group:
From: jasiek@berlin.snafu.de (Robert Jasiek)
Newsgroups: rec.games.go
Subject: A Simple Question:Fighting Or Disturbing Ko?
Date: Sun, 09 Jun 1996 13:11:40 GMT
Organization: Unlimited Surprise Systems, Berlin
triple ko with an eye,2 intern kos,1 extern ko,unclear status of surrounding
B
group:
It might be a n-move approach move ko (fighting ko) or a disturbing death with W dead in lower left.
The position on the right side and upper part of the board may be as
well arbitrary.
. . . . [DK = disturbing ko; FK = fighting ko]
In "Go World" No. 73,p.11,Dia.11 the following diagram 2 is termed as
DK,because internal ko threats are used and it is to be considered
as a string
ko.What is a "ko threat of a ko that is not the whole string ko" and
what is a
string ko? I regard the position to be FK, because at no moment of
the proper
move-sequence one side can tenuki without causing disturbance of the
sequence.
[diagram simplified]
Black plays 1
Disturbing ko:
Ing rules:"(...)The player who starts a disturbing ko is called the disturber.By attacking his opponent or using a double ko, the disturber creates a disturbing ko with no hot stones. After one cycle, the disturber is never allowed to continue disturbing."
There are exactly two types of DK: DLife and DDeath. Why are there not more types? Why is there no DK, in which one side has a living string and a dead string involved?
DLife is DK, in which all involved strings are alive. In the case of ko strings they are alive by being paired up with ko strings of the opposite colour and having balancing breaths. The disturber is the player, who is the first to capture a ko stone in the DK and to threaten an alive involved string of the opponent in the ko. Correct? Or is it the player to play the first move of a cycle of the DK? Only a player, whose opponent has an alive string in the DK, is allowed to become disturber. Correct?
In a DK only one player is allowed to become disturber. Even if the other player might have become disturber before the first player has earned the title disturber, as soon as the title is given to the first player, the other must not any longer become disturber. Correct?
In a DK it is only allowed to play one cycle in total. This is even true, if there might occur different cycles within the same DK. Correct? After the end of the cycle of a DK the DK falls into a static state, in which no player must try to attack the life of an opponent's string. Moves that lead to capture of own strings, however, are allowed. Correct?
What happens after structural changes in a DK? A structural change is caused by moves that change the available move-sequences within the ko. What is allowed to happen? An example of a structural change is a change from quintuple-ko (DK) to quadruple-ko (DK) to triple-ko (FK). What is allowed after a change from FK to DK? Is a ko after a structural change a DK, then are there defined not to have been a disturber nor a cycle yet?
It is necessary to know what a "cycle" is. A cycle of a DK shall be
a move-sequence, such that:
1) The sequence consists of alternating moves of both players.
2) Only the last move of the sequence may be a pass play.
3) All board plays in the sequence are ko stones in the DK.
4) The sequence could be repeatedly executed.
5) During the sequence each player repeats the board position at most
once.
Note: A cycle can be interrupted by intervening moves. Correct?
Note: The board positions before and after the sequence are the same.
Note: The ko position before the first move of the sequence does not
need to be stable. "Stable" means: No player can prohibit all cycles
in the ko position. Is it not necessary, that the ko position before
a cycle and thus maybe after a cycle is stable? Is the above a correct
definition?
Is it always the odd number moves, that are prohibited in a DK?
Now I will deal with the difficulty of defining DDeath. A definition that is helpful for intuitive understanding, but wrong: "All involved strings of one colour are alive and all involved strings of the other colour are dead." For proof of invalidity I present diagram 3:
All W stones are dead. The five B stones are also dead, but after capturing them B can finally capture all W stones. Life and death are settled; it is DK. W is finally dead; thus DDeath.
A new definition of DDeath might make use of the concept of life and death of the Nihon Kiin 1989 rules: "Stones are said to be 'alive', if they cannot be captured by the opponent, or if capturing them would enable a new stone to be played that the opponent could not capture."
In diagram 3 the five B stones are dead under Ing rules and alive under Japanese rules.
Under Ing rules it is necessary for determining the ko position in diagram 3 as DDeath to consider it locally to characterize, which points of the board, that are involved in the ko, can finally be occupied by living B stones or will count as B territory at the end of the game.
Note, however, that in diagram 3 at the end of the game the points might all belong to W after several spectacular B tenukis.
As a result to diagram 3 one has to know, which board points are involved
in the settlement of life and death of a ko position, what a final
capture of all stones of one colour within a local ko position is and
how to determine these things given an arbitrary board position. Since
the Ing 1991 rules neither give a definition of local ko position nor
a (constant-time-)algorithm for determining settlement of all locally
involved strings, the Ing 1991 ko rules are again proven to be incomplete!
Some ko positions under Ing 1991 rules are analyzed [according to the SST rules].
1. The diagram on a 7x4 board with white to play may be called
quadruple ko.
To cut the problem short only the ko stones will be noted for a
move-sequence. Move (0) is equivalent to the diagram.
(0) xxxo
(1) xxoo
(2) xxox
(3) xoox
(4) xoxx
(5) xoxo
(6) xxxo
(7) oxxo
(8) oxxx
(9) ooxx
(10) xoxx
(11) xoxo
(12) xxxo
- (0) is the starting position.
- White is the first to play and capture a ko stone.
- (1), (3), (5), (7), (9), (11) are positions with balanced ko breaths.
- (1), (3), (5), (7), (9), (11) can be termed "stable", where stable
means, that no player can prohibit all cycles in the ko position.
- (1) is the first stable position.
- Since the prologue from the instable position (0) to a first stable
position (1) is forced and gives a quadruple ko, (0) has also been
quadruple ko and is to be similar.
- Since the prologue of move (1) creates stability, no move in the
prologue is of disturbing character.
- (2), (4), (6), (8), (10), (12) disturb stable positions.
- (2) is the first disturbing move. Thus black is the player to become
the first disturber in the ko.
- (6), (10), (11), (12) repeat prior positions.
- (6) is the first repeatition caused by the disturber.
- (7) is the first stable position after the first repeatition caused
by the disturber.
- (10) is the first repeatition since there has been a disturber.
- (11) is a) the first stable position after the first repeatition
since there has been a disturber, b) the first repeatition caused by
the first player to play in the ko, c) the first repeatition of a stable
position.
- (12) is the first move after a move with features as in (11a/b).
- (1) need not be repeated at all by infinite, cyclical play.
- (3) is the first stable position after a disturber has arisen.
Ing rule: "After one cycle, the disturber is never allowed to continue disturbing." The problem is, what is a definition of "cycle". Some people say, (3) would be the last move of the cycle. Ru Lai Fo in Go World 71, "A Comparison of the New Ko Rules", p. 16 says: "The disturbing ko rule forbids [the disturber] the move which recycles the board positions, i. e. one move after the board position is repeated for the first time."
After the first repetition (6) of the position and a recreation (7)
by the opponent of the disturber of a stable state (8) is the first
move that is prohibited for the disturber. (7) is the last move of
the cycle. (8) to (12) are invalid.
2. & 3. In the general case it is impossible to distinguish between fighting ko and disturbing death. [(!) This would have to mean that the SST ko rule cannot be enforced. -wjh] However, diagrams 2, 3 present good hints of the difference of character.
2 
3 
Analysis of dia. 2: White's right string has an eye breath an shares a ko breath with black of the pair of kos. White's left string cannot get two permanent breaths in an isolated state and cannot capture and connect a. Therefore black permanently has two ko breaths and is alive. After white a, black b, white c, black a white must never play a as a continuation of disturbance again. White's left is dead in moonshine life. Thus white's right is also going to die. The position is disturbing death.
Analysis of dia. 3: A white move at a creates a disturbing life with three normal strings involved. If black wins the ko at a, the position reverts to dia. 2.
Within the local pair of kos b-c either side might start threatening the opponent's number of liberties. After the opponent takes the other ko stone of the pair, the starting player must locally pass before continuing to play locally and cyclically. However, a cycle must not contain pass plays. Thus for the starting player the cycle ends with his opponent's first answer. (The opponent might thereafter also locally start threatening.)
After black a, white c, black b, white a, black c, white b, black a
ko threats cannot be retrieved any longer on b-c by either player.
Threats are to be played elsewhere then. According to who wins the
ko at a, white might live or die. White's strings are unsettled, thus
it is a fighting ko. Temporarily the b-c disturbance could be involved.
4. When analyzing Ing ko positions one must not believe one's eyes: Here is a position where black has a balanced pair of one external and one internal shared beath, what is equivalent to one eye breath.
c-d are paired ko breaths. White has also an eye breath. a and b are
a miai eye for black. It is disturbing life.
5. Big ko spaces. Determine life and death of ko stones. Might
be fighting ko, string ko, or no ko.
6. Molasses ko once more. Here is shown, that it is fighting
ko.
Consider as a start a position with both normal strings having two
liberties. The cyclical move-sequence must contain pass plays if infinitely
executed. Positions with balanced liberties arise. However, such positions
are not stable! Not both players may pass without losing a normal string.
There is no coexistence. Thus it is a fighting ko. [Which moves in
the cycle are illegal? -wjh]
Note: Cycles of disturbing kos must not contain a pass play. [Why not? -wjh]
-------------------------------------------
Robert Jasiek
jasiek@berlin.snafu.de