THE GAME OF GO (Effectively Applicable Model for The Japanese Rules of Go from 1989)
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(model created 2012-12-25, newest contents 2013-11-26)
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original rules from: http://www.cs.cmu.edu/~wjh/go/rules/Japanese.html
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Go is a game in which two players compete in skill by playing stones on a board.
The goal of the game is to have more points at the end of the game.
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The Go Universe:
* There is a COLOR, that has no single other opposite, called EMPTY.
* There is space.
* There are horizontal and vertical lines that are forming individuel intersections
and a BOARD that contains all intersections and the lines between.
* There are two colors that are the opposite of eachother, called BLACK and WHITE.
* There is time.
* There is nothing that has more than one color at a time.
* At a time every intersection has a color.
* There are (always enough) STONEs of opposed colors.
* There are PLAYERs with opposed colors, who own everything of their color,
making the players opposing eachother.
* A player has SKILL if and only if he has time.
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The Skill in the Go Universe:
* The skill of color is to enable existence.
* The skill of empty is that it will be there if something is removed.
* The skill of space is to contain something.
* The skill of a line is to run from one intersection to an adjacent intersection.
* The skill of the board is to fix the position of lines and intersections.
* The skill of an intersection is to know its color.
* The skill of time is to enable change.
* The skill of a stone is to occupy an intersection with its own color.
* The skill of a player is to make a move.
* The skill of Go is to enable a game.
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A game follows the order:
* beginning-of-the-game
* competition by playing a move-sequence
* analysis (confirming-life-and-death and scoring)
* end-of-the-game (counting the points)
* game-result
except :
- it finishes because a cycle-end during the competition or
- a resumtion-request during the analysis
[- or finishes imediately by resignation or forfeit of a player]
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BEGINNING-OF-THE-GAME
Set up the board (empty). [board-size 19 x 19]
Attach the players to an opposed color.
Start the competion (with blacks turn).
COMPETITION
The competition starts (or resumes) with a move-sequence.
When this move-sequence finishes with two passes then the competition is stopped,
else the game finishes with cycle-end.
~~
A 'Game of Go' refers to the moves played in the move-sequence(s) during the competition.
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Assume: The competion has stopped with two passes.
That asserts:
* Every chain has at least one liberty.
* There is no ko-ban.
ANALYSIS
1) CONFIRMING-LIFE-AND-DEATH
Make a status-analysis for each chain.
(During this status-analysis the player of the chain that gets analysed is called "defender"
and the opponent "attacker".)
Finally every chain is market either "alive" or "dead".
2) SCORING
Apply the territory-detecting for each (emty) intersection (from that is not known yet
wether it is an eye-points or dame).
{For the result the order is irrelevant,
though (sometimes) some orders are faster than others.}
Finally every empty intersection is marked as territory or dame.
All intersections with dead chains which can be taken of as prisoners are also marked as
territory for the opponent.
~~
Stones which are alive and adjacent to territory are said to 'surround territory'.
Stones which are alive and adjacent to dame are said to be in 'seki'.
Stones which are dead and adjacent to territory are said to be 'prisoners'.
{Stones which are dead and adjacent to dame could be called in 'anti-seki'.}
~~
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END-OF-THE-GAME
Every empty point marked as territory gives one point (to that player),
every as territory marked intersection with a prisoner gives two points
(one for the prisoner and one for the territory there), and
every prisoner from the competition gives one point (for the player who made the capture).
Count all these points for each player [and add komi to whites points].
GAME-RESULT
The player with more points has won the game (and the opponent has lost).
If no player has more points then the game is a tie.
[This may or may not include a cycle-end in the competition.]
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General definitions:
Two intersections are "adjacent" if there is a line but no other intersection(s) between.
"An intersection i is adjacent to a set of intersections" if
i is adjacent to at least one intersection of that set and i is not an element of that set.
Two intersections of the same color are "connected" if they are adjacent or
if they are both connected to a third intersection.
A "chain" is a stone and all stones that are connected to this stone.
A "liberty" of a chain is an empty intersection adjacent to this chain.
A "string" is an intersection and all intersections that are connected to this intersection.
The exact distribution of the color of every individuel intersection is called "position".
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Definitions for the competition:
[...] // "cycle", "cycle-end" and "move-during-the-competition" as usual.
A "move-sequence" during the competition starts with a move of one player,
lets the player alternately make one move at a time and
finishes as soon as a pass follows directly on a pass or exceptionally with a cycle-end.
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RESUMTION option
After the competition has stopped and before the end-of-the-game
(that means during the analysis) a player can make a "resumtion-request".
Then the competition continues by playing an additional move-sequence
from the position where the competition has stopped (and with that prisoner numbers)
and the opponent has the turn first.
After a player made a resumtion-request this player is never allowed
to make a resumtion-request in the same position again (for the rest of the game).
If both players make a resumtion-request at the same time then black has the first turn and
both players are never allowed to make a resumtion-request again in this position.
If a resumption of the competition happens then the moves of previous move-sequence(s) during
the competitions does not matter anymore for cycles, it is a new move-sequence, that means
the position where the competiton had stopped is the very first position in the following
move-sequence.
Everything done so far in the analysis becomes irrelevant.
~~
Of corse one could agree to use some previous informations that were not affected by the
resumtion. It's also possible to use the resumtion option to force an undo for a mistake in
the analysis, so it wiser to give the opponent an undo freely - even more when considering
that the analysis is not part of the competition, but only to decide the result of the
competition.
~~
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SYNTAX DEFINITIONS to mark (or describe) a set of intersections:
"Reachable" means there is a path from one intersection to another intersection
only over adjacent intersections; it depends on the given rule from where to where is allowed.
A rule looks like: x --> y with x, y are colors
and means: for each x-colored intersection that is already in the set add all adjacent
intersections that are y-colored, and so on for all the new found intersections.
":=" means 'is'.
"|" means 'or'.
"%" means 'nowhere'.
~~
The application of this method: Start with (a set of) one given intersection and
recursively add adjacent intersections in all directions accordingly to the given rule.
It is only important not to forget an intersection, it never matters if you add an
intersection more than one time - for a human it should be impossible to get in a
cycle here 
~~
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Definitions for the analysis:
A "ko-capture" is a play that:
* captures exactly one stone and
* the just played stone is not adjacent to any stones of its color //single stone
* and has exactly one liberty. // in atari
A "ko-stone" is a stone that could be ko-captured (at this moment).
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HYPO-SEQUENCE
Definitions for the hypo-sequences:
~~
Stones that are captured in a hypo-sequence does not affect the score.
The term 'ko-shadow' is used instead of 'ko-ban' and
the ko rules are different than in the competition.
~~
A "ko-shadow" does not change or hide the color of an intersection, it only matters
for ko- and cycle-rules and has no effect on other rules.
A "move" consists of either:
- making a play
- making a "ko-pass" for one specific ko-shadow of your own color
(illegal if there is no) by removing this ko-shadow.
- making a 'pass'
A "play" consists of placing one own stone at an intersection that is
neither occupied by a stone nor by a ko-shadow of the same color as the player,
and then removing any (if there are any) opposing chains that have no liberties. //capture
If the play is a ko-capture then put on the position of the removed stone a ko-shadow of
the color of that stone.
A play is illegal, if the placed stone has no liberties at the end of the play
(and does not remove any oposing stones so that there are liberties after this). //suicide
A "tactical-situation" is the information of:
* the color of every intersection
* the exact position of all ko-shadows
* whose turn it is.
If a tactical-situation is equal to a tactical-situation before (in this hypo-sequence)
it is called "tactical-cycle".
The "intersections of the tactical-cycle" referes to all intersections on wich a stone was
played between the previous occurence of this tactical-situation and this one.
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A hypo-sequence follows the order:
Eleminate all ko-shadows with the same color as the player to-move if a play at this
intersection right now would not be a ko-capture or if a play there would be illegal
for a reason different than the ko-rules (e.g. already occupied or suicide).
When a tactical-situation occurs that is equal to a previous from this hypo-sequence:
if the tactical-cycle contains at least one interesection of the chain c
then the hypo-sequence finishes with a tacical-cycle
else the player to-move must make a (forced-)pass with his next move.
{technically, for the rules this is absolutely the same as a normal pass}
Remember this tactical-situation (to notice if a tactical-cycle occurs in the future).
Now the player makes his move.
If a pass follows directly on a pass then the hypo-sequence is finished
else the opponent has the turn.
This repeats until the hypo-sequence is finished.
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STATUS-ANALYSIS (for a chain c)
~~
The compensation-region does not affect the hypo-sequence in itself,
but is used only for the interpretation of the result.
~~
{Shortcut: To make things faster there is also the possibility to analyse more chains of the
same color in the same analysis if the attacker is confident to prove all the chains dead.
Then the compensation-region consits of all compensation-regions of all chains to analyse.
If the attacker cannot prove all analysed chains dead then all these chains are alive.
At least if the hypo-sequence does not finish with a tactical-cycle then it is equal or more
difficult for the attacker and equal or more easy for the defender.}
The "compensation-region" (of the chain c) := an intersection of c and all intersections
that are reachable from there by:
empty --> all
black --> black | empty
white --> white | empty
Start a hypo-sequence from the position where the competition has stopped
with the attacker having the turn.
If the hypo-sequence has finnished with a tactical-cycle
then treat all intersections of the tactical-cycle as beeing empty.
Now the result gets interpretated:
If there is a stone from the defender:
- on an intersection of the chain c or
- on on an intersection of the compensation-region (of the chain c) where before
no stone from the defender was
then the chain c is alive,
else it is dead.
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TERRITORY-DETECTING (for an intersection i)
~~
The construction of the territory-region can be stopped as soon as it is clear,
that the intersection i must be a dame, because this does not imply anything for other
intersections (except for the string of the intersection i, of corse).
~~
"territory-region" (of the intersection i) := i and all intersections
that are reachable from there by:
empty | dead --> all
alive black --> black | empty
alive white --> white | empty
<ko-stone> --> black | white // apply this rule in addition to the other rules!
//shortcut: dame, (anti-)seki
If the territory-region (of i) contains:
* at least one alive black stone and
* no dead black stones and
* no alive white stones
then all empty or white intersections from the territory-region (of i) are black-territory
(and prisoners)
else if the territory-region (of i) contains:
* at least one alive white stone and
* no dead white stones and
* no alive black stones
then all empty or black intersections from the territory-region (of i) are white-territory
(and prisoners)
else the intersection i (and the string containing i, of corse) is dame.
~~
Note: If intersection i is an eye-point, then all empty or dead intersections from the
territory-region are also eye-points (and prisoners), but if intersection i is dame,
this does not imply that the other marked intersections are dame !!
Marking other intersections than i as territory is not necessary and could be considered
as a shortcut, because you could apply the territory-detecting on an intersection with a
stone (to see if it is a prisoner).
{In general it is possible that there are two empty intersection x and y,
where the investigation of x proves x and y are territory,
but investigating y only proves that y is territory and gives no information about x.}
~~
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SHORTCUTS:
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DAME-transfer-procedure (from an dame intersection i)
!! It must be already known that intersection i is dame !!
{or start from a stone from that is already known that it is in seki (or anti-seki)}
~~
Applying the territory-detecting on an intersection that is territory is quite efficent
because (normally) it proves territory on other intersections, too.
But in cases with a lot of dame it would require an investigation of each string.
The dame-transfer should make things faster and easier as well.
~~
"dame-region" (of i) := i and all intersections
that are reachable from there by:
empty --> all
alive black --> black | dead white | emty
alive white --> white | dead black | empty
dead --> dead | empty
All empty intersections of the dame-region are dame and
no of the stones of the dame-region surrounds territory.
~~
If this procedure is used as shortcut then it can be stopped at any point or one may
skip intertersections in the for-each, because when an intersection is detected as dame,
this will not change anymore, so, for example, there is no need to keep on in a direction,
that is already marked as dame (or seki).
~~
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(Whose) EYE-STRING OR DAME-STRING (for an empty {or dead} intersection i)
~~
This function might be faster than territory-detecting (for i) if intersection i is dame.
On the other hand, if intersection is is proved as an eye-string (of one color)
it does NOT imply that the intersection i is territory.
This function can only proves that it is not territory for one color or for both colors.
For humans to built the eye-region is not really a shortcut because it is anyway quite
obviously, and in practise one can normally exclude that it is territory for one side and
thus only needs to test two possibilities.
But it can be used to define 'eye-string' and could be used to classify different types of
(anti-)sekis. (Though this classification is irrelevant for this rules.)
~~
"eye-region" (of i) := i and all intersections
that are reachable from there by:
empty | dead --> empty | dead
If the eye-region (of i) :
* contains no black stone and
* is adjacent to at least one black stone and
* is not adjacent to a white stone
then the eye-region is a black eye-string
else if the eye-region (of i) :
* contains no white stone
* is adjacent to at least one whith stone and
* is not adjacent to a black stone
then the eye-region is a white eye-string
else the eye-region (of i) is a dame-string
{and the stones inside could be called 'alive in antiseki'}.
~~
Note: During the 'marking' of the territory-region, if you reach an intersection that is
(part of) a dame-string then you can stop; reaching an eye-string does not prove anything,
except you reach eye-strings for both players.
{You can also stop if you reach a stone from that is known it is in seki (or anti-seki).}
~~
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Copyright
My rules may be used freely if and only if:
* The intention is not bad for Go and
* they are not used commercially (without my permission).
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