1996-9-23 last update, 1996-7-7 first day
Robert Jasiek, jasiek@berlin.snafu.de
Copyright: All rights of the author are preserved according to the international law.

Examples 1

Introduction
Examples
Links

Introduction

This page intends to ease understanding of The New Ko Rules. For further important, difficult or extraordinary examples see Examples 2. Conventions are defined.

Examples

Examples on Definitions for Ko
Examples on Definitions of Ko Types
Examples on Rules

Examples on Definitions for Ko

MSs and ko strings

Examples of cyclical MSs as defined in Ing ko explanation are W[aa], W[aaaa], W[aa]*, W[bb], W[bccb], B[edfedf], B[edfedf]*.
For example, W[bc] is not a cyclical MS.
In all mentioned MSs all played stones are ko strings. All of the ko strings are single ko stones. All captured ko strings are complete ko strings.
All noted MSs are ko stone MSs.

ko mouths, ko couplings, and ko positions

On the board are 19 ko stones, 16 ko strings, 13 single ko stones, 3 double ko stones, 16 ko mouths, 5 ko couplings, and 7 ko positions.
All ko strings are complete ko strings. A stone played on c or n would not yet be a complete ko string. After another move two spaces left of n there would be two ko strings in one ko mouth and neither be a complete ko string.
Examples of cyclical MSs are B[cedfecfd], B[qppq].
The ko mouths on the board are - denoted by a letter #together# with the unmarked string adjacent to the letter point - a, b, c-d, e-f, g, h, i, j, k, l, p, q, r, s and m together with the point right of it and n-o together with the two points left of n. These ko mouths consist of 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, respectively 4 board points.
The marked strings are strings of ko couplings. 5 ko positions have a ko coupling. Note: A ko coupling does not belong to a ko position itself.
The ko positions are - given by the letters #together# with the ko strings - a-b-c-d-e-f, g-h-i, j-k-l, m, n-o, p-q, and r-s. These ko positions consist of 12, 6, 6, 2, 4, 4, respectively 4 board points.
p-q is an example for a ko position with a ko coupling of three strings, r-s an example for more than three.

Examples on Definitions of Ko Types

There are FKs and DKs. A DK may be a DLife or a DDeath. A DLife may have a ko coupling or not. If a DLife has a ko coupling, then it may be in one of two states: stable DLife or instable DLife.

DLifes with a ko coupling

Three ko positions a-b, c-d, e-f-g-h are on the board. Their ko couplings are marked.
c, d are ko mouths of 4 board points.
All of the strings of all ko couplings have at least two breaths each.
After W[ba] the B string of the ko coupling of a-b has regained its second breath. In the other ko positions a second breath can be regained similarly without repeating the board position.
In neither of the ko mouths c or d a ko stone could be played, so that it would not be adjacent to a ko stone of its colour and adjacent to a ko stone of the opposing colour. (Even after B[cd] such a played ko stone would not reduce a string of the ko coupling to one breath.)
Thus all of the ko positions are in a state of stable DLife. (And after B[cd] the ko position c-d would it be again.) They are DLifes and thus DKs.
Each of the ko stone moves b, c, d, e, f, g, respectively h reduces a string of a ko coupling to one breath. But in each case the move a, d, c, g, g, e, respectively e then would transform the corresponding ko position into a state of stable DLife. Thus after the first move it would be in a state of instable DLife.
Stability means coexistence for the time being, instability means irreversable threat of one player's strings.
After B[a] the ko position a-b still remains stable.
Stability is a kind of balance as can be observed for example by playing a proper MS in the ko position c-d.
Each of the ko stone moves a, b, c, d, e, f, g, h in a ko position in a state of stable DLife disturbs a DK due to an reduction of the breath number of at least one string of the opponent
A ko position in stable DLife behaves like a seki. It is balanced and can remain unchanged on the board until the end of the game. Temporary periods of instability may make life a little bit more exciting.

If a DLife has no ko coupling, then it is a single DLife. The name reflects its number of ko mouths: one.

single DLifes

All reasonable known ko mouth types are shown.
The ko positions a-b, c-d-e, f-g, h, i-j-k, l-m-n are single DLifes. They do not have ko couplings.
The positions of o and p do not have single DLifes. In the ko mouth of o respectively p an infinite ko stone MS can be played. This is also possible in c-d-e, a ko mouth of the same shape as the ko mouth in p : 4 board points in a row. p has two ko strings, c-d-e not. Since B will not play at e (and W not at c in the mirrored formation), in c-d-e no infinite ko stone MS will ever occur in actual play. The ko mouth p has become a FK.
In the ko position a-b B[baM] is a cyclical MS.
In the ko position c-d-e a typical MS is W[cdttteMt]. It is used for ko threats.
In a-b, f-g, h, i-j-k, respectively l-m-n no infinite ko stone MS exists. Therefore they are single DLifes.
The position f-g, h, i-j-k, respectively l-m-n cannot be a ko position, if no proper further ko stones are on the board. However, as given on the board, corresponding cyclical MSs exist.
i-j-k and l-m-n have triple ko stones.
B[b], W[c], B[h] disturb one of the ko positions.
The reader is asked to play through possible MSs.
A single DLife may behave like a seki and remain on the board til the end of the game, if it is not disturbed, or else its future is unclear, when for the possession of the board points of the ko mouth is fought with the aid of other ko positions.

A DDeath may have a ko coupling or not. If a DDeath has a ko coupling, then it may be in one of two states: stable DDeath or instable DDeath. In such a DDeath all cyclical MSs, during which all ko strings of the ko position are captured, violate the basic ko rule.

DDeaths with a ko coupling

The ko couplings are marked. The ko positions on the board are a-b, c-d, e-f, g-h. They all have two ko mouths. Each ko mouth consists of two board points.
Each of a-b, e-f, g-h also have a ko stone of each colour, at least one string of a ko coupling with only one breath, and the strings of the other colour of the ko couplings have at least two breaths.
Thus the ko positions a-b, e-f, g-h are in a state of stable DDeath.
The W string of the ko coupling of the ko position c-d has exactly the breaths of the ko position, i. e. c and d, as its breaths. Thus the ko position c-d is in a state of instable DDeath.
B[c] or B[d] transforms the DDeath into a state of stable DDeath. B[cttc]# or B[dttd]# disturb the DDeath by transforming it from a state of stable DDeath into instable DDeath.
W[b], B[f], respectively W[h] give the corresponding ko position ko strings of only one colour, so it ceases to be in a state of stable DDeath. Then one W, two B, respectively two W strings of the corresponding ko coupling have in each case exactly the breaths of the ko position a and b, e and f, respectively g and h as their breaths. The state is transformed into instable DDeath. The corresponding moves b, f, h disturb a DDeath.
In a DDeath a so called eye breath like i or j prevailes over a so called ko breath like c or g. Stability is given during an occurance of a pair of ko breaths of ko stones of different colour and allows the capture of so called dead strings.
The reason of predominance of an eye breath over a ko breath is as follows: Starting from instability as in the ko position c-d after a ko capture like B[c] the player of the string of the ko coupling with possible breaths only being in ko mouths, i. e. W, must answer with a ko threat B[ct]# elsewhere due to the basic ko rule. Starting from stability as in the ko position g-h after a ko capture W[h] the player of the strings of the ko coupling with possible breaths only being in ko mouths, i. e. again W, must after his opponent's possible answer W[hg]#, which is not prohibited by rule of basic ko, play a ko threat W[hgt]# elsewhere due to the basic ko rule. In both cases the basic ko rule forces one and only one player to make ko threats, while the other side's normal string is alive. So it is reasonable to define such ko positions as DDeath.

If a DDeath has no ko coupling, then it is a single DDeath. The name reflects its number of ko mouths: one.

single DDeaths

No ko coupling exists.
In both ko positions a and b of all adjacent strings to the ko mouths the B have at least two breaths, what is already enough, while with a B ko stone in each ko mouth the W have only one breath each and cannot gain more. Thus a and b are single DDeaths.
B[atta]# and B[bttb]# disturb a DDeath.
As can be seen from the examples, in a single DDeath all adjacent strings to the ko mouth of one and only one player are threatened to become captured in the moment of ceasing ko mouth existence.

A ko position, that is not a DK, is a FK. In general the nature of FKs can be described as so called unsettled life and death of involved ko strings.

FKs

Three classical ko positions: a-b-c is a triple ko, d is a basic ko (this most common ko shape may occur in various surroundings), and e-f is an eternal life.
The triple ko has a ko coupling (marked stones). It is not a DLife, because neither have nor can have after a move all strings of the ko coupling at least two breaths. It is no DDeath, because it has more than two ko mouths. So it is a FK.
In the basic ko a ko stone MS of infinite length can be played. All adjacent strings to the ko mouth have more than one breath. Thus it is neither a single DLife nor a single DDeath. It is a FK.
Also on the eternal life an infinite ko stone MS can be played. The ko mouth consists of more than two board points. Thus the ko position is a FK.
Ko stone MSs let the ko positions still be FKs.
In each of the three ko positions the fighting rule applies.

Examples on Rules

basic ko rule (1)

The B ko stone is a single ko stone. W[a] captures it by placing a new single ko stone on the board. By rule of basic ko this new stone must not be recaptured immediately.
E. g. W[attatta] with intervening ko threats is possible.
The beginner's needle in a haystack: All other ko shapes scarcely occur. The easiest way is to ignore them.
Note also the fighting rule.

basic ko rule (2)

This is a double ko, that is in a state of stable DLife. Nevertheless also the basic ko rule applies.
B[aa]# and B[abb]# are not allowed due to rule of basic ko.

fighting rule (1) - at b shall be a B stone, at d shall be a W stone.

The eternal life (traditional name) is a FK. Without rules B[acbd] would be a competently played cyclical MS.
Application of the fighting rule gives B[attcttbttdtt] as a possible MS.
In eternal life the burden for the search for ko threats is the same as in basic ko.
Note: Before b and d are on the board, b is not played in a FK. After B[b] the ko position exists and is a single DLife. So W may answer at d. Then it is a FK, but still B may answer, too. But then for that B's move the fighting rule applies, i. e. W cannot play c immediately.
Note: Under Ing ko rules B[attcttbd] is the proper MS.

fighting rule (2)

The triple ko has a ko coupling (marked) and is a FK.
After W[a] B must not play on a or c due to the fighting rule.
W[atta]# must not be answered with a or b, likewise W[attc]# not with b or c.
The triple ko is fought, as if it would be a basic ko.

disturber rule (1)

This triple ko is in a state of stable DLife; it is a DK.
If B wants to play in the ko position, he may disturb it with B[a]. By disturber rule B as the first to disturb the ko position during a ko stone MS in it becomes the disturber of it.
Play may proceed as in B[acbacb]. The ko position of the DK before the occurance of the disturber, i. e. before the MS, is repeated for the first time after the MS. By disturber rule the disturber B is then not allowed to disturb the DK. This remains true while he is disturber or will be true due to the prohibition rule.
B needs to tenuki: B[acbacbt]#. This ends the ko stone MS in the DK and thus B ceases to be disturber by disturber rule.
B[act], B[acbat] are also conceivable and lead to an earlier end of the played ko stone MS in the DK and B's disturber title.
If W wants to play in the ko position, he may disturb it with W[c] and become disturber. After W[cb] W must not capture any ko stone in the DK due to rule of basic ko. W[cbt]# ends the ko stone MS and W ceases to be disturber.
Note, that after B[ac], B[acba], B[acbacb], or W[cb] the DLife is again stable.

disturber rule (2)

The ko position is a single DDeath.
B[a] does not disturb the DK. B[atta]# disturbs it and W becomes the disturber. After B[attat] W has ceased to be disturber.

prohibition rule (1)

Three basic FKs are on the board. With more than one ko position on the board (called string ko) the prohibition rule becomes relevant.
With B[c] B plays the first ko stone in a fighting ko during the starting ko stone MS, that may continue as B[cbac].
So far the configuration of stones on the board position except all ko positions, that existed before the MS, has been maintained, i. e. repeated, by each move of the MS. Also the set of board points of the union of all ko positions has been repeated. Under these conditions no player has played twice in a fighting ko a ko stone. So the prohibition rule does not apply yet.
B[cbacb]# and B[cbacba]# are also not prohibited.
Even B[cbacbac]# is allowed as the exception of the prohibition rule, that ignores the first ko stone in a fighting ko.
Finally the prohibition rule hinders W from playing B[cbacbacb]#. Due to the rules of basic ko and fighting W also must not recapture c.
If a forth basic ko with a B ko stone in it would exist on the board, then no rule would prohibit W to capture its ko stone. However, the reality tells W to play a ko threat B[cbacbact]#. This changes the configuration of the stones on the union of all board points, that are not part of a ko position. This virtually lets the prohibition rule forget about all prior reasons for prohibition. After an answered ko threat both players might again opt for the trouble of playing through a long ko stone MS followed by a ko threat etc., e. g. B[cbacbacttcabcabctt..].
If the players do not like long and fruitless ko stone MSs, they may restrict themselves to a handy MS like [ctt] and repeat it during the ko fight.
Now the purpose of the prohibition rule has become clear: String kos should be played out, as if only one basic ko would be on the board. Only under special circumstances the players should be interested in a derivation from simplicity.

prohibition rule (2)