2006-04-28 last update, 2006-04-28 first day, Robert
INDEX | GO | RULES
Parity of Komi (First Move Compensation Points)
Preliminary note: Here full count komi are considered. To get Chinese half
count komi, divide a full count komi by 2. E.g., the full count komi 7.5
equals the half count komi 3.75.
Both Area Scoring and Territory Scoring can let a game's score assume
every integer number. (Of course, under Area Scoring the score is not greater
than the number of the board's intersections.) So either player wins by
0, 1, 2, ... or X points. However, in playing practice one often observes
This difference is caused by the following parity aspects:
Area Scoring: Nearest scores differ by 2 points.
Territory Scoring: Nearest scores differ by 1 point.
All parity aspects could also be considered together and together they
are either even or odd.
Pi: Parity of the number of intersections of the board: Usually a 19x19
board is used. It has 361 intersections. This number has the parity odd.
As long as boards of odd parity size are used, this parity aspect is constent.
Pn: Parity of the number of not scoring intersections: Usually the number
of not scoring intersections in the scoring position is 0 or 2. These numbers
have the parity even. As long as an even number (0, 2, 4, ...) of not scoring
intersections occurs in the scoring position, this parity aspect is even.
The number of not scoring intersections is 0 if there are no coexistences
in the scoring position. The number of not scoring intersections is 2 if
there is eaxctly one coexistence with exactly two "neutral intersections"
in the scoring position or if there are exactly two coexistences each with
exactly one "neutral intersection" in the scoring position. - If the number
of not scoring intersections in the scoring position is odd (1, 3, 5, ...),
the parity aspect is odd. E.g., this is the case if there is exactly 1
not scoring intersection in exactly one coexistence in the scoring position.
This is scarce. Therefore usually (but not always) the number of not scoring
intersections in the scoring position is even.
Pk: Parity of the integer part of komi: The parity of the integer part
of komi is odd if the komi are (2n + 1) or (2n + 1.5) for some positive
or negative natural number n. The parity of the integer part of komi is
even if the komi are 2n or (2n + 0.5) for some positive or negative natural
Now we shall consider the effect of the komi parity in the usual case
that (Pi + Pn) has the parity odd. Then with so called Standard Area
Komi (2n + 1.5), the winner of a game at the scoring position is the
same under Area Scoring or under Territory Scoring, unless exceptional
circumstances (like asymmetrical coexistences or one-sided "neutral intersections")
create additional scoring differences! This has been proven in general
mathematically. Besides, under Area Scoring rules, both the komi (2n +
1.5) and the komi (2n + 0.5) always create the same winner, as long as
(Pi + Pn) is odd. E.g., if the komi 7.5 lets Black win by 1.5 under Area
Scoring rules, then Black wins by 0.5 under Territory Scoring rules and
Black wins by 0.5 under Area Scoring rules with the komi 6.5.
The nearest score difference 2 versus the nearest score difference 1 is
an aesthetical aspect. (With Chinese half counting, this becomes 1 versus
0.5.) However, the aspect is not one of practical strategic complexity
of the endgame. In both cases, the aim of the game is to win. Strategic
skill is the ability to distinguish move-sequences that lead to a win of
Black from those move-sequences that lead to a win of White. Before the
last few moves of a game, reading ahead move-sequences is always by far
beyond human capability. This is independent of nearest possible scores.
Only the omniscient player would read so far ahead already during the middle
game that he can distinguish move-sequences not only due to the winner
but also due to the parity of not scoring intersections in scoring positions.
For Area Scoring, it makes sense to use some Standard Area Komi so that
usually the score is the same as under Territory Scoring. If winning percentages
suggest a komi increment and if auction komi should not be considered an
option, then the komi increment should be 2 for Area Scoring or 1 for Territory
However, if one does not care whether in games with tiny winning margins
occupation of the "neutral intersections" often lead to different winners
under Area Scoring versus Territory Scoring, then one may as well select
komi on the grounds of the most profound among the available statistics
of professional games.
Examples on an Odd Board (7x5) with an Even Number (0) of Neutral Intersections
. . . # . . .
. # # # # # .
# # # # # # #
O O O O O O O
. O O O O O .
. . . . . . .
. # # # # # .
# # # # # # #
O O O O O O O
. O O O O O .
Discussion for Area Scoring and Territory Scoring
||Score for Example (1) under Area Scoring
||Score for Example (2) under Area Scoring
||Score for Example (1) under Territory Scoring
||Score for Example (2) under Territory Scoring
|7.75 (Button Go)
With a Standard Area Komi like 7.5, the winner (here White) is the same
in all cases.
Discussion for Spight Area Button Rules
Spight Area Button Rules are a possible compromise ruleset. They use Area
Scoring and exactly one 1/2-point button (think of it as a joker playing
card) available as a third move type. It has the strategic effect that
"neutral intersections" are worth 0 points.
In example (1), White gets the button. In example (2), Black gets the
Spight Area Button Rules ought to use Standard Area Komi plus 1/4. Then
the winner is the same for Button Go, Area Scoring, and Territory Scoring.
(For Button Go, this has not been proven in general mathematically yet,
but the author believes a proof to be possible.)
Other komi are not suitable for Button Go because the winners differ
in the case (1) for Area Scoring and Territory Scoring.
Playing inside one's territory as one's last play before the button
is taken cedes the button to the opponent. Thus, strategically, removals
should occur after taking of the button. The button, if taken after the
endgame, separates exciting alternation from the removals encore.