Kee Rules of Go

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Table of contents Table of diagrams
Why more complicated rule variants B and C?
Are rule variants B and C different?
More case study #1: Can Black now capture White?
More case study #2: Can Black now capture White?
More case study #3: Can Black now capture White?
Simple ko in 2-player game
Simple ko in 2-player game (cont.)
Simple ko in 2-player game (cont.)
Simple ko in 2-player game (cont.)
Simple ko in 3-player game
Simple ko in 3-player game (cont.)
Simple ko in 3-player game (cont.)
Simple ko in 3-player game (cont.)
Simple ko in 3-player game - Scenario 1 (White passes)
Simple ko in 3-player game - Scenario 2 (White captures)
Simple ko in 3-player game - Scenario 2 (cont.)
Simple ko in 3-player game - Scenario 2 (cont.)
Sending two first
Sending two first (cont.)
Sending two first (cont.)
Sending two first (cont.)
Returning one first
Returning one first (cont.)
Returning one first (cont.)
Returning one first (cont.)
2x1 board
2x1 board (cont.)
2x1 board (cont.)
2x1 board (cont.)
2x1 board (cont.)
2x2 board
2x2 board (cont.)
2x2 board (cont.)
2x2 board (cont.)
2x3 board
2x3 board (cont.)
2x3 board (cont.)
2x3 board (cont.)
Special simple ko in 3x4 board
Special simple ko in 3x4 board (cont.)
Index of sub-pages

KEE RULES OF GO

Last updated by Wilton Kee on 5-Jan-2012.


I. BEAUTY OF KEE RULES

1. Applicable to any types of boards with any sort of connections between intersections for stone placement.

2. Applicable to any number of players (even 3 or more).

3. For finite boards, all games end within finite plays by consecutive pass plays of all players and with a definite score - see (a) below.

4. Compatible no matter whether suicide is allowed - see Rule 12.

5. Compatible with both area and territory scoring systems - see (b) below.

6. Flexibility in allowing rectification of unforeseeable cyclic plays without penalty (if all players agree) - see (c) below.

7. Flexibility in allowing rule variants for different definitions of a forbidden intersection in a game with 3 players or more - other rule variants not listed below are also possible.

Notes:

(a) The possibility of endless cycle is elimiated by Rules 13 to 15 (they are the key differences of Kee Rules from other rule variants).

(b) Area scoring system is chosen in Rule Section H only as default and can be altered as a variant rule set.

(c) It can be understood that at the time of stone placement, it may be difficult to realise that such a stone play will end up being retrospectively prohibited. So for practical reason, rahther than replacing such a stone play with a forced pass play as required by Rule 15, the rule can be loosen to allow replacing it with another stone play of the same player. Since the game resumes from there, it makes no difference from the situation where the player made such another stone play in the first place (i.e. no advantage taken from the cyclic plays).


II. CONTENTS OF KEE RULES

A. Equipment

1. A board consists of intersections, where intersections are adjacent to some of the others in a pre-defined way. In usual circumstances, a board is marked with 19 parallel vertical lines and 19 parallel horizontal lines, making 361 intersections.

2. The number of stones shall be sufficient to end a game. In a two-player game, usually lens-shaped black and white stones are used.

B. Play

3. During a game, each player possesses one colour of stones.

4. In usual circumstances, a game starts with an empty board, where all intersections on the board are unoccupied.

5. Each player makes a play by alternately placing one stone on an unoccupied intersection of the board ("stone play") to occupy such intersection. In a two-player game, usually black player makes the first play, then white player, and then black player again and so on in alternation until the end of the game.

6. After a stone has been placed on the board, it cannot be moved to any other intersection.

7. A stone play is the right of a player. In any play, a player can give up the right of a stone play and choose to pass instead ("pass play").

C. Liberties

8. An unoccupied intersection which is adjacent to a stone on the board is called the liberty of such stone.

9. When a stone is adjacent to another stone of the same colour, these two stones are connected and belong to a single stone unit, and the liberty of any one of these stones is considered to be the liberty of the whole stone unit.

D. Removal of stones

10. Forbidden intersection: For a stone play, a forbidden intersection of a player is an unoccupied intersection on the board which, if occupied by such stone play, would leave the newly formed stone unit with no liberties but:

Rule variant A: fail to take the last remaining liberty of any opponent stone unit(s).

Rule variant B: fail to take the last remaining liberty of any opponent stone unit(s) assuming all opponents are of the same colour.

Rule variant C: fail to take the last remaining liberty of at least one stone unit of every opponent who already has stones adjacent to such unoccupied intersection.

[Diagram]

Why more complicated rule variants B and C?

Rule variants B and C is to avoid situations in a 3-player (or more) game where a player can play on an intersection without liberty when one of his opponent still has. Here the 3rd player is playing after Black but before White. Without such restriction, the 3rd player can play on the red triangle such that White can play on black+square to make himself alive, which White cannot do by himself.

[Diagram]

Are rule variants B and C different?

Under rule variant C, if the 3rd player can capture at least one stone unit of each opponent with stones adjacent to the intersection to be placed, then it is not forbidden (as shown), where both the two Black stones on left and the two White stones on right would be captured. However it is still forbidden under rule variant B.

[Diagram]

More case study #1: Can Black now capture White?

Here the red circle denotes the stone of the third player Red.

First note that rule variant A is always more generous than rule variants B and C to the player placing the stone.

In this case Black can capture White with rule variant A and B, but not C.

[Diagram]

More case study #2: Can Black now capture White?

In this case Black can capture White with all rule variants A, B and C.

[Diagram]

More case study #3: Can Black now capture White?

In this case Black can capture White with rule variant A and C, but not B.



11. Capture rule: After each stone play, if it was not made on a forbidden intersection, all opponent stone units whose last remaining liberty was taken away by such stone play are immediately removed from the board.

E. Immediate prohibition

12. Suicide rule: If suicide is not allowed, a player may not make a stone play on a forbidden intersection. If suicide is allowed, when a player makes a stone play on a forbidden intersection, the newly formed stone unit is immediately removed from the board.

13. Pass-lifting positional superko rule: A player may not make a stone play to produce a board position which would be identical to a previous board position unless consecutive pass play(s) have ever been made by any N-1 player(s) (where N is the number of players) on another board position after the last occurrence of such previous board position.

F. Retrospective prohibition

14. Retrospective prohibition: When a player has made a pass play on a board position immediately after a stone play, and if the same player has previously made a pass play on an identical board position without a pass play immediately before such previous pass play, then the first stone play after such previous pass play is retrospectively prohibited.

15. Forced pass play: Once a stone play has been retrospectively prohibited, the player who made such stone play is now forced to replace it with a pass play, and the game resumes at the point immediately after such forced pass play.

G. End of game

16. The game ends when there have been 2N-1 consecutive pass plays. The last board position would be used for scoring.

17. The game also ends when the ranking can be agreed by all players.

H. Scoring

18. At the end of a game where ranking cannot be agreed by all players, the ranking would be determined by scoring.

19. For the board position used for scoring:

(a) Stone(s) is/are removed from the board if all players agree.

(b) With respect to each player, each intersection occupied by a stone of such player on the board, as well as each unoccupied intersection which is fully enclosed by stone(s) of such player, is counted towards one point of such player.

(c) An unoccupied intersection which is enclosed by stone(s) of more than one players on the board are not counted towards any points of any player.

(d) The ranking is determined according to the total point(s) obtained by each player. The higher the total point(s) obtained by a player, the higher is the ranking.


III. EXAMPLES

A. Simple ko on fully occupied board

1. Simple ko in 2-player game

[Diagram]

Simple ko in 2-player game

Question: Is White able to capture the black stones with only one liberty and one simple ko if all the intersections sensible for stone placement are fully occupied?

[Diagram]

Simple ko in 2-player game (cont.)

If Black captures the ko by B1, White is prohibited to recapture the ko immediately under Rule 13. So W2 can only be a pass play. After that, Black cannot fill the ko due to lack of liberty, so B3 can only be another pass play.

[Diagram]

Simple ko in 2-player game (cont.)

With pass play in between, White is allowed to recapture the ko by W4. Again Black is prohibited to recapture the ko immediately under Rule 13. So B5 can only be a pass play.

[Diagram]

Simple ko in 2-player game (cont.)

White can then capture all the black stones. Therefore, White is able to win the game by capturing the black stones with only one liberty and one simple ko.



2. Simple ko in 3-player game

[Diagram]

Simple ko in 3-player game

Question: Is Black able to capture the white stones with only one liberty plus one simple ko under similar "fully occupied" board even if there is a third player helping White to defend?

[Diagram]

Simple ko in 3-player game (cont.)

Same as the previous example, if Black captures the ko by B1, White is prohibited to recapture the ko immediately under Rule 13. So W2 can only be a pass play.

[Diagram]

Simple ko in 3-player game (cont.)

What if now there is a third player (coloured red) coming to capture the black stone by placing on the red triangle (Red 3)? Black is prohibited to capture the red stone immediately under Rule 13 (because it repeats the board position produced by the pass play of W2 with no pass plays afterwards). So B4 can only be a pass play.

After that, White and Red do not have any sensible stone plays, so they pass.

[Diagram]

Simple ko in 3-player game (cont.)

With all the pass plays, Black is allowed to recapture the ko by B7. After this, there are two possible scenarios - (1) White passes, or (2) White captures.

[Diagram]

Simple ko in 3-player game - Scenario 1 (White passes)

In Scenario 1, if White passes, such pass play would be identical to the pass play W2. The first stone play after the pass play W2 (i.e. the stone play Red 3) would be retrospectively prohibited under Rule 14. Then Red is forced to replace Red 3 with a pass play and the game resumes from there under Rule 15.

After Red passes, the new B4 would then be a stone play to capture all White stones.

[Diagram]

Simple ko in 3-player game - Scenario 2 (White captures)

In Scenario 2, if White captures the black stone directly by W8, Red has nothing to do but pass.

[Diagram]

Simple ko in 3-player game - Scenario 2 (cont.)

According to Rule 13, at least 2 consecutive pass plays are needed to lift the ko, so Black cannot recapture the ko by B10. So Red 9, Black 10, White 11 and Red 12 are all pass plays. According to Rule 16, 5 consecutive pass plays are needed to end the game. Now Black 13 can do what he desired to do at B0 - to recapture the ko.

[Diagram]

Simple ko in 3-player game - Scenario 2 (cont.)

White 14 cannot recapture immediately, so he passes. Now it resembles Scenario 1, where such pass play would be identical to the pass play W2. The first stone play after the pass play W2 (i.e. the stone play Red 3) would be retrospectively prohibited under Rule 14. Then Red is forced to replace Red 3 with a pass play and the game resumes from there under Rule 15.

After Red passes, the new B4 would then be a stone play to capture all White stones.



Therefore, in both scenarios, Black is able to win the game by capturing the white stones with only one liberty plus one simple ko even if there is a third player helping White to defend.



B. Sending two returning one on fully occupied board

1. Sending two first

[Diagram]

Sending two first

Question: Is Black able to prolong the game by sending-two-returning-one type of cycle?

[Diagram]

Sending two first (cont.)

B1 sends two stones and W2 returns one stone.

[Diagram]

Sending two first (cont.)

B3 is prohibited by Rule 13 since it repeats the board position before B1 without any pass play in between.

[Diagram]

Sending two first (cont.)

With no sensible stone plays, Black passes. White is able to stop Black from prolonging the game by capturing the black stones by W4.



2. Returning one first

[Diagram]

Returning one first

Question: Is Black able to prolong the game if the game starts with one white stone returned?

[Diagram]

Returning one first (cont.)

Black captures the white stone by B1. White passes and Black sends two again by B3.

[Diagram]

Returning one first (cont.)

Since after the starting board position a pass play on another board position was made (W2), White is allowed to capture the two black stones by W4. However, with the same reason as the previous example, B5 is prohibited by Rule 13 since it repeats the board position before B3 without any pass play in between.

[Diagram]

Returning one first (cont.)

With no sensible stone plays, Black passes. White is again able to stop Black from prolonging the game by capturing the black stones by W6.



C. Greedy Black in boards with width of 2

1. 2x1 board

[Diagram]

2x1 board

Question: Starting from an empty board, can Black do better than a draw?

[Diagram]

2x1 board (cont.)

B1 and W2 are obvious as above. They are followed by two consecutive pass plays since immediate recapture of ko is prohibited by Rule 13.

[Diagram]

2x1 board (cont.)

B5 to recapture the ko is allowed with pass plays in between. Again, it is followed by two consecutive pass plays since immediate recapture of ko is prohibited by Rule 13.

[Diagram]

2x1 board (cont.)

W8 to recapture the ko is allowed with pass plays in between. It is followed by a pass play of Black (B9) since immediate recapture of ko is prohibited by Rule 13. Such pass play would be identical to the pass play B3. The first stone play after the pass play B3 (i.e. the stone play B5) would be retrospectively prohibited under Rule 14. Then Black is forced to replace B5 with a pass play and the game resumes from there under Rule 16.

[Diagram]

2x1 board (cont.)

This results in three (N+1) consecutive pass plays (from B3 to B5) which end with the above board position to be used for scoring. Since White would win 2 points with the above board position, Black would not start the game by occupying an intersection by B1, and Black cannot do better than in a draw.



2. 2x2 board

[Diagram]

2x2 board

Question: Starting from an empty board, can Black do better than a draw?

[Diagram]

2x2 board (cont.)

Black tries to do better than a draw by B3. We will see whether White can avoid this happening.

[Diagram]

2x2 board (cont.)

White captures the two black stones by W4.

[Diagram]

2x2 board (cont.)

Black's only possible answer would then be either a stone play at B5 or a, with White responding with its first pass play. Since the succeeding plays will end up being a cycle, the next stone play will eventually turn into a forced pass play, and the above board position will be used for scoring. Since White would win 1 point with the above board position, Black would not occupy an intersection by B3 to be immediately captured, and Black cannot do better than in a draw.



3. 2x3 board

[Diagram]

2x3 board

Question: Starting from an empty board, can Black do better than a draw?

[Diagram]

2x3 board (cont.)

Black tries to do better than a draw by B5. We will see whether White can avoid this happening.

[Diagram]

2x3 board (cont.)

White captures all black stones by W6.

[Diagram]

2x3 board (cont.)

Black's only possible answer would then be B7, with White responding with its first pass play. Since the succeeding plays will end up being a cycle, the next stone play will eventually turn into a forced pass play, and the above board position will be used for scoring. Since White would win 2 points with the above board position, Black would not occupy an intersection by B5 to be immediately captured, and Black cannot do better than in a draw.



D. Special simple ko in 3x4 board

1. Special simple ko in 3x4 board

[Diagram]

Special simple ko in 3x4 board

Question: Starting from B1, who will win the game?

It is undesirable for either of the two players to fill the ko after capturing it. See SpightRules/Example.

[Diagram]

Special simple ko in 3x4 board (cont.)

Similar to the 2x1 board example above, it turns out that the board position after White's capture by W2 will be used for scoring. With White winning by 2 points, B1 is not an optimal play (because B1 can do better at least at a).


This is a copy of the living page "Kee Rules of Go" at Sensei's Library.
(OC) 2012 the Authors, published under the OpenContent License V1.0.
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