:

black-analysis: White moves first: moves 1 to 6

5 4 # 3 O # O O . #
2 O O O O # O O . #
O O # # # # # O # #
# # # . # . # O # #

The move 1 is a pass. The move 6 captures at 2.

moves 7 to 17

9 # 11O O # O 147 #
# O O O O # 12O 8 #
O O # # # # # 10# #
# # # . # . # O # #

The moves 13, 15, 16, 17 are passes.

position at the end of the black-analysis

O . O O O # . # . #
. O O O O # # . # #
O O # # # # # # # #
# # # . # . # . # #

Black control B

# # # . O B B B B B
. O O O O B B B B B
O O B B B B B B B B
B B B B B B B B B B

Black-score = 16.

Conclusion: The players should play the black-analysis and the white-analysis like in examples (4) or (5). The score should be 18 favouring Black. Note: It would have been a strategic mistake if Black had played the bent-4-in-the-corner ko fight already during the alternation.

(7)

Comparison: One analysis results in the score 8 if the players ended the alternation too early or in the score 9 otherwise. Two analyses (the black-analysis and the white-analysis) result in the score 18 if the players ended the alternation in time; the score coincides with AJT.

Immortal Ponnukis

Why must the players fill their controlled regions by stones and ponnukis rather than by just more relaxed immortal shapes? The ponnukis allow an easy rule text for the term "control": It is easy to specify "adjacent".

Easy Examples for Control

The following examples illustrate how the concepts "control" and "immortal" are applied to the final-position in practice.

traditional name: independent life
board: 4x2
frequency: very high

final-position

. . . .
# # # #

intersections

a b c d
# # # #

To determine the intersections controlled by Black or White, the black-analysis and then the white-analysis are performed.

***

Black-analysis:
The players choose to play as follows:
O[pbpdppp]

This ends in the following reference position:

. # . #
# # # #

In this reference position, each of the black stones is immortal. To prove this, White plays the following move-sequence while Black always passes:
O[ppp]

White does not remove any of the black stones in the reference position.

Now this information is applied to the final-position: In it Black controls each intersection. The reason for this is that in the reference position each intersection is either occupied by an immortal black stone or has immortal black stones on all its adjacent intersections.

***

White-analysis:
The players choose to play as follows:
#[bppp]

This ends in the following reference position:

. # . .
# # # #

In this reference position, there is no white stone. Therefore there is no immortal white stone.

Now this information is applied to the final-position: In it White does not control any intersection. The reason for this is that in the reference position none of the intersections is occupied by an immortal white stone and none has immortal white stones on all its adjacent intersections.

***

To summarize the information about control, we get the following diagram:

Black controls B / White controls W / both players control 2

B B B B
B B B B

This diagram means that each intersection is controlled by Black, none of the intersections is controlled by White, and none of the intersections is controlled by both players.

***

To determine the score, the information about control is applied to the final-position:

Black controls 4 empty intersections.
Black controls 0 intersections with white stones on.
White controls 0 empty intersections.
White controls 0 intersections with black stones on.
Thus the score is 4 + 2*0 - 0 - 2*0 = 4.

traditional name: each player has an independent life with opposing dead stones inside
board: 4x7
frequency: very high

final-position

. O # .
O O # #
. O # .
O O # #
. O # .
# O # O
# O # #

intersections

z O # u
O O # #
. O # .
O O # #
a O # d
b O # e
c O # #

To determine the intersections controlled by Black or White, the black-analysis and then the white-analysis are performed.

***

Black-analysis:
The players choose to play as follows:
O[pdppp]

This ends in the following reference position:

. O # .
O O # #
. O # .
O O # #
. O # #
# O # .
# O # #

In this reference position, each of the black stones on the right side is immortal. Proof: White tries the following move-sequence while Black always passes:
O[apbpcpzppp]

White does not remove any of the black stones on the right side. The no-suicide rule hinders him. White cannot approach enough liberties of the black stones on the right side. In fact, White cannot occupy even one of their liberties.

Now this information is applied to the final-position: In it Black controls the intersections marked by B in the following diagram. The reason for this is that in the reference position each of these intersections is either occupied by an immortal black stone or has immortal black stones on all its adjacent intersections.

Black controls B:

. O B B
O O B B
. O B B
O O B B
. O B B
# O B B
# O B B

Black does not control the intersections b or c since in the reference position the stones on these intersections are not immortal.

***

White-analysis:
The players choose to play as follows:
#[dacbppeppp]

This ends in the following reference position:

. O # .
O O # #
. O # .
O O # #
O O # #
O O # #
. O # #

In this reference position, each of the white stones on the left side is immortal. Proof: Black tries the following move-sequence while White always passes:
#[uppp]

Black does not remove any of the white stones on the left side.

Now this information is applied to the final-position: In it White controls the intersections marked by W in the following diagram. The reason for this is that in the reference position each of these intersections is either occupied by an immortal white stone or has immortal white stones on all its adjacent intersections.

White controls W:

W W # .
W W # #
W W # .
W W # #
W W # .
W W # O
W W # #

White does not control the intersection e since in the reference position the stone on this intersection is not immortal.

***

For convenience, the information about control can also be shown in one diagram:

Black controls B / White controls W / both players control 2

W W B B
W W B B
W W B B
W W B B
W W B B
W W B B
W W B B

***

To determine the score, the information about control is applied to the final-position:

Black controls 3 empty intersections.
Black controls 1 intersections with white stones on.
White controls 3 empty intersections.
White controls 2 intersections with black stones on.
Thus the score is 3 + 2*1 - 3 - 2*2 = -2.

traditional name: seki
board: 5x2
frequency: occasional

final-position

. O O O .
# # # # #

intersections

a O O O b
# # # # #

To determine the intersections controlled by Black or White, the black-analysis and then the white-analysis are performed.

***

Black-analysis:
The players choose to play as follows:
O[ppp]

This ends in the following reference position:

. O O O .
# # # # #

In this reference position, none of the black stones is immortal:
O[apbppp]

White removes each of the black stones in the reference position. Therefore none of these black stones is immortal.

Now this information is applied to the final-position: In it Black does not control any intersection. The reason for this is that in the reference position none of the intersections is occupied by an immortal black stone and none has immortal black stones on all its adjacent intersections.

***

White-analysis:
The players choose to play as follows:
#[pabppp]

This ends in the following reference position:

. . . . #
# # # # #

In this reference position, there is no white stone. Therefore there is no immortal white stone.

***

The information about control can be summarized in the following diagram:

Black controls B / White controls W / both players control 2

. O O O .
# # # # #

I.e., none of the intersections is controlled by Black, controlled by White, or even controlled by both players.

***

To determine the score, the information about control is applied to the final-position:

Black controls 0 empty intersections.
Black controls 0 intersections with white stones on.
White controls 0 empty intersections.
White controls 0 intersections with black stones on.
Thus the score is 0 + 2*0 - 0 - 2*0 = 0.

As could be seen, with the concept "control" the rules do not even need to define "seki" to prevent that a seki has any scoring intersections at all. In a seki, neither player controls anything because in his analysis he cannot establish immortal stones on any of a seki's intersections.

Examples for NAJ or NAJN with Unexpected Scores

Only such examples are shown that, if all dame, teire, dame kos, and points of value are played during the alternation, have a score different from that one under the Japanese 2003 Rules or that behave particularly unexpectedly. Examples with long-cycle-ties under NAJN are shown in a different chapter.

One class of examples with unexpected scores has the frequency scarce: 1000-year-ko and seki elsewhere on the board. This is the price for having applicable Japanese style rules. - By adding further definitions and rules (about "ko-pass"), such examples would have expected scores but at the same time most players and referees would not be able to apply the rules correctly. This is the experience during referee workshops in that the author taught rules of play.

Interclude

The following is an extract of some of the possible rules additions for "ko-pass". Because of the third move type other definitions must also be changed, what is not shown here.

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-capture is a play that is in a ko and removes exactly one stone.
A ko-pass by a player is announced as "ko-pass" if a ko-capture by the player in some ko is currently available but prohibited.
An analysis-move is either a play, a ko-pass, or a pass.
{ko-pass} During the black-analysis or the white-analysis, between a player's ko-capture on one intersection of a ko and the next ko-pass by him or his opponent, an opponent's ko-capture on the other intersection is prohibited.

All other known examples are rare or very rare (so that an amateur player would have maybe one of those examples in his life's games) and there are only a few known classes of such examples. Most of those have the score "undefined" under amateur-Japanese go rules tradition. - By adding yet further definitions and rules (introducing some suitable concepts that require scoring controlled intersections to be surrounded), one could make the scores in such example classes less unexpected. It is not possible to make them completely expected due to the "undefined" AJT scores.

Interclude

The following is an extract of some of the possible rules additions for surrounded. This concept is introduced implicitly by describing the connected objects "black-lake" / "whilte-lake" and by using the phrase "adjacent and only adjacent" in the definitions of "black-territory" / "white-territory". The necessary definitions of "black-string" and "white-string" are not shown. Besides the definition of "score" must be changed: "[...] the number of empty intersections that are black-territory [...]".

In the final-position, a black-string / white-string is alive if Black / White controls each of its intersections and White / Black controls none of them.
In the final-position, a black-lake / white-lake is an intersection that Black / White controls, White / Black does not control, and is empty and, recursively, any adjacent intersection that Black / White controls, White / Black does not control, and is empty or occupied by a white / black stone.
In the final-position, an intersection is black-territory / white-territory if it is of a black-lake / white-lake that is adjacent and only adjacent to one or more than one alive black-strings / white-strings.

The rules extensions of the intercludes have not been tested carefully yet, but the author expects them to work as intended, i.e. not to produce too many side-effects. If one wanted to approach tradition as closely as possible, one might use the Japanese 2003 Rules right away instead of changing NAJ to make the resulting ruleset more and more complicated. The intercludes might be understood as a warning about what happens if one prefers traditional behaviour of scarce and rare positions to applicable rules.

For essentially all not shown but practically occurring positions, NAJ or NAJN agree to amateur-Japanese go rules tradition! Therefore NAJ or NAJN, respectively, is a very good model and either can be used to formalize amateur-Japanese go rules in future.

The following examples are discussed for NAJ and NAJN.

traditional name: three-points-without-capturing
board: 6x5
frequency: very rare
scores: NAJ: -3, NAJN: -3, AJT: undefined, J2003: 0

final-position

. # # O . O
O # # O O .
# O O O O O
# # # # # #
# # # . # .

intersections

a c e O . O
b d f O O .
# O O O O O
# # # # # #
# # # . # .

Black-analysis:
O[pabdcaebfppp]

White-analysis:
#[padcefacbeppp]

Black controls B / White controls W / both players control 2

B W W W W W
B B W W W W
B W W W W W
B B B B B B
B B B B B B

Score = -3.

By coincidence(?!), this agrees to the traditional name and the score under the Japanese 1949 Rules!

traditional name: three-points-without-capturing adjacent to a seki shape
board: 8x5
frequency: very rare
scores: NAJ: 2, NAJN: 2, AJT: undefined, J2003: 0

final-position

. O # # . O # .
# # O # . O # .
# # O # # O # .
O O O O O # # .
. . . . O O # #

intersections

a b # # g i # .
c d O # h j # .
e f O # # k # .
O O O O O # # .
. . . . O O # #

Black-analysis:
O[pabdcaegbhfippp]

White-analysis:
#[padcefacbe..]

Black controls B / White controls W / both players control 2

. O B B B B B B
W # W B B B B B
W W W B B B B B
W W W W W B B B
W W W W W W B B

Score = 2.

traditional name: bent-4-in-the-corner adjacent to or part of a seki shape
board: 7x7
frequency: rare
scores: NAJ: 16, NAJN: 16, AJT: undefined, J2003: -2

final-position

O . O # O . #
. O O # O O #
O O O # # O #
# # O O # O .
# # O # # O O
# # # O # # #
. # . O . # .

intersections

O . O # O a b
. O O # O O c
O O O # # O d
# # O O # O e
# # O # # O O
# # # O # # #
h # g O f # z

Black-analysis:
O[paecbagdhf..]

White-analysis:
#[pfgaeppp]

Black controls B / White controls W / both players control 2

W W W B B B B
W W W B B B B
W W W B B B B
# # W W B B B
# # W B B B B
# # # O B B B
. # . O B B B

score = 16

[Acknowledgement: Ing Chang-ki]

traditional name: triple-ko with one external basic-ko
board: 6x9
frequency: rare
scores: NAJ: 3, NAJN: 3, AJT: undefined, J2003: 26

final-position

. # # # # #
# # . # O #
O O # O . O
. O O O O O
O # # # # #
# # . # . #
# # # # # #
O O O O O O
O O . O . O

intersections

z # # # # #
# # c # e #
O O d O f O
a O O O O O
b # # # # #
# # . # . #
# # # # # #
O O O O O O
O O . O . O

Black-analysis:
One of:
O[pacbzppp]
O[pfcaedbppacbzppp]

White-analysis:
One of:
#[acfbdepcfpaedbfcpedppp]
#[acfbdepcfppedpfcaedbppp]
#[acfbdeppfcaedbpcfppedppp]

Black controls B / White controls W / both players control 2

. # # # # #
# # . # O #
O O # O . O
B O O O O O
B B B B B B
B B B B B B
B B B B B B
W W W W W W
W W W W W W

score = 3

traditional name: double-ko-seki adjacent to string that is adjacent to a shape with a hidden basic-ko that is adjacent to a basic-ko
board: 11x6
frequency: very rare
scores: NAJ: 8, NAJN: 8, AJT: undefined, J2003: 44

final-position

. O O . O . O # . # O
O # # O O O O # # O O
# # . # # O # # O . O
. # # # O # # # # O O
# # O O O O O # # . O
O O O . O . O # # # O

intersections

b c d e O f O # g h O
a # # O O O O # # O O
# # . # # O # # i j O
. # # # O # # # # O O
# # O O O O O # # k O
O O O . O . O # # # O

Black-analysis:
O[pbgedckepdppp]

White-analysis:
#[pgjppihppp]

Black controls B / White controls W / both players control 2

B B B B O . O # . # O
B B B O O O O # # O O
B B B B B O # # O . O
B B B B W # # # # O O
B B W W W W W # # . O
W W W W W W W # # # O

score = 8

Notes: The concept controls under the basic-fixed-ko rules produces an unexpected result. However, this result is pretty meaningful because it indicates how far Black can approach the shape. The same applies if the basic-ko rule is the only ko rule.

traditional name: double-ko-seki adjacent to bent-4-in-the-corner that is adjacent to basic-ko
board: 9x8
frequency: very rare
scores: NAJ: 3, NAJN: 3, AJT: undefined, J2003: 54

final-position

# # # . O # . # O
. O O O O # # O O
O O O O O # O . O
. O O O O # # O O
O # # # O # # . O
# # # # # O # # #
. # . # O O O O O
# # # # O O . O .

intersections

d e f g O # h i O
c O O O O # # O O
O O O O O # j k O
b O O O O # # O O
a # # # O # # l O
# # # # # O # # #
. # . # O O O O O
# # # # O O . O .

Black-analysis:
O[pcgedchkdbfappp]

White-analysis:
#[pcpgehkpjippp]

Black controls B / White controls W / both players control 2

# # # . O # . # O
. O O O O # # O O
O O O O O # O . O
B O O O O # # O O
B B B B O # # . O
B B B B B W # # #
B B B B W W W W W
B B B B W W W W W

score = 3

traditional name: double-ko-seki adjacent to bent-4-in-the-corner
board: 8x5
frequency: very rare
scores: NAJ: -36, NAJN: -36, AJT: undefined, J2003: -36

final-position

. O . # O . O #
O # # # O O # #
. # O O O # . #
# # O O O O # #
O O O O O O . #

intersections

c d e # O f g #
b # # # O O # #
a # O O O h i #
# # O O O O # #
O O O O O O j #

Black-analysis:
O[pfiphgaeppp]

White-analysis:
#[pcfipaebhgcdfa..]

Black controls B / White controls W / both players control 2

W W W W W W W W
W W W W W W W W
W W W W W W W W
W W W W W W W W
W W W W W W W W

score = -36

traditional name: direct-ko
board: 6x4
frequency: scarce
scores: NAJ: 5, NAJN: 5, AJT: 5, J2003: 5

alternation, White to move just after Black's ko-capture

O O O # O .
. O # . # O
O O # # # #
. O # . # .

intersections

O O O a c d
. O # b # e
O O # # # #
. O # . # .

Alternation:
O[pdpp]

final-position: prisoner-difference = 2

O O O # . #
. O # . # .
O O # # # #
. O # . # .

Black-analysis:
O[ppp]

White-analysis:
#[ppp]

Black controls B / White controls W / both players control 2

W W W B B B
W W B B B B
W W B B B B
W W B B B B

score = 5

traditional name: direct-ko with local ko-threat
board: 7x4
frequency: rare
scores: NAJ: 1, NAJN: 1, AJT: undefined, J2003: 0

alternation, White to move just after Black's ko-capture

O . O O # O .
. . O # . # O
O . O # # # #
. # O # . # .

intersections

O . O O c O e
. a O # d # f
O b O # # # #
z # O # . # .

NAJ, NAJN:

O[pp] is legal.

Black-analysis:
O[dabcpeppp]

White-analysis:
#[ebpapzppp]

score = 1

J2003:

O[pp] is illegal.

O[pepp].

score = 0

[Acknowledgement: Robert Pauli]

Examples for NAJ or NAJN with Long-cycle-tie under NAJN

Only a few examples are given since they are representative for all those rare positions in that long cycles are reasonable.

traditional name: double-ko-seki and fighting-ko
board: 13x5
frequency: rare
scores: NAJ: -16, NAJN: long-cycle-tie, AJT: no-result, J2003: long-cycle-tie

Black to move during the alternating-sequence

# # . O # . # O . O # . O
# # O O # # # O O O # # O
# . # O # . # O . O # O O
# # O O # # # O O O # O .
# O . O # # # O O O # # O

intersections

# # . O # . # O . O # z O
# # O O # # # O O O # # O
# a a O # . # O . O # O O
# # O O # # # O O O # O k
# a a O # # # O O O # # k

NAJN:

Alternation:
One of:
#[kaakaa]
#[kaakaa]*[kaakaa]

The players would agree or the referee would let the players agree to end the game in a no-result.

***

NAJ:

Alternation:
One of:
#[pp]
#[aakaakpp]
#[kaakaapp]

final-position

# # . O # . # O . O # . O
# # O O # # # O O O # # O
# . # O # . # O . O # O O
# # O O # # # O O O # O .
# O . O # # # O O O # # O

Black-analysis:
O[zaapaappp]

White-analysis:
One of:
#[pz..]
#[aakaakpz..]
#[kaakaapz..]

Black controls B / White controls W / both players control 2

# # . O B B B W W W W W W
# # O O B B B W W W W W W
# . # O B B B W W W W W W
# # O O B B B W W W W W W
# O . O B B B W W W W W W

score = -16

Notes: Other positions like 1) double-ko-death and fighting-ko or 2) double-ko-seki and dead-ko (also known as moonshine-life) agree to AJT.

traditional name: triple-ko
board: 5x4
frequency: rare
scores: NAJ: -19, NAJN: long-cycle-tie, AJT: no-result, J2003: long-cycle-tie

Black to move during the alternation:

O O O O O
. O . O #
O # O # .
# # # # #

intersections

O O O O O
a O c O e
b # d # f
# # # # #

NAJN:

Alternation:
One of:
#[afcbed]
#[afcbed]*[afcbed]

The players would agree or the referee would let the players agree to end the game in a no-result.

***

NAJ:

Alternation:
One of:
#[pp]
#[afcbedpp]

Black-analysis:
O[fppp]

White-analysis:
#[afcbedpf..]

Black controls B / White controls W / both players control 2

W W W W W
W W W W W
W W W W W
W W W W W

score = -19

traditional name: eternal-life
board: 9x4
frequency: rare
scores: NAJ: -27, NAJN: long-cycle-tie, AJT: no-result, J2003: long-cycle-tie

Black to move during the alternation:

. O . # . O # . .
# O O O # # O O O
# # # # # O O . O
O O O O O O . O O

intersections

e f a b c d j k l
# g h i # # O O O
# # # # # O O . O
O O O O O O . O O

NAJN:

Alternation:
One of:
#[acbd]
#[acbd]*[acbd]

The players would agree or the referee would let the players agree to end the game in a no-result.

***

NAJ:

Alternation:
One of:
#[pp]
#[acbdpp]
etc.

Black-anaylsis:
O[a..]

White-analysis:
#[acbdpa..]

Black controls B / White controls W / both players control 2

W W W W W W W W W
W W W W W W W W W
W W W W W W W W W
W W W W W W W W W

score = -27

1000-year Kos

Among the scarce and rare shapes, probably 1000-year ko is the most frequent of those shapes where in some positions the New Amateur-Japanese Rules alter optimal strategy compared to traditional Japanese style rules. Therefore 1000-year-kos shall be discussed.

How frequent are 1000-year kos with a not connected ko stone at the end of the alternation? A non-representative database query at gobase.org gives 36 games with a 1000-year ko in the corner. Of them 18 were resigned, 18 counted. Of the 18 counted games the database server permitted replaying 9 the games. 1 game used Chinese rules (not interesting since under Area Scoring rules a 1000-year ko can be dissolved until the end of the alternation) and 8 games used Japanese style rules. Among these 8 counted games under Japanese rules, in 8 games the 1000-year ko was dissolved due to a ko fight or connected to avoid a ko fight (rather than just to simplify scoring) before the end of alternation. In 0 of these 8 games the 1000-year ko was left unconnected at the end of alternation. Hence quite likely a game with a strategically correctly unconnected 1000-year ko at the of the alternation is rare.

Not each final-position with an unconnected 1000-year ko is hot under NAJ; there must also be some suitable ko threats on the board. Furthermore, not necessarily each position must involve significantly different strategies during the alternation under NAJ and AJT. By the way, it is not particularly clear how AJT treat 1000-year ko at the end of the alternation, except that the World Amateur Go Championship Rules provide a precedental ruling.

Other kos than 1000-year kos that are indirect (in some traditional meaning) and remain unconnected at the end of the alternation might also lead to different strategies under NAJ and under AJT in some final-positions with suitable ko threats. One such other shape is bent-5-in-the-corner. However, presumably such shapes are even rarer than 1000-year ko.

As an additional remark, the Korean Baduk Association's Rules of 1992 have a precedental ruling for indirect kos. Korean professionals do not understand that rule: Every professional that is aware of that rule at all has a different opinion on what that rule might mean.

Concluding, hardly it is a too great luxury of NAJ that unconnected 1000-year ko at the end of the alternation might sometimes lead to a non-traditional score. It would be an overkill to modify NAJ just because of undissolved indirect kos.

Example (1): 1000-year ko with few ko threats of intermediate size for both players

(1.1)

final-position with connected ko stone

# # # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

Score = 2.

(1.2)

final-position with ko stone of the ko's possible defender

# . # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

black-analysis: variation 1

moves 1 to 6 (White moves first)

# 3 # 2 O # . # O # #
O # # 5 O # # # O 4 #
O O O O O # . # O 6 #
O O O O O # # # O O #

The move 1 is a pass.

position after move 6

. O . . O # . # . # #
O . . O O # # # . # #
O O O O O # . # . # #
O O O O O # # # . . #

moves 7 to 13

. O . . O # . # . # #
O . . O O # # # 10# #
O O O O O # . # . # #
O O O O O # # # 8 . #

The moves 7, 9, 11, 12, 13 are passes.

position at the end of the black-analysis

. O . . O # . # . # #
O . . O O # # # # # #
O O O O O # . # . # #
O O O O O # # # # . #

Black control B

# . # . O B B B B B B
O # # . O B B B B B B
O O O O O B B B B B B
O O O O O B B B B B B

Black-score = 14.

Note: If White answered the ko threat, then Black would control the left side and have a bigger black-score.

black-analysis: variation 2

moves 1 to 3 (White moves first)

# 1 # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

The moves 2, 3 are passes.

moves 4 to 10

4 7 # 6 O # . # O # #
O # # 9 O # # # O 8 #
O O O O O # . # O 10#
O O O O O # # # O O #

The move 5 is a pass. The remaining moves are not shown. The black-score is 14, like in variation 1.

black-analysis: variation 3

moves 1 to 7 (White moves first)

4 1 # 3 O # . # O # #
O # # 6 O # # # O 5 #
O O O O O # . # O 7 #
O O O O O # # # O O #

The move 2 is a pass.

position after move 7

# . # . . # . # O . .
. # # # . # # # O O .
. . . . . # . # O O .
. . . . . # # # O O .

moves 8 to 21

# . # . 18# . # O . .
. # # # . # # # O O .
8 . 12. 16# . # O O .
. 10. 14. # # # O O .

The moves 9, 11, 13, 15, 17, 19, 20, 21 are passes.

position at the end of the black-analysis

# . # . # # . # O . .
. # # # . # # # O O .
# . # . # # . # O O .
. # . # . # # # O O .

Black control B

B B B B B B B B O # #
B B B B B B B B O . #
B B B B B B B B O . #
B B B B B B B B O O #

Black-score = 31.

Conclusion on black-analysis: The players would play the black-analysis either like in variation 1, variation 2, or a similar variation. Then the black-score is 14.

white-analysis:

moves 1 to 4 (Black moves first)

# 1 # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

The moves 2, 3, 4 are passes.

position at the end of the white-analysis

# # # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

White control W

# # # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

White controls nothing.

White-score = 0.

Note: Other variations for the white-analysis are not particularly interesting, either.

Score = black-score - white-score = 14 - 0 = 14.

(1.3)

final-position with ko stone of the ko's possible defender's opponent

. O # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

black-analysis: variation 1

moves 1 to 4 (White moves first)

2 O # 1 O # . # O # #
O # # 4 O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

The move 3 is a pass. The remaining moves are not shown. The black-score is 33.

black-analysis: variation 2

moves 1 to 8 (White moves first)

2 5 # 4 O # . # O # #
O # # 7 O # # # O 6 #
O O O O O # . # O 8 #
O O O O O # # # O O #

The moves 1, 3 are passes.

position after move 8

. O . . O # . # . # #
O . . O O # # # . # #
O O O O O # . # . # #
O O O O O # # # . . #

moves 9 to 15

. O . . O # . # . # #
O . . O O # # # 12# #
O O O O O # . # . # #
O O O O O # # # 10. #

The moves 9, 11, 13, 14, 15 are passes.

position after the end of the black-analysis

. O . . O # . # . # #
O . . O O # # # # # #
O O O O O # . # . # #
O O O O O # # # # . #

Black control B

. O # . O B B B B B B
O # # . O B B B B B B
O O O O O B B B B B B
O O O O O B B B B B B

Black-score = 14.

Conclusion on black-analysis: The players would play the black-analysis like in variation 2. Then the black-score is 14.

white-analysis: variation 1

moves 1 to 6 (Black moves first)

3 O # 2 O # . # O # #
O # # 5 O # # # O 4 #
O O O O O # . # O 6 #
O O O O O # # # O O #

The move 1 is a pass.

position after move 6

# . # . . # . # O . .
. # # # . # # # O O .
. . . . . # . # O O .
. . . . . # # # O O .

moves 7 to 13

# . # . . # . # O . 8
. # # # . # # # O O .
. . . . . # . # O O 10
. . . . . # # # O O .

The moves 7, 9, 11, 12, 13 are passes.

position at the end of the white-analysis

# . # . . # . # O . O
. # # # . # # # O O .
. . . . . # . # O O O
. . . . . # # # O O .

White control W

. O # . O # . # W W W
O # # . O # # # W W W
O O O O O # . # W W W
O O O O O # # # W W W

White-score = 12.

white-analysis: variation 2

moves 1 to 9 (Black moves first)

. O # 2 O # . # O # #
O # 6 4 O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

The moves 1, 3, 5, 7, 8, 9 are passes.

position at the end of the white-analysis

. O . O O # . # W W W
O . O O O # # # W W W
O O O O O # . # W W W
O O O O O # # # W W W

White control W

W W W W W # . # O # #
W W W W W # # # O . #
W W W W W # . # O . #
W W W W W # # # O O #

White-score = 9.

white-analysis: variation 3

moves 1 to 6 (Black moves first)

1 3 # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

The moves 2, 4, 5, 6 are passes.

If White 2 threatened in the seki, then Black would answer, White would capture the ko, Black would pass, White would approach the ko, Black would capture the ko, and White would not have another ko threat. White would control nothing.

position at the end of the white-analysis

# # # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

White control W

. O # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

White controls nothing.

White-score = 0.

Conclusion for white-analysis: If both players play strongly, then the white-score is 0.

Score = black-score - white-score = 14 - 0 = 14.

(1.4)

position with Black to move during the alternation and with ko stone of the ko's possible defender

# . # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

Variation 1: If Black connects and then both players pass, the score will be 2.

Variation 2: If Black passes and White passes, the score will be 14.

Variation 3: If Black passes, then White captures the ko, and then both players pass, the board-score will be 0, White will have 1 prisoner, so the score will be -1. (White could play more aggressively with move 4 but Black would benefit.)

Variation 4:

moves 1 to 7

# 2 # 1 O # . # O # #
O # # 4 O # # # O 3 #
O O O O O # . # O 5 #
O O O O O # # # O O #

The moves 6, 7 are passes.

position at the end of the alternation

. O . . O # . # . # #
O . . O O # # # . # #
O O O O O # . # . # #
O O O O O # # # . . #

The board-score is 2. The prisoner-difference is 0. The score is 2.

Conclusion:

Variation 1 or 4 are perfect play. The score is 2.

(1.5)

position with White to move during the alternation and with ko stone of the ko's possible defender

# . # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

Variation 1: If White passes, then Black connects, and then both players pass, the score will be 2.

Variation 2: If White passes and Black passes, the score will be 14.

Variation 3: If White captures the ko, and then both players pass, the board-score will be 0, White will have 1 prisoner, so the score will be -1. (Black could play more aggressively with move 2 but White would benefit. White could play more aggressively with move 3 but Black would benefit.)

Variation 4: If White passes and Black attacks like in (1.4), variation 4, then the score will be 2.

Conclusion:

Variation 3 is perfect play. The score is -1. (Compare the analysis for the final-position with a white ko stone, see (1.3).)

(1.6)

position with Black to move during the alternation and with ko stone of the ko's possible defender's opponent

. O # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

Variation 1: If both players pass, then the score is 0. (Compare (1.5), variation 3.)

Variation 2:

moves 1 to 6

1 4 # . O # . # O # #
O # # . O # # # O 2 #
O O O O O # . # O 3 #
O O O O O # # # O O #

The moves 5, 6 are passes.

position at the end of the alternation

. O # . O # . # . # #
O # # . O # # # . # #
O O O O O # . # . # #
O O O O O # # # . . #

The board-score (Black controls the middle and right side while White controls nothing) is 7. The prisoner-difference is 5. The score is 12.

Variation 3:

moves 1 to 8

1 4 # 3 O # . # O # #
O # # 6 O # # # O 2 #
O O O O O # . # O 5 #
O O O O O # # # O O #

The moves 7, 8 are passes.

position at the end of the alternation

. O . . O # . # . # #
O . . O O # # # . . #
O O O O O # . # . # #
O O O O O # # # . . #

The board-score is 3. The prisoner-difference is 2. The score is 5.

Variation 4:

moves 1 to 3

1 O # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

The moves 2, 3 are passes. The board-score is 14 (see (1.2)). The prisoner-difference is 1. The score is 15.

Variation 5:

moves 1 to 9

1 4 # 3 O # . # O # #
O # # 6 O # # # O 5 #
O O O O O # . # O 7 #
O O O O O # # # O O #

The moves 2, 8, 9 are passes.

position at the end of the alternation

. O . . O # . # . # #
O . . O O # # # . # #
O O O O O # . # . # #
O O O O O # # # . . #

The board-score is 2. The prisoner-difference is 1. The score is 3.

Conclusion:

Variation 2 is perfect play. The score is 12.

(1.7)

position with White to move during the alternation and with ko stone of the ko's possible defender's opponent

. O # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

Variation 1: If both players pass, then the score is 0. (Compare (1.5), variation 3.)

Variation 2: If White passes, Black captures the ko, and then both players pass, then the score is 15. (Compare (1.2).)

Variation 3: White passes, then see (1.6), variation 2. The score is 12.

Variation 4: White approaches the ko, etc. This results in Black getting the left and White the right side. The score is 22.

Conclusion: Variation 3 is perfect play. The score is 12.

(1.8)

Summary for NAJ:

If during the alternation the position starts with a black ko stone, then the score is 2 or -1, depending on whether Black or White moves first.

If during the alternation the position starts with a white ko stone, then in the final-position the right side's seki will be dissolved in Black's favour and the 1000-year ko remains with a white ko stone on the board. The score is 12.

(1.9)

Score under AJT:

(Recall that AJT stands for "Amateur-Japanese rules tradition".)

Since it is unclear how AJT treats a 1000-year ko, several possible interpretations must be studied.

Interpretation A: Like under World Amateur Go Championship Rules.

Since the players have not fought the ko, Black must connect the 1000-year ko. If necessary, just before Black must capture the ko. A precedental ruling for 1000-year kos says so.

final-position

# # # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

Board-score = 2. Prisoner-difference: 0 or 1, depending on whether a black or white ko stone was in the ko until just before the end of the alternation. Score: 2 or 3, depending on the same.

Interpretation B: Naive assessment of life, death, and territory.

final-position with a black ko stone

# . # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

Without clear reasoning, naive assessment assigns the status "alive" to each string, identifies two sekis, and claims the score 2.

final-position with a white ko stone

. O # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

Without clear reasoning, naive assessment fails to assign status to the ko stone and the black string adjacent to it, assigns the status "alive" to each other string, identifies two sekis, and claims the score 2.

Comment: The advantage of naivity is speed unless a referee is called.

Interpretation C: Some (partially) formal Japanese style ruleset is used, be it either the Japanese 2003 Rules or the Japanese 1989 Rules with the Japanese 2003 Rules as their backup.

Application of the Japanese 2003 Rules to the example position requires so much space that it is beyond the scope of this webpage. To state just the conclusion: The score is 2, regardless of which ko stone is in the ko.

Summary: For the sake of keeping this webpage readable, we shall ignore the strategic variety under interpretation A and assume AJT to produce the score 2.

(1.10)

AJT: position with Black to move during the alternation and with ko stone of the ko's possible defender

# . # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

Variation 1: If Black connects and then both players pass, the score will be 2.

Variation 2: If Black passes and White passes, the score will be 2.

Variation 3: If Black passes, then White captures in the ko, and then both players pass, the board-score will be 2, White will have 1 prisoner, so the score will be 1. (White could play more aggressively with move 4 but Black would benefit.)

Variation 4:

moves 1 to 7

# 2 # 1 O # . # O # #
O # # 4 O # # # O 3 #
O O O O O # . # O 5 #
O O O O O # # # O O #

The moves 6, 7 are passes.

position at the end of the alternation

. O . . O # . # . # #
O . . O O # # # . # #
O O O O O # . # . # #
O O O O O # # # . . #

The board-score is 2. The prisoner-difference is 0. The score is 2.

Conclusion:

Variation 1, variation 4, or a similar variation are perfect play. The score is 2.

(1.11)

AJT: position with White to move during the alternation and with ko stone of the ko's possible defender

# . # . O # . # O # #
O # # . O # # # O . #
O O O O O # . # O . #
O O O O O # # # O O #

Variation 1: If White passes, Black connects, and both players pass, the score will be 2.

Variation 2: If White passes and Black passes, the score will be 2.

Variation 3: If White captures in the ko, Black passes, and White passes, then the score will be 1.

Variation 4:

moves 1 to 7

# 3 # 2 O # . # O # #
O # # 5 O # # # O 4 #
O O O O O # . # O 6 #
O O O O O # # # O O #

The moves 1, 7, 8 are passes.

position at the end of the alternation

. O . . O # . # . # #
O . . O O # # # . # #
O O O O O # . # . # #
O O O O O # # # . . #

The board-score is 2. The prisoner-difference is 0. The score is 2.

Conclusion:

Variation 3 is perfect play and the score will be 1.

(1.12)

AJT: The other cases during the alternation shall be an excercise for the reader.

(1.13)

Comparison of NAJ and AJT:

As (1.5) and (1.11) show, in some positions with 1000-year ko and ko threats strategies during the alternation, perfect play, and correct scores can differ between NAJ and AJT. Strategies and perfect play differ because the scores of some of the possible final-positions differ.