Written by Wilton Kee on 11-Dec-2007. Dedicated to Wing.
Homepage: http://www.geocities.com/kee_rules/kee_rules_of_go.html
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").
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).
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.
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.
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.
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).
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
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
1. The current player makes a play on the current board position by placing stone or making pass.
1. If placing stone, dead stones are removed to produce a new board position.
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.
1. A game ends with N+1 consecutive passes (where N is the number of players).
1. A new board situation is produced, i.e. the next player is going to make a play on the new board position.
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.
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 to capture the ko.
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.
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, (unlike White 2) can snap back because with the pass of White 2 such prohibition has been erased.
After snap back of , 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.
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.
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.
Now the third player, say Red, captures the Black stone to help White (probably due to consideration out of this area).
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.
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, (unlike Black 4) can snap back because with the pass of Black 4 such prohibition has been erased.
After snap back of , 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.
So should snap back. This is also not prohibited because of the passes before
. 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.
With pass of Red 9, is not prohibited even with
.
After snap back of , 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.
Black wins the game by Black 13 ().
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.
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 again to prolong the game by sending two. Is Black still without hope to win the game?
White cannot return one under traditional superko rule (both positional and situational). However under Kee Rules, 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 , 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.
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.
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, (unlike Black 3) can snap back because with the pass of Black 3 such prohibition has been erased.
After snap back of , 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.
As discussed above, with Prohibition Two in place, is prohibited. Therefore, White 6 can only pass.
Black 7 is satisfied with the two points for Black and therefore passes.
With 3 consecutive passes, the game ends with this board position and Black wins by 2 points under area scoring.
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 to capture the two white stones.
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 .
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.
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 , 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.
Black is prohibited to place stone on the upper corner with Prohibition Two. Black therefore places stone on the lower corner instead.
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.
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.
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.
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).
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 .
may be on the opposite corner but it does not matter.
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 .
This is the only choice for White 12 ().
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.
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.
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.