2001-12-22 last update, 1997-2-1 first day,
Copyright: All rights of the author are preserved according
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| RULES | DEFINITIONS
- KO - END - TOURNAMENT
Game End Rules
Game end rules formally handle the part of a game after the last move that
altered the score. A game end leads to scoring. There are different types
of scoring and game phases before.
Game end rules say what to score, how to score, how to prepare the board
position before scoring, and how to dissolve infinite or exceptionally
long play not properly treated by ko rules. Scoring may have modifications.
Special circumstances may lead to special game ends.
Go is a contest about sharing a go board. Play leads to a board position
at the game end that is scored. Each player has a score that is measured
in points. The difference of scores determines the win and the winning
margin. Sharing refers to the grid points of the board. Each grid point
is worth one point for scoring. The scoring operation is the sum. Two colours
- black and white - share the grid points. It is natural to consider all
grid points for sharing. Rules that virtually do this are called area rules.
During a game alternating play results in about an equal number of grid
points with black respectively white colouring. Rules that use this fact
are called territory rules. A further simple scoring method exists. Primitive
rules even completely avoid scoring.
Instead of determining the winner by scoring primitive rules let the first
player without an available move lose the game. Such rules omit passes.
Games tend to be very long and are so called pass fights. Their final stage
consists of suicides respectively attempts to prohibit those of the opponent.
They are important in mathematics.
The simplest scoring method considers
grid points only. Both players fill as many grid points as they can. Only
single eye points or small shared spaces remain. The final positions naturally
become terminal. To minimize empty grid points it is of great strategical
importance to connect own groups.
Basically area rules score the grid points as
Generally the score of a player is the grid points of his colour plus all
empty grid points that are monochromely surrounded by his colour. The scoring
allows moves inside own territory that are free of cost. Thus all removals
can be solved by actual play.
Basically territory rules score only empty grid points but add prisoners:
Generally the score of a player is all empty grid points that are monochromely
surrounded by his colour plus all prisoners of the other colour (with each
prisoner being worth one point).
Since stones on the board are not added to the score, removals are not
caused by board plays but left for the confirmation phase in which, however,
most removals cannot be logically performed.
Shared grid points
Grid points that are not monochromely surrounded by one colour are called
shared points. Counting varies:
4 is currently used in no rule set. 1 to 3 are equivalent.
counted for both players' scores
proportionally shared : each grid point is shared in proportion to the
number of surrounding grid points of a colour
Several rule sets have special treatments for special shapes. Some shapes
as parts of board positions are called alive or dead or seki or with other
names. Severe bearings on scorings follow.
Various counting methods exist. Methods are designed to fit scoring methods.
Often application is only possible with particular scoring methods.
According to the rules in use adjustments for handicaps and penality
points need to be considered together with common komi. - Proportional
sharing needs special arithmetics.
This can be applied for stone or area rules. All scored grid points are
filled with stones. With stone scoring for each group the tax of two eye
points is not scored. A single odd number empty point of all shared points
is not filled.
After filling two ways of comparison exist. One is point-symmetrical
arrangement of all stones on the board. The black respectively white stones
are put on the upper respectively lower half of the board and the center
grid point possibly becomes the odd shared point. The second way is putting
away from the board pairs of two stones of black and white.
The score is the resulting difference of both colours' stones.
Point By Point Counting
This method is mainly used for area rules or in implementations. All scored
points are counted. For each counted colour the board is scanned like reading
and the grid points scoring for a colour counted directly. The difference
of colour counts is the winning margin.
Point By Point Half Counting
In case of a half count only one colour is counted using the point by point
method. The count is compared with half of the number of grid points. If
there are shared grid points, then comparison refers to half of the difference
of the number of board points and the number of shared points. Half komi
values are to be used. To gain the normal score the difference is multiplied
Chinese Half Counting
With this method for area rules only one colour is counted. The count is
compared with half of the number of grid points. If there are shared grid
points, then comparison refers to half of the difference of the number
of board points and the number of shared points. Half komi values are to
be used. To gain the normal score the difference is multiplied by two.
Unlike point by point counting the board position is rearranged. The
empty regions of the counted colour are ordered for eased counting (rectangular
shapes). Rearrangement must keep the numbers of surrounded grid points
constant, of course. To achieve multiples of 10 (to fit the decimal system)
stones of the counted colour can be taken off the board. Also stones of
the colour could be added. The value for empty grid points is stored. Then
the stones of the counted colour that are then on the board are arranged
in blocks of 10 (as far as possible). The stone number is counted and added
to the stored empty point number. Then the total value is used for comparison.
Japanese Territory Counting
Naturally this is only valid for territory rules. Together with Japanese
rules point by point counting is scarce. For Japanese territory couting
it is essential to keep any prisoner captured or removed from the board
before the end of the game together with possible pass stones.
The empty territory regions on the board of both players are conveniently
rearranged. The numbers of surrounded grid points must be constant. Single
empty grid points can be tranferred between regions of the same colour.
All prisoners of a colour are filled into empty regions of the colour as
far as possible.
The remaining empty grid points of black respectively white are added.
Remaining prisoners are substracted. Both colours' sums are compared as
Fill-in counting requires area rules and an equal number of black and white
stones throughout the game of which the sum is the number of board points
or the number of board points minus one.
Fill-in allows a clear use of scoring by sharing the board between two
colours. The winner and the winning margin are obvious at a glance. The
method reduces possibilities of counting mistakes. However, proper means
are necessary for easy handling of stone numbers. Bowls are used to keep
all unplayed or captured stones of one colour.
All stones are filled on the board. First shared empty grid points are
filled equally sharing them. If there is a single odd empty grid point,
it remains unfilled. Then own stones are filled in empty areas surrounded
by own stones only. Then half as many stones as compensation points exist
altogether (if divisable by two, this is generally the case) are put as
stones of the colour giving the points in an empty surrounded area of the
other colour. Finally remaining stones are filled as so called losing stones
in the remaining empty area of the opponent. Compensation stones and losing
stones must be positioned separately. (If compensation stones do not have
enough space to be put in opponent's area, then a proper number of opponent's
stones become losing stones by placing them in area of the player with
compensation points. If, on the other hand, not enough stones as compensation
stones are available, then the number is completed by taking stones from
The winning margin in favour of the opponent of the losing stones' player
is twice the number of losing stones plus possibly one point for an empty
grid point adjacent to losing stones.
A simplified game phase structure is:
A setup is used for placement of handicap stones or in special rule sets.
The alternation phase is the main part of the game consisting of alternating
moves of black and white. A move is a board play or a pass. Mostly with
two successive passes the game stops. Then in the confirmation phase removals
due to rules or the players' agreement take place. If this is done, then
the game ends. This means that without fail counting is to be performed.
The phases alternation, end, and counting are sufficient for a game.
Simple area rules, e.g., know this. Else in a confirmation phase removals
due to the players' agreement or with the aid of life and death rules occur.
Some rule sets allow resumption of alternation phase or partition the confirmation
phase into different phases.
The alternation phase is identical in most rule sets. Only very few
do not know passes. All other phases have different rulings in the various
Another phase structure shows the type of board plays made during the
Examples are available.
The main classification of game end rules is done as to their scoring class
and usage of game phases. The following are the most important game end
outset : empty board
optional setup : placement of handicap stones (while opponent possibly
alternating competition moves (possibly incl. fight to gain/ avoid first
dame points, defense-inside-territory points, elimination of opposing ko
threats (during alternation phase or as far as possible during confirmation
optional removals by mutual verbal agreement or required by life-death
possibly removals of opposing stones by alternating play (possibly under
exceptionally Korean removals of superfluous own stones
exceptionally ancient encore of filling as far as not causing removal
exceptionally greedy ancient encore as an extended ancient encore dissolving
Examples are available.
Primitive, stone, and simple area rules omit stop and confirmation phases.
In agreement rules confirmation is done by agreement of the players. In
life-death rules confirmation happens due to rulings.
In the alternation phase a single pass by one player signals that he thinks
he cannot alter the score by a board play. The first pass play of a game
(except passes during the setup) has in some cases an effect on the rules.
In most cases two passes played successively by both players are required
for a game stop. Sometimes this is equal to the game end. A confirmation
phase can be structured using further occurances of (mostly two successive)
passes and often its end is formally indicated by two successive passes.
A few rule sets allow both area and territory scoring while giving the
same count. This is enabled by an adjustment value. An often applied means
is the use of pass stones.
As long as during alternating play no passes occur the numbers of played
stones of each colour remain equal (with white having moved last). Furthermore,
for each prisoner removed from the board the other player is to play exactly
one stone on the board. So while one occupied point of one colour is added
to an area's score, one prisoner point for the score of the same colour
is added to a territory's score.
If one player passes and the other moves with a board play, then the
territory score is not directly affected, but the area score alters by
one in favour of the player not passing. To keep the balance the passing
player gives his opponent a pass stone as a prisoner if territory rules
are used. Thus also with territory rules the net effect is one point in
favour of the player not passing.
Rules with pass stones need to take care of an odd number of moves.
E. g., this is possible by forcing white to move last. In handicap games
different measures might be necessary depending on the rules.
Komi are compensation points added to the white score. Komi can be used
to make even or handicapped games fair, to include penality points or adjust
or replace pass stones.
In even games without komi black wins by far most of the games. In professional
play a komi of 5.5 and of 7.5 has given black a chance of roughly 53%.
So maybe 9.5 komi might be more appropriate. The broken values avoid tied
Chinese counting evaluates only half of the board. Therefore komi must
be half of normal values: 2.75 instead of 5.5, e. g.
Fill-in counting allows easy handling if komi can be divided by two.
Furthermore, an odd board size and rarely occuring odd numbers of odd sekis
most often lead to an odd winning margin. Thus the difference between smallest
black respectively white wins is two. So different komi can only be distinguished
properly if they differ by at least two. Altogether fill-in komi should
be 2, 4, 6, 8,... with black winning ties.
Similarly and due to black's 50% chance to get an extra board play area
rules with other counting mechanisms need 1.5, 3.5, 5.5, 7.5, 9.5, ...
Handicap stones besides the first in area rules add just by being placed
on the board one point to the black score each. This can be adjusted by
Special Game Ends
A void game is a game ending without result. This can be caused by cyclical
play of infinite character if ko rules do not prohibit it, extremely long
move-sequences similar to cyclical play, or disagreements aiming at a game
end between players that are allowed by the rules.
To name a few examples: If ko rules only treat basic ko, then the ko
stones of a triple ko can be captured endlessly. With improper ko rules
and n basic kos on the board about two to the power of n moves might occur
before a first repetition of the board position. This could need millions
of years. So a referee might want to intervene and adjudge the game as
void. If removals in the confirmation phase are to be resolved by mutual
agreement, disagreements are likely to occur and result in a void game.
Constant Game End
Good ko rules achieve short move-sequences for all kinds of ko positions.
Still some exceptional cases allow extremely long move-sequences. To ensure
a game end after a reasonable move number all rule sets should include
a constant game end rule:
What should be the constant value? So far the record for a 19x19 game is
about 425 moves. However, ko play easily might exceed this. For each basic
ko capture a ko threat is played. Thus at least double the number of grid
points might be necessary to fill the whole grid. So the minimal value
must be roughly 750. 1024 is chosen for easier complexity calculations.
If some ko threats within kos shall be possible, then such a higher or
even a greater number is appropriate.
The 1024th board play of a game is required to be followed by passes.
Insufficient performance during the alternation phase might make it almost
impossible to gain a winning score at the game end. In such cases a player
has the option of immediately ending the game with his loss by announcing
Lack of Time
If under set conditions the allotted time is exceeded by a player, then
this causes his immediate loss and ends the game.
A misbehaving player violating rules or human conventions forfeits a game.
This means his loss and the game end. In tournaments it is the task of
referees respectively tournament directors to judge in such cases.
Suspension is a game end without result and due to extraordinary circumstances
or based on some tradition. Natural forces are one example. In Japan the
higher ranked player was traditionally considered to have the right of
suspension at any time.
All board positions at a game end are called terminal. In a strict mathematical
sense a more restrictive view is possible. Game theory is interested in
positions allowing clear decompositions of the grid as to scoring and unalterable
scores. In practice some rule sets allow scoring for any position, others
have a strong desire to score only certain classes of positions. You will
get a good idea of terminal positions by looking at examples.
Some - mostly former - rule sets had exceptional preferences. The following
cannot be expected complete.
Ancient Chinese rules had a group tax. For each independently living group
on the board two points were deducted from the score. This had historically
evolved from stone scoring. Obvious fill-in encores were omitted and the
tax kept. This explains the existence of Japanese rules, in which games
are shortened and territory is counted but logical scoring got lost.
Old Korean rules, that used territory scoring, followed the removals of
opposing dead stones during the confirmation phase by removals of own stones
so that own empty regions are enlarged but still completely safe. A maximal
number of superfluous stones surrounding empty regions could be taken off
the board. This requires further hypothetical analysis of possible play
and has a severe effect on strategy and tactics in the alternation phase.
History has breeded rule sets owning precedents. These are special board
positions being used as exceptional rulings. Many are owed to traditions.
Game end rules have not been spared. Famous examples are bent-4-in-the-corner,
three-points-without-capturing, and ten-thousand-year-ko.
Simple area rules, agreement area rules, and territory rule sets shall
Simple Or Agreement Area Rules?
Simple area rules have concise rule texts and a simple game structure (alternation,
end, counting), but they need a few extra moves to remove stones from the
board before the end. Agreement area rules often allow a short confirmation
of removals, but their texts are longer, the game structure is complicated
by stop and confirmation phases, and with the players' disagreement the
extra moves for removals are also needed.
Possible agreements in most cases are a compromise for all who want
to avoid the elegance of simple area rules. People preferring agreements
argue removal moves blot the position. So they keep blotting it with hypothetical
play instead and are afraid of being forced to use a minute for a game
end in alternation.
Area Or Territory Rules?
Area rules are concise, simple, and logical. The only disadvantage is that
more points are counted. Territory rules are long, complex, and illogical.
(If they are logical, then because of having approached area rules.) The
arguments clearly favour area rules.