Kee Rules Of Go / VMay 2008

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 13 to play
Black 16 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
White 10 to play - not prohibited in Affirming Phase
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 - prohibited
Black 19 to play - still prohibited
Black 21 to play - not prohibited in Affirming Phase
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 18-May-2008. 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 Primary 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 Primary 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 Primary 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 Primary Prohibition) since then.

[Diagram]

Simple Ko

As an example, consider this simple ko on a fully occupied board. If Primary 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 Primary Prohibition is not lifted, wrong timing of cycle (White 4 instead of Black 5) would be prohibited.



D. Why is Primary 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 Primary 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 Primary Prohibition.

E. Why does Secondary Prohibition apply on the board which has ever been consecutively passed by N-1 players?

Ans: It is because repetition cannot be extinguished even after a free local second stone has been allowed.

If there is no such Secondary Prohibition, the player would at best encounter the same pass plays by all opponents again. Afterwards it is just the same free local second stone on the same board position by the same player.

Without Secondary Prohibition, the game would be destined to certain cycle with some board positions from which repetition can actually be extinguished if given a free local second stone.

F. Why does the Playing Phase end upon 2N-1 consecutive pass plays?

Players shall be free from Primary 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 Primary prohibition), then Playing Phase shall end as no different plays would be expected afterwards if there is no change in both board position and prohibition status.

G. What is the purpose of the Affirming Phase and why does Reversed Secondary Prohibition apply in the Affirming Phase?

Ans: The purpose of the Affirming Phase is to release Secondary Prohibition and see whether any player can suggest dissatisfaction about the final board position by using his/her stone play if there is no Secondary Prohibition.

The principle is that the game shall not end with a board position from which certain player can make a change by his/her stone play assuming the game starts there (i.e. no cyclic prohibitions exist).

To effectively test whether possible stone play was once blocked by Secondary Prohibition in the Playing Phase, no stone play other than those really blocked in the Playing Phase would be allowed in the Affirming Phase.

H. Why does the game end with Cyclic Scoring if the last play was a stone play in the Affirming Phase?

Ans: The stone play suggests that the game ends in the Playing Phase just because of Secondary Prohibition. The game is therefore cyclic in nature and the final board position is not single but multiple. The previous board position which was identical to the final board position and produced by a crystallized stone play 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 were ever changed by stone plays during the cycle were neutral and should be excluded from scoring for or against one player. Only the intersections which are permanently with stone of the same color or permanently surrounded by stones of the same color 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 by consecutive pass plays of all players.

3. Game ends with a definite score.

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

5. Compatible no matter whether suicide is allowed.

6. Compatible with both area and territory scoring systems.


III. CONTENTS OF KEE RULES

1. Playing Phase

The game starts with an initial board position as the Playing Phase.

2. Alternate Plays

Players play alternately either by stone play or pass play.

3. Crystallization

If a stone play is immediately followed by N-1 consecutive pass plays (where N denotes the number of players), such stone play is crystallized.

4. Primary Prohibition

In the Playing Phase, a stone play may not produce a board position which is identical to any previous board position (including the initial board position), unless there have been a crystallized stone play on or after such previous board position.

5. Secondary Prohibition

In the Playing Phase, a stone play of a player may not produce a board position which is identical to any previous board position produced by a crystallized stone play of such player.

6. Affirming Phase

The game changes from the Playing Phase to the Affirming Phase immediately after 2N-1 consecutive pass plays.

7. Reversed Secondary Prohibition

In the Affirming Phase, a stone play of a player may not produce a board position which is not identical to any previous board position produced by a crystallized stone play of such player.

8. Termination

The game ends immediately after a stone play or N consecutive pass plays if all such plays are within the Affirming Phase.

9. Cyclic Scoring

If the last play was a stone play, the resulting board position must, by definition, be identical to the previous board position produced by one and only one crystallized stone play in the Playing Phase. The game would be scored using the final board position, but any intersections ever changing from the previous board position produced by such crystallized stone play to the final board position would be uncounted.

10. Single Board Scoring

If the last play was not a stone play, the game would be scored solely using the final board position.


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: 2x3 board, some but not all players disturbing on a fully occupied board (e.g. sending two returning one)

"Free local second stone" can be utilized if given to type 2, i.e. can be solved using secondary prohibition.

Type 3

Examples: 2x1 board, 2x2 board, all players (no matter whether 2-player or 3-player game) disturbing on a fully occupied board, 1x8 board (see below)

[Diagram]

1x8



"Free local second stone" cannot be utilized if given to type 3, the game should be concluded under "Cyclic Scoring" mechanism.


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 types 2 and 3 to anomaly. "No result" would be eliminated.

C. Spight Rules

Spight Rules give scores to types 2 and 3 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 "Secondary Prohibition" and type 3 is given score by "Cyclic Scoring" which considers the oscillation 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 Primary 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. After such pass, Black is subject to Secondary Prohibition upon the resulting board position of Black 1.

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 such Primary Prohibition has been erased.

With Secondary 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 Primary 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. Please note that after such pass, Black is still not subject to Secondary Prohibition upon the resulting board position of Black 1 because Red has not yet passed.

[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 Primary Prohibition. Black 4, White 5 and Red 6 then pass. After Black and Whites's passes, Red is subject to Secondary Prohibition upon the resulting board position of Red 3.

[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 such Primary Prohibition has been erased.

With Secondary Prohibition in place, if White 8 is a pass, Red 9 can only pass.

[Diagram]

White 8 to play

So W8 should snap back. This is also not prohibited because of the passes of Black 4 and White 5. Red 9 also passes. Please note that after such pass, White is still not subject to Secondary Prohibition upon the resulting board position of White 8 because Black has not yet passed.

With Primary Prohibition in place, Black 10 can only pass. After such two passes, White is subject to Secondary Prohibition upon the resulting board position of White 8. White and Red have nothing else to do and White 11 and Red 12 pass as well.

[Diagram]

Black 13 to play

Black 13 can now snap back.

With Primary Prohibition and Secondary Prohibition in place, White 14 can only pass.

With Secondary Prohibition in place, Red 15 can only pass.

[Diagram]

Black 16 to play

Black wins the game by Black 16.



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 Primary 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 Primary Prohibition in place, White 2 can only pass. After such pass, Black is subject to Secondary Prohibition upon the resulting board position of Black 1.

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 such Primary Prohibition has been erased.

[Diagram]

Black 5 to play - prohibited

As discussed above, with Secondary Prohibition 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 Primary 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. After such pass, White is subject to Secondary Prohibition upon the resulting board position of White 2.

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 such Primary Prohibition has been erased.

[Diagram]

White 6 to play - prohibited

As discussed above, with Secondary Prohibition in place, W6 is prohibited. Therefore, White 6 can only pass. After such pass, Black is subject to Secondary Prohibition upon the resulting board position of Black 5.

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

[Diagram]

White 8 to play - still prohibited

With Secondary Prohibition still in place during the Playing Phase, White 8 can only pass and the Playing Phase ends with 3 consecutive passes.

[Diagram]

White 10 to play - not prohibited in Affirming Phase

In the Affirming Phase, Black 9 passes. W10 is not prohibited because it was prohibited under Secondary Prohibition in the Playing Phase (i.e. Reversed Secondary Prohibition). This leads the game to Cyclic Scoring (from W2 to W10) and both intersections have ever changed and thus are just neutral points. 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

White 6 passes. After such pass, Black is subject to Secondary Prohibition upon the resulting board position of Black 5.

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

The outcome is the same no matter W8 is on the upper or lower corner. Readers may verify by themselves.

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

Assumes Black 9 passes. After such pass, White is subject to Secondary Prohibition upon the resulting board position of White 8.

[Diagram]

White 10 to play

White captures the two black stones again. This capture is allowed because with pass of White 6 such Primary Prohibition have been erased.

[Diagram]

Black 11 to play

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

[Diagram]

White 12 to play

White 12 passes. After such pass, Black is subject to Secondary Prohibition upon the resulting board position of Black 11.

[Diagram]

Black 13 to play

Black is not satisfied with the current board position and places stone on Black 13 to capture the two white stones. This capture is allowed because with pass of Black 9 such Primary Prohibition have been erased.

[Diagram]

White 14 to play

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

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

Assumes Black 15 passes. After such pass, White is subject to Secondary Prohibition upon the resulting board position of White 14.

[Diagram]

White 16 to play

White captures the two black stones again. This capture is allowed because with pass of White 12 such Primary Prohibition have been erased.

[Diagram]

Black 17 to play - prohibited

Black is prohibited to place stone on both the upper and lower corner with Secondary Prohibition in place. Black 17 can therefore only pass. White 18 is satisfied with the current board position and passes as well.

[Diagram]

Black 19 to play - still prohibited

With Secondary Prohibition still in place during the Playing Phase, Black is prohibited to place stone on both the upper and lower corner. Black 19 can only pass and the Playing Phase ends with 3 consecutive passes.

[Diagram]

Black 21 to play - not prohibited in Affirming Phase

In the Affirming Phase, White 20 passes because White was prohibited under Reversed Secondary Prohibition to place stone on any intersection (because the resulting board position was not prohibited by Secondary Prohibition in the Playing Phase).

Black 21 is not prohibited because it was prohibited under Secondary Prohibition in the Playing Phase (i.e. Reversed Secondary Prohibition). This leads the game to Cyclic Scoring (from Black 5 to Black 21) and all 4 intersections have ever changed and thus are just neutral points. The game (2x2 board) would therefore be scored as a draw.

It should be noted that if Black 21 was placed on the lower-left, it still leads to Cyclic Scoring from Black 11 (instead of Black 5) to Black 21 and the score would be the same.



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. After such pass, Black is subject to Secondary Prohibition upon the resulting board position of Black 7.

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. After such pass, Black is subject to Secondary Prohibition upon the resulting board position of Black 9.

Black is not satisfied with the current board position and places stone on Black 11.

[Diagram]

White 12 to play

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. After such pass, White is subject to Secondary Prohibition upon the resulting board position of White 12.

[Diagram]

White 14 to play

The outcome is the same no matter White 14 is on the upper or lower corner. Readers may verify by themselves.

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

Assumes Black 15 passes. After such pass, White is subject to Secondary Prohibition upon the resulting board position of White 14.

[Diagram]

White 16 to play

White captures the three black stones again. This capture is allowed because with the pass of White 8 such Primary Prohibition have been erased.

[Diagram]

Black 17 to play - prohibited

Black 17 is prohibited with Secondary Prohibition in place. Black can therefore only pass.

[Diagram]

White 18 to play - White wins

White 18 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 / VMay 2008" at Sensei's Library.
(OC) 2011 the Authors, published under the OpenContent License V1.0.
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