Kee Rules Of Go/v Dec 2007

Sub-page of KeeRulesOfGo

Table of contents Table of diagrams
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
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 - prohibited
White 6 to play - White wins
Initial board position - Black 1 to play
White 2 to play
Black 3 to play
Black 5 to play
White 6 to play - prohibited
White 8 to play – still prohibited
Scoring board position
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
White 8 to play
White 10 to play
Black 11 to play
White 12 to play
Black 13 to play
White 14 to play
White 16 to play
Black 17 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
White 10 to play
White 12 to play
White 14 to play
White 16 to play
Black 17 to play - prohibited
White 18 to play - White wins
Index of sub-pages

KEE RULES OF GO

Written by Wilton Kee on 11-Dec-2007. Dedicated to Wing.

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


EVOLUTION OF CYCLIC PROHIBITION IN GO RULES

1. Traditional simple ko

EFFECT: Prohibition of immediately repetitive board position

EXAMPLES: Majority of rules used in tournaments (e.g. Chinese Rules, Japanese Rules)

IMPLICATION: It fails to give a score to long cycles such as 3-ko, 4-ko and chosei (typically concluded as "no result" or "draw").

2. Traditional superko

EFFECT: Prohibition of repetitive board position / situation

EXAMPLES: Minority of rules used in tournaments (e.g. Ing Rules, New Zealand Rules)

IMPLICATION: Anomaly occurs in certain fully occupied boards (see EXAMPLES A.1 & B.2 below).

3. Pass-lifting positional superko

EFFECT: Prohibition of repetitive board position without pass in between

EXAMPLE: Spight Rules

IMPLICATION: Anomaly is eliminated, but a game may end with pass of a single player even when another player is still placing stones.

4. Pass-lifting positional superko + Cyclic prohibition

EFFECT:

Prohibition 1: Prohibition of repetitive positional board without pass in between

Prohibition 2: Prohibition of board change upon repetitive non-overlapping situational cycle

EXAMPLE: Kee Rules

IMPLICATION: Anomaly is eliminated while the principle of "ending a game by consecutive passes" is preserved.


CONTENTS OF CYCLIC PROHIBITION IN KEE RULES

PROHIBITION ONE: Prohibition of repetitive positional board without pass in between

- A player may not place a stone to produce a board position which is identical to any previous one unless a pass has been made in between.

PROHIBITION TWO: Prohibition of board change upon repetitive non-overlapping situational cycle

- Cycle is retrospectively formed between two identical board situations if plays in between were not all passes.

- Prohibited path of such cycle, which is the path from board situation at cycle start to board situation after first stone placement, is identified.

- Prohibited path must be in the form of:

(a) just "stone placement"; or

(b) "pass", "stone placement"; or

(c) "pass", "pass", "stone placement"; or

(d) "pass", ..., "pass", "stone placement".

- A player may not place a stone in a way which, together with previous passes (if applicable), is identical to the prohibited path of any cycle formed.


PRINCIPLES OF KEE RULES

1. A game shall be applicable to any number of players (even 3 or more).

2. A game shall end in finite plays on all types of finite boards.

3. A game shall end with consecutive passes of all players.

4. A game shall end with a definite score.

5. Rule of cyclic prohibition shall be compatible with different preferences on suicide (whether or not suicide is allowed).

6. Rule of cyclic prohibition shall be compatible with different scoring systems (both area and territory scoring).


GAME FLOW

A. Initial setting

B. General play

C. Dead stone removed

D. Prohibition checked

E. Termination checked

F. Board Situation produced

G. Prohibition updated

H. Return to B for play of next player


GAME FLOW DETAILS

A. Initial setting

1. Recent Path (a series of board situations): The first player to play on initial board position

2. List of Prohibited Boards (a set of board positions): Initial board position

3. List of Prohibited Paths (a set of board paths): Empty

B. General play

1. The current player makes a play on the current board position by placing stone or making pass.

C. Dead stone removed

1. If placing stone, dead stones are removed to produce a new board position.

D. Prohibition checked

1. If placing stone:

(a) The new board position may not be identical to any in List of Prohibited Boards.

(b) The path to produce the new board position may not be identical to any in List of Prohibited Paths.

E. Termination checked

1. A game ends with N+1 consecutive passes (where N is the number of players).

F. Board Situation produced

1. A new board situation is produced, i.e. the next player is going to make a play on the new board position.

G. Prohibition updated

1. If placing stone, the new board position is added to List of Prohibited Boards.

2. If making pass, all board positions previously added to List of Prohibited Boards are deleted from the current List of Prohibited Paths.

3. If the last N plays (including the current play) are not all passes and the new board situation is identical to any in Recent Path:

(a) The sub-path in Recent Path from such board situation to the first board situation with a changed board position is added to List of Prohibited Paths.

(b) All board situations previously added to Recent Path are deleted from the current Recent Path.

4. The new board situation is added to Recent Path.


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 Prohibition One 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. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board position encountered by Black 1) are erased. Black has nothing else to do and Black 3 passes as well.

[Diagram]

White 4 to play

This board situation is not cyclic because both White 2 and Black 3 are passes.

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 such prohibition has been erased.

After snap back of W4, the new board situation repeats the one for Black 1 to play (as recorded in Recent Path). All records in Recent List are erased and the sub-path of how cycle started is stored in List of Prohibited Path. In other words, Black cannot place a stone in a way of how the cycle previously started (i.e. Black 1) in the future. Therefore, with this Prohibition Two 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 not sure whether stronger Black can capture all white stones.

[Diagram]

White 2 to play

With Prohibition One 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. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board position encountered by Black 1) are erased.

[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 Prohibition One. Black 4, White 5 and Red 6 then pass. With Black 4's pass, all previous records in List of Prohibited Boards (i.e. board position encountered by White 2 and Red 3) are erased.

[Diagram]

Black 7 to play

This board situation is not cyclic because all Black 4, White 5 and Red 6 are passes.

Under traditional superko rule, White 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 such prohibition has been erased.

After snap back of B7, the new board situation repeats the one for White 2 to play (as recorded in Recent Path). All records in Recent List are erased and the sub-path of how cycle started is stored in List of Prohibited Path. In other words, Red cannot place a stone in a way of how the cycle previously started (i.e. White 2 followed by Red 3) in the future. Therefore, with this Prohibition Two in place, if White passes on this board position in the future, Red can only pass.

[Diagram]

White 8 to play

So W8 should snap back. This is also not prohibited because of the passes before B7. Red 9 also passes. With this pass, all previous records in List of Prohibited Boards (i.e. board position encountered from Black 4 to White 8) are erased.

[Diagram]

Black 10 to play

With pass of Red 9, B10 is not prohibited even with B7.

After snap back of B10, the new board situation repeats the one for White 8 to play (as recorded in Recent Path). All records in Recent List are erased and the sub-path of how cycle started is stored in List of Prohibited Path. In other words, White cannot place a stone in a way of how the cycle previously started (i.e. White 8) in the future. Therefore, with this Prohibition Two in place, White can only pass. With White's pass, as discussed before, Red can also only pass under Prohibition Two as well.

[Diagram]

Black 13 to play

Black wins the game by Black 13 (B3).



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 Prohibition One). 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 Prohibition One in place, White 2 can only pass. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board position encountered by Black 1) are erased.

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 there is already no such board position in the current List of Prohibited Boards with the pass of White 2.

After W4, the new board situation repeats the one for Black 1 to play (as recorded in Recent Path). All records in Recent List are erased and the sub-path of how cycle started is stored in List of Prohibited Path. In other words, Black cannot place a stone in a way of how the cycle previously started (i.e. Black 1) in the future.

[Diagram]

Black 5 to play - prohibited

As discussed above, with Prohibition Two in place, B5 is prohibited. Therefore, Black 5 can only pass.

[Diagram]

White 6 to play - White wins

White wins the game by W6.



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 Prohibition One 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. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board positions encountered by Black 1 and White 2) are erased. White has nothing else to do and White 4 passes as well.

[Diagram]

Black 5 to play

This board situation is not cyclic because both Black 3 and White 4 are passes.

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 such prohibition has been erased.

After snap back of B5, the new board situation repeats the one for White 2 to play (as recorded in Recent Path). All records in Recent List are erased and the sub-path of how cycle started is stored in List of Prohibited Path. In other words, Black cannot place a stone in a way of how the cycle previously started in the future. In other words, White cannot place a stone in a way of how the cycle previously started (i.e. White 2) in the future.

[Diagram]

White 6 to play - prohibited

As discussed above, with Prohibition Two in place, W6 is prohibited. Therefore, White 6 can only pass.

Black 7 is satisfied with the two points for Black and therefore passes.

[Diagram]

White 8 to play – still prohibited

With Prohibition Two in place, W8 is still prohibited. White 8 can only pass.

[Diagram]

Scoring board position

With 3 consecutive passes, the game ends with this board position and Black wins by 2 points under area scoring.



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.

[Diagram]

White 6 to play

White 6 passes. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board positions encountered from Black 1 to Black 5) are erased. Black is not satisfied with the current board position and places stone on B7 to capture the two white stones.

[Diagram]

White 8 to play

It is important for White to place stone on the upper instead of lower corner. Readers may verify by themselves that placing stone on the lower corner would eventually prohibit W10.

It is unwise for Black 9 to place stone. Please try to verify this.

Assumes Black 9 passes. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board positions encountered from White 6 to White 8) are erased.

[Diagram]

White 10 to play

White captures the two black stones again. This capture is allowed because with pass of Black 9, the previous board positions in List of Prohibited Boards have been erased.

After W10, the new board situation repeats the one for Black 5 to play (as recorded in Recent Path). All records in Recent List are erased and the sub-path of how cycle started is stored in List of Prohibited Path. In other words, Black cannot place a stone in a way of how the cycle previously started (i.e. Black 5) in the future.

[Diagram]

Black 11 to play

Black is prohibited to place stone on the upper corner with Prohibition Two. Black therefore places stone on the lower corner instead.

[Diagram]

White 12 to play

White 12 passes. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board positions encountered from Black 9 to Black 11) are erased.

[Diagram]

Black 13 to play

With pass of White 12, Black 13 (B3) captures the two white stones again.

[Diagram]

White 14 to play

It is important for White to place stone on the upper instead of lower corner. Readers may verify by themselves that placing stone on the lower corner would eventually prohibit White 16.

It is unwise for Black 15 to place stone. Please try to verify this.

Assumes Black 15 passes. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board positions encountered from White 12 to White 14) are erased.

[Diagram]

White 16 to play

White captures the two black stones again. This capture is allowed because with pass of Black 15, the previous board positions in List of Prohibited Boards have been erased.

After White 16, the new board situation repeats the one for Black 11 to play (as recorded in Recent Path). All records in Recent List are erased and the sub-path of how cycle started is stored in List of Prohibited Path. In other words, Black cannot place a stone in a way of how the cycle previously started (i.e. Black 11) in the future.

[Diagram]

Black 17 to play

Black is prohibited to place stone on both the upper and lower corner with Prohibition Two in place. Black 17 can therefore only pass. White 18 is satisfied with the current board position and passes as well. Even with two passes, Prohibition Two remains for Black 19. Black 19 can also only pass.

With 3 consecutive passes, the game ends with this board position and White wins by 2 points under area scoring.

Thus, Black 3 is a non-optimal play and the optimal score for 2x2 board shall a draw (under the board position encountered by Black 3).



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

White 8 is fine to respond by a pass. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board positions encountered from Black 1 to Black 7) are erased. Black 9 is not satisfied with the current board position and places stone on B9. B9 may be on the opposite corner but it does not matter.

[Diagram]

White 10 to play

White 10 is again fine to respond by a pass. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board positions encountered from White 8 to Black 9) are erased. Black 11 is not satisfied with the current board position and places stone on B1.

[Diagram]

White 12 to play

This is the only choice for White 12 (W2).

It is unwise for Black 13 to place stone. Please try to verify this.

Assumes Black 13 passes. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board positions encountered from White 10 to White 12) are erased.

[Diagram]

White 14 to play

The orientation is important this time. Readers may verify by themselves that placing stone on the lower right corner would eventually prohibit White 16.

It is unwise again for Black 15 to place stone. Please try to verify this.

Assumes Black 15 passes. Under Kee Rules, all previous records in List of Prohibited Boards (i.e. board positions encountered from Black 13 to White 14) are erased.

[Diagram]

White 16 to play

White captures the three black stones again. This capture is allowed because with the passes in between, the previous board positions in List of Prohibited Boards have been erased.

After White 16, the new board situation repeats the one for Black 7 to play (as recorded in Recent Path). All records in Recent List are erased and the sub-path of how cycle started is stored in List of Prohibited Path. In other words, Black cannot place a stone in a way of how the cycle previously started (i.e. Black 7) in the future.

[Diagram]

Black 17 to play - prohibited

Black 17 (B7) is prohibited with Prohibition Two in place. Black can therefore only pass.

[Diagram]

White 18 to play - White wins

White 18 (W8) wins the game by 6 points.

Thus, Black 5 is a non-optimal play and the optimal score for 2x3 board is a draw (under the board position encountered by Black 5).


This is a copy of the living page "Kee Rules Of Go/v Dec 2007" at Sensei's Library.
(OC) 2011 the Authors, published under the OpenContent License V1.0.
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