Kee Rules Of Go / VFeb 2009

Sub-page of KeeRulesOfGo

Table of contents
Table of diagrams
Simple Ko
Sending Two Returning One
1x8
Initial Board Position - Black 1 to play
White 2 to play
White 4 to play
White 6 to play - White wins
Initial board position - Black 1 to play
White 2 to play
Red 3 to play - Third player's intervention
Black 4 to play
Black 7 to play
White 8 to play
Red 12 to play - Third player's intervention again
Black 13 to play
Initial board position - Black 1 to play
White 2 to play
Black 3 to play - prohibited
White 4 to play - White wins
Initial board position - Black 1 to play
White 2 to play
White 4 to play
Black 5 to play
Initial board position - Black 1 to play
White 2 to play
Black 3 to play
Black 5 to play
White 6 to play
White 8 to play
Initial board position - Black 1 to play
White 2 to play
Black 3 to play
White 4 to play
Black 5 to play
White 6 to play
Initial board position - Black 1 to play
White 2 to play
Black 3 to play
White 4 to play
Black 5 to play
White 6 to play
Black 7 to play
White 8 to play
Index of sub-pages

KEE RULES OF GO

Written by Wilton Kee on 7-Feb-2009. Dedicated to Wing.

Homepage: [ext] http://www.geocities.com/kee_rules/kee_rules_of_go.html


I. JUSTIFICATION OF KEE RULES

To prevent cycles, one might argue that traditional go rules already serve the purpose. Simple ko rule prohibits cycle within 1 turn (with each player playing once) and superko rule prohibits longer cycles. Why do we need something different? The rationale of each component of Kee Rules is illustrated as follows.

A. Why is the cyclic prohibition superko (rather than simple ko) in nature?

Ans: Cycles like 3-ko, 4-ko and chosei can be longer than 1 turn. Superko can provide a sensible resolution to these long cycles.

B. Why is the cyclic prohibition positional in nature?

Ans: A good rule shall penalize the one who produces the repeated board position. Consider a 3-player game with "Board A -Player 1-> Board B -Player 2-> Board A -Player 3-> Board A -Player 1-> Board B". It is more reasonable to prohibit "Board B -Player 2-> Board A" (if positional) than to prohibit the second "Board A -Player 1-> Board B" (if situational).

C. Why is the cyclic Prohibition lifted after N-1 consecutive pass plays?

Ans: In classical ko, after a player has placed a stone to produce a board position, the first local repetitive response by opponents would be prohibited so as to allow the same player to further locally place a second stone freely, with hope of the possibility of such repetition being permanently extinguished by the second stone.

"Pass plays by all opponents" can be viewed as successful prohibition of their local repetitive response. To be consistent with classical ko, the game shall start freely (i.e. without the prohibition) since then.

[Diagram]

Simple Ko

As an example, consider this simple ko on a fully occupied board. If the cyclic prohibition is not lifted, no opportunity can be given to White when Black has nothing to do after winning the ko.



[Diagram]

Sending Two Returning One

Also consider this "sending two returning one" situation where Black keeps playing as a cycle after White has already passed (in White 2). If the cyclic prohibition is not lifted, wrong timing of cycle (White 4 instead of Black 5) would be prohibited.



D. Why is the cyclic prohibition not lifted until at least N-1 consecutive pass plays?

Ans: From the perspective of each player, only "own play" and "combination of plays of opponents" can be seen. Consider a 3-player game with "Board A -Player 1-> Board B -Player 2-> Board B -Player 3-> Board A -Player 1-> Board B".

If the cyclic prohibition is lifted by the pass play of Player 2 so that only "Board A -Player 1-> Board B" is prohibited, it is unfair to Player 1 as he/she can only see "Board A -Player 1-> Board B -Opponents-> Board A".

"Board B -Player 3-> Board A" shall have been prohibited like simple ko because there are actually still at least two players fighting using the cyclic prohibition.

E. Why does the game end upon 2N-1 consecutive pass plays?

Players shall be free from the cyclic prohibition after N-1 consecutive pass plays. If all players still pass after N-1 consecutive pass plays (i.e. under an environment free from the cyclic prohibition), then the game shall end as no different plays would be expected afterwards if there is no change in both board position and prohibition status.

F. Why are the intersections treated as neutral if they have ever changed between the two identical situations?

Ans: The result of the game is cyclic in nature and the final board position should therefore be not single but multiple. The previous board position which was identical to the final board position and produced by an unconditional play (after the cyclic prohibition was lifted) was the starting point of such cycle.

To avoid putting all weights to the single final board position which is just one within a cycle of many board positions, it is reasonable to argue that any intersections which have ever been changed by stone plays during the cycle were neutral and should be excluded from scoring for or against one player. Only an intersection which is permanently occupied by a stone of the same color or permanently fully enclosed by stones of the same color during the cycle should be counted in scoring.


II. STRENGTHS OF KEE RULES

1. Game ends in finite plays on all types of finite boards.

2. Game ends with a definite score.

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

4. Compatible no matter whether suicide is allowed (suicide is not allowed in the following rules as default).

5. Compatible with both area and territory scoring systems (territory scoring is chosen in the following rules as default).


III. CONTENTS OF KEE RULES

A. Equipment

1. The board consists of intersections, where intersections are adjacent to some of the others in pre-determined way. In usual circumstances, the 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. Move

3. During a game, each player possesses one color 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 move 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 move, 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 move, a player can give up the right of a stone play and choose to pass instead ("pass play").

C. Liberties

8. The unoccupied intersections which are adjacent to a stone on the board are called the liberties of such stone.

9. When a stone is adjacent to another stone of the same color, these stones are connected and form a single stone unit, and the liberties of any one of these stones are considered to be the liberties of the whole stone unit.

10. For any stone unit, when an opponent stone is placed adjacent to it, such opponent stone takes a liberty away from it. When all the liberties of a stone unit have been taken away and no liberties are left, such stone unit has to be removed from the board.

D. Removal of stones

11. A stone unit without liberties is removed from the board. There are two cases:

(a) When a stone is played so as to take the last remaining liberty of any opponent stone unit, all such opposing stone unit(s) is/are immediately removed from the board.

(b) When a stone is played so as to take the last remaining liberty of any opponent stone unit but would also leave the newly formed stone without liberties, all such opponent stone unit(s) is/are immediately removed from the board.

E. Refreshing

12. After consecutive pass plays of all opponents of a player (i.e. N-1 consecutive pass plays if the number of players is N), the game is "refreshed".

F. Invalid stone play

13. A forbidden intersection of a player is an intersection on the board which, if occupied by a stone of such player, would leave the newly formed stone unit without liberties but fail to take all the liberties of any opponent stone unit. A player may not place a stone on a forbidden intersection.

14. A player may not make a stone play to produce a board position which would be identical to a previous board position unless the game has been refreshed on another board position after the last such previous board position.

G. End of game

15. The game ends when all players agree that there will be no more stone plays.

16. The game ends when all players agree on the ranking of all players during the game.

17. The game ends when all players have consecutively made a pass play (i.e. N consecutive pass plays) immediately after the game has been refreshed (i.e. 2N-1 consecutive pass plays in total).

18. Other than the above circumstances, the game ends when the game is refreshed again on the same board position by all opponents of the same player, and the game is considered to end "cyclically".

H. Living and dead stones

19. If a game ends cyclically, intersections which have ever changed during the cycle are called "neutral intersections". For a game not ending cyclically, there are no neutral intersections on the board at all.

20. After the game ends, stones which all players agree to remove from the board are called "dead stones".

21. After the game ends, stones which are neither placed on neutral intersections nor dead are called "living stones".

I. Scoring

22. At the end of a game where ranking cannot be agreed by all players, the ranking would be determined by point counting. After all stones which are placed on neutral intersections or dead have been removed from the board, with respect of each player, the intersections occupied by the living stones of such player, as well as the non-neutral unoccupied intersections which are fully enclosed by those living stones, are counted towards the points of such player.

23. Unoccupied intersections situating between the living stones of different players are not counted towards the points of any player.

24. The ranking is determined according to the total points of each player. The higher the total points of a player, the higher is the ranking.


IV. TYPES OF CYCLES

Type 1

Examples: Boards with 3-ko, 4-ko or chosei

Type 1 can be solved using traditional superko.

Type 2

Examples: 2x1 board, 2x2 board, 2x3 board, some players disturbing on a fully occupied board, 1x8 board (see below)

[Diagram]

1x8



The game would be concluded under "cyclic scoring" mechanism (use of definition of neutral intersections).


V. TYPES OF CYCLIC PROHIBITIONS

A. Simple ko

Too weak to disallow all kinds of long cycles (all long cycles concluded as "no result").

B. Superko

Too strong to turn type 2 to anomaly. "No result" would be eliminated.

C. Spight Rules

Spight Rules give scores to type 2 using the single last board position upon game termination despite the fact in some situation that such single board position was just one within a cycle of many board positions.

D. Kee Rules

Kee Rules give scores to all types. Type 2 is given score by "cyclic scoring" which considers the oscillation of board positions during the cycle.


VI. EXAMPLES

A. Simple ko on fully occupied board

1. Simple ko in 2-player game

[Diagram]

Initial Board Position - Black 1 to play

All black stones would be captured if Black loses the ko but white stones would not be captured even if White loses the ko. Even without hope to capture the white stones, Black places B1 to capture the ko.

[Diagram]

White 2 to play

With the cyclic prohibition in place, White cannot immediately snap back. Since the board is fully occupied and there is no other empty intersection for White to place stone, White 2 can only pass.

Black has nothing else to do and Black 3 passes as well.

[Diagram]

White 4 to play

Under traditional superko rule, White can never snap back because otherwise the board position would be repeated. However under Kee Rules, W4 (unlike White 2) can snap back because with the pass of White 2 the cyclic prohibition has been lifted.

With the cyclic prohibition in place, Black 5 can only pass.

[Diagram]

White 6 to play - White wins

White wins the game.



2. Simple ko in 3-player game

[Diagram]

Initial board position - Black 1 to play

This time all white stones would be captured if White loses the ko but black stones would not be captured even if Black loses the ko. With help of the third player, we are going to see whether stronger Black can capture all white stones.

[Diagram]

White 2 to play

With the cyclic prohibition in place, White cannot immediately snap back. Since the board is fully occupied and there is no other empty intersection for White to place stone, White 2 can only pass.

[Diagram]

Red 3 to play - Third player's intervention

Now the third player, say Red, captures the Black stone to help White (probably due to consideration out of this area).

[Diagram]

Black 4 to play

Black cannot immediately snap back with the cyclic prohibition. Black 4, White 5 and Red 6 then pass.

[Diagram]

Black 7 to play

Under traditional superko rule, Black can never snap back because otherwise the board position would be repeated. However under Kee Rules, B7 (unlike Black 4) can snap back because with the passes of Black 4 and White 5 the cyclic prohibition has been lifted.

[Diagram]

White 8 to play

Now W8 can snap back. This is not prohibited because the passes of Black 4 and White 5 has lifted the cyclic prohibition. Red 9 also passes.

With the cyclic prohibition in place, Black 10 can only pass.

[Diagram]

Red 12 to play - Third player's intervention again

Like White 2, with the cyclic prohibition in place, White 11 cannot immediately snap back. Therefore White 11 passes.

However, Red can snap back again because the cyclic prohibition has been lifted by the passes of Red 9 and Black 10.

[Diagram]

Black 13 to play

Black cannot immediately snap back with the cyclic prohibition. Black 13, White 14 then pass, which is repeating the N-1 consecutive passes of Black 4 and White 5.

The game ends here with 2 neutral intersections. In other words, Black cannot capture the White stones if the third party (Red) offers help.



B. Sending two returning one on fully occupied board

1. Sending two first

[Diagram]

Initial board position - Black 1 to play

Without hope to win the game, Black places B1 to prolong the game by sending two.

[Diagram]

White 2 to play

W2 responds normally by returning one.

[Diagram]

Black 3 to play - prohibited

B3 is prohibited under both traditional positional superko rule and Kee Rules (with the cyclic prohibition). Notice that the effect under situational superko rule can be different but we are not going to discuss into details here.

[Diagram]

White 4 to play - White wins

White wins the game.



2. Returning one first

[Diagram]

Initial board position - Black 1 to play

What if the game starts from here? Black places B1 in the same way.

[Diagram]

White 2 to play

With board fully occupied and the cyclic prohibition in place, White 2 can only pass.

Black places B3 again to prolong the game by sending two. Is Black still without hope to win the game?

[Diagram]

White 4 to play

White cannot return one under traditional superko rule (both positional and situational). However under Kee Rules, W4 can return one because with the pass of White 2 the cyclic prohibition has been lifted.

[Diagram]

Black 5 to play

B5 is not prohibited because White 2 pass has lifted the cyclic prohibition. However, as White 6 would pass again, the 3 intersections would become neutral.

Such result would be less favourable to Black as compared to the score Black can obtain if allowing usual seki (2 points less now).



C. Boards with width of 2

1. 2x1 board

[Diagram]

Initial board position - Black 1 to play

Black starts the game by placing stone on B1.

[Diagram]

White 2 to play

W2 immediately snap back.

[Diagram]

Black 3 to play

With the cyclic prohibition in place, Black cannot immediately snap back. Since the board is fully occupied and there is no other empty intersection for Black to place stone, Black 3 can only pass.

White has nothing else to do and White 4 passes as well.

[Diagram]

Black 5 to play

Under traditional superko rule, Black can never snap back because otherwise the board position would be repeated. However under Kee Rules, B5 (unlike Black 3) can snap back because with the pass of Black 3 the cyclic prohibition has been lifted.

[Diagram]

White 6 to play

With the cyclic prohibition in place, White cannot immediately snap back. Since the board is fully occupied and there is no other empty intersection for White to place stone, White 6 can only pass.

Black has nothing else to do and Black 7 passes as well.

[Diagram]

White 8 to play

W8 (unlike White 6) can now snap back because with the pass of Black 7 the cyclic prohibition has been lifted.

Black 9 cannot immediately snap back and can only pass, which leads the game to "cyclic scoring". Since both intersections have ever changed during the cycle and thus are just neutral intersections. The game (2x1 board) would therefore be scored as a draw.



2. 2x2 board

[Diagram]

Initial board position - Black 1 to play

Black starts the game by placing stone on B1.

[Diagram]

White 2 to play

White replies by placing stone on W2.

[Diagram]

Black 3 to play

Greedy Black tries to win by 1 point under area scoring by placing stone on B3.

[Diagram]

White 4 to play

White captures the two Black stones by placing stone on W4.

[Diagram]

Black 5 to play

Black puts one stone back. The outcome is the same no matter B5 is on the upper or lower corner. Readers may verify by themselves.

[Diagram]

White 6 to play

The correct response for White 6 should be pass. With this, the cyclic prohibition is lifted and Black will only fall into "cyclic scoring" where all intersections will neutral. In other words, the game will be a draw and Black cannot win.



3. 2x3 board

[Diagram]

Initial board position - Black 1 to play

Black starts the game by placing stone on B1.

[Diagram]

White 2 to play

White replies by placing stone on W2.

[Diagram]

Black 3 to play

Greedy Black tries to win by 1 point under area scoring by placing stone on B3.

[Diagram]

White 4 to play

White draws the game back to a tie by placing stone on W4.

[Diagram]

Black 5 to play

Black continues to be greedy by placing stone on B5.

[Diagram]

White 6 to play

White captures the three Black stones by placing stone on W6.

[Diagram]

Black 7 to play

This is the only choice for B7.

[Diagram]

White 8 to play

The correct response for White 8 should be pass. With this, the cyclic prohibition is lifted and Black will only fall into "cyclic scoring" where all intersections will neutral. In other words, the game will be a draw and Black cannot win.


This is a copy of the living page "Kee Rules Of Go / VFeb 2009" at Sensei's Library.
(OC) 2012 the Authors, published under the OpenContent License V1.0.
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