Kee Rules Of Go / VMay 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
Black 10 to play
White 11 to play
Scoring board position
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
Black 7 to play
White 8 to play
White 10 to play
Black 11 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
Black 9 to play
Black 11 to play
White 12 to play
White 14 to play
White 16 to play
Black 17 to play
Index of sub-pages

KEE RULES OF GO

Written by Wilton Kee on 12-May-2009.

Based on principles set up on 14-Mar-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 in Kee Rules 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 in Kee Rules 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 a pass play?

Ans: This is to draw consistency between a non-fully-occupied board and a fully-occupied board. In a non-fully-occupied board, to a player who has just occupied a ko position but actually hopeless to take further step on it, an irrelevant play on elsewhere on the board by his opponent can already be treated as a effective ko-threat to him because the board position has been altered. As the hopeless player finds no way to take further step on it, the opponent can take back the ko position and win the ko.

However, in a fully-occupied board, no where on the board is available for the opponent to make such a irrelevant ko-threat play. If cyclic prohibition cannot be lifted by a pass, i.e. a pass is not assumed to have altered the board position or treated as the weakest ko-threat, the ko position would be forever occupied by the hopeless player and the game would be halted there. This is inconsistent with the non-fully-occupied board and undesirable.

[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 capturing 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 does the game end when the same player passes on the same board position again?

After a pass play, the player is free from any previous cyclic prohibition. If the same player passes on the same board position again, there is actually no change in both board position and prohibition status (i.e. free from any previous cyclic prohibition) from the previous identical pass play. The game can end without any complaint because any desired possibility should have already been be tried out after the previous identical pass play.

E. Why are all the board positions consecutively passed by all players considered as the scoring board positions?

Ans: If there is any stone play after the initial scoring play, the result of the game is cyclic in nature. Instead of putting all weights to the single final board position which is just one within a cycle of many board positions, it is reasonable to allow certain board positions within the cycle to be used for scoring.

It is easy to understand that board positions which are not consecutively passed by all players should not be used for scoring. It is because there is at least one player does not agree on such board position to be used for scoring by successfully making stone play on it.

On the other hand, a player passes on a board position either because he agrees on such board position to be used for scoring, or is forced to pass because of cyclic prohibition. As the end of a game means the desired possibility has been tried out, a player forced to pass will still be forced to pass next time even if the game continues. In such case, the player cannot say he does not agree if situation does not allow. Therefore, all the board positions consecutively passed by all players can be considered as the scoring board positions.


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 (area scoring is chosen in the following rules as default).


III. 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 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 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 color, 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.

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(s), all those opponent 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 unit with no liberties, only all those opponent stone unit(s) is/are immediately removed from the board and the newly formed stone unit is not removed.

E. Invalid stone play

12. A forbidden intersection of a player is an unoccupied intersection on the board which, if occupied by a stone of such player, would leave the newly formed stone unit with no liberties but fail to take the last remaining liberty of any opponent stone unit(s). A player may not place a stone on a forbidden intersection.

13. A player may not make a stone play to produce a board position which would be identical to a previous board position unless a pass play has ever been made by any player after the last such previous board position.

F. End of game

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

15. The game also ends when a player makes a pass play on a board position which he has previously made a pass play on. The series of plays after but not including such previous pass play is called the "scoring cycle".

G. Scoring

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

17. For the scoring cycle, if any stone play exists, the series of all pass play(s) before the first such stone play, if any, is repositioned to follow the last play. A board position which has been consecutively passed by all players in the scoring cycle after such reposition, if any, is called a “scoring board position”.

18. For each scoring board position:

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

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

(c) Unoccupied intersection(s) which is/are enclosed by stones of different players on the board are not counted towards the point(s) of any player.

19. If there are no scoring board positions after the game has ended, the game is draw.

20. The ranking is determined according to the average of total point(s) earned by each player from each of the scoring board position(s). The higher the point(s) earned by 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



Type 2 can be concluded with a definite score under "cyclic scoring" in Kee Rules which considers the board positions passed by all players during the cycle.


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 a definite score by "cyclic scoring" which considers the board positions passed by all players 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 pass of Black 4 the cyclic prohibition has been lifted.

[Diagram]

White 8 to play

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

[Diagram]

Black 10 to play

Now B10 can snap back. This is not prohibited because the pass of Red 9 has lifted the cyclic prohibition.

[Diagram]

White 11 to play

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

[Diagram]

Scoring board position

The game ends here. In other words, Black cannot capture the White stones if the third party (Red) offers help. This board position is the only one consecutively passed by all players, and therefore it is the scoring board position.



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". During the cycle, since both board positions have been consecutively passed by both players, 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.

The board position is favorable to White for scoring even if White 6 passes. So White 6 passes.

[Diagram]

Black 7 to play

B7 cannot pass, otherwise such board position may be used for scoring.

[Diagram]

White 8 to play

White puts one stone back. The outcome is the same no matter W8 is on the upper or lower corner. Readers may verify by themselves.

The board position is favorable to Black for scoring even if Black 9 passes. So Black 9 passes.

[Diagram]

White 10 to play

W10 cannot pass, otherwise such board position may be used for scoring.

[Diagram]

Black 11 to play

Black puts one stone back. If Black 11 is on the lower corner, it would lead to more steps, but the result is the same. Readers may verify by themselves.

When White 12 passes, it is identical to White 6. The game ends here. Since there is no scoring board position formed, the game is draw.



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.

The board position is favorable to White for scoring even if White 8 passes. So White 8 passes.

[Diagram]

Black 9 to play

Black puts one stone back. The outcome is the same no matter B9 is on the left or right corner. Readers may verify by themselves.

The board position is favorable to White for scoring even if White 10 passes. So White 10 passes.

[Diagram]

Black 11 to play

Black 11 captures the three White stones by placing stone on B1.

[Diagram]

White 12 to play

This is the only choice for White 12.

The board position is favorable to Black for scoring even if Black 13 passes. So White 13 passes.

[Diagram]

White 14 to play

White 14 puts one stone back. The outcome is the same no matter W4 is on the left or right corner. Readers may verify by themselves.

The board position is favorable to Black for scoring even if Black 15 passes. So Black 15 passes.

[Diagram]

White 16 to play

White 16 captures the three Black stones by placing stone on W6.

[Diagram]

Black 17 to play

This is the only choice for Black 17.

When White 18 passes, it is identical to White 8. The game ends here. Since there is no scoring board position formed, the game is draw.


This is a copy of the living page "Kee Rules Of Go / VMay 2009" at Sensei's Library.
(OC) 2016 the Authors, published under the OpenContent License V1.0.
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