Kee Rules Of Go/v Aug 2007

Sub-page of KeeRulesOfGo

Table of contents
Table of diagrams
Initial board position
Hopeless Black
White recaptures in compliance with Kee Rules
White wins
Initial board position
Black obviously in advantage
Red's intervention
Black recaptures
Black wins
Initial board position
Black tries to prolong the game
Black 3 is always prohibited
Initial board position
Black does the same
Can White recapture?
Black is prohibited instead
Initial board position
Black tries to open the game
Black recaptures
White recaptures
Black 11 is prohibited
Initial board position
Greedy Black
A trap to White
Scenario 1: B7 prohibited
Scenario 1: B9 not prohibited
Scenario 2: W6 passes
Scenario 2: Inevitable move of White
Scenario 2: White 12 is good to pass
Scenario 2: Black recaptures
Scenario 2: Passes to lift the ban
Scenario 2: Can White 22 recapture?
Scenario 2: Black cannot recapture after Black 25
Initial board position
Greedy Black again
Patient White
Scenario 1: If Black is patient as well
Scenario 1: White would win the game
Scenario 2: If Black becomes impatient
Scenario 2.1: Black may choose to capture
Scenario 2.1: White recaptures
Scenario 2.1: Black tries from another direction
Scenario 2.1: White would win the game
Scenario 2.2: Now Black 17 passes
Scenario 2.2: White always passes
Scenario 2.2: White wins the game
Scenario 3: If Black is always impatient
Scenario 3: Black 15 (B5) to Black 19 (B9)
Scenario 3: Black 23 (B3) breaks the superko rule
Scenario 3.1: From White 26 (W6), if Black 27 (B7) passes...
Scenario 3.1: White would win the game
Scenario 3.2: From White 26, if Black 27 (B7) captures...
Scenario 3.2: White 28 recaptures to break the superko rule
Scenario 3.1: White would win the game
Index of sub-pages

KEE RULES OF GO - AUG 2007 EDITION

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


PRINCIPLES

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

2. Game shall end with a score on all types of boards.

3. Game shall end in finite plays on all types of finite boards.

4. Game shall end with consecutive passes of all players.

5. Game shall not end with untried play due to superko ban.


SUMMARY

In general, positional superko rule would be applied. Kee distinguishes itself in the sense that a pass can lift the superko ban provided that superko rule has never been broken since the pass. On the other hand, the superko rule shall never be broken if no new board position has ever appeared since the last occurrence of such board situation.


CONTENTS

A. General

1. Players move alternately.

2. A move of a player is either:

    (a)  a play - to place one of his/her stones on the board position to play; or
    (b)  a pass.

3. In a play, after a stone is placed by a player:

    (a)  All his/her opponent stones without liberty (if any) would first be removed simultaneously.
    (b)  All his/her own stones without liberty (if any) would then be removed.
    (c)  The resulting board position becomes the board position to move by his/her next player.

Note: A play which results in an unchanged board position is considered as a pass instead.

B. Kee Specific 1 - Records

Record Type 1: Historical ordered board position set

    - It contains a set of historical ordered board positions commonly shared by all players.
    - It is cumulative.
    - It records all board positions ever encountered by players each with move number of next move.
    - Initially it contains the initial board position with move number 1st.

Record Type 2: Superko-starting move number

    - It contains one superko-starting move number individually for each player.
    - It can be replaced.
    - It records the move number after which any board positions would be considered under superko rule.
    - Initially the move number for every player is 1st.

Record Type 3 (for each game): Repetitive board situation set

    - It contains a set of repetitive played board situations commonly shared by all players.
    - It is cumulative but can be fully erased at certain circumstances.
    - It records all repetitively played board situations after all new board positions, where board situation is defined as the combination of board position and player to move next.
    - Initially the set is empty.

C. Kee Specific 2 - After Moves

After Pass of Player X

    - The pass is recorded in the historical set (record type 1).
    - The superko-starting move number for player X (record type 2) is replaced by the move number of the next move of the pass.

After Play of Player X

(a) Superko Rule: Check if the resulting board position appears in the historical set (record type 1):

    - If (a) is NO:
    The play is allowed and recorded in the historical set (record type 1).
    All records in the repetitive set (record type 3) are erased.
    - If (a) is YES:

(b) Check if the move numbers of all such board positions in the historical set (record type 1) are smaller than the superko-starting move number of player X (record type 2):

    - If (b) is NO, the play is prohibited.
    - If (b) is YES:

(c) Check if the resulting board situation appears in the repetitive set (record type 3):

    - If (c) is YES, the play is prohibited.
    - If (c) is NO:
    The play is allowed and recorded in the historical set (record type 1).
    The superko-starting move numbers for all players (record type 2) are replaced by 1st.
    The play is recorded in the repetitive set (record type 3).

D. Kee Specific 3 - End of Game

The game ends with two cycles of consecutive passes of all players.


Published by Wilton Kee on 18-Aug-2007.

Dedicated to Wing.


VALIDITY TESTS

Kee Rules have been tested against:

A. Simple ko on a fully occupied board

Desired result: The player who can have further action after winning the ko shall win the game.

1. Simple ko between 2 players in a 2-player game.

[Diagram]

Initial board position

[Diagram]

Hopeless Black

Knowing that Black would all be captured if losing the ko, B1 chooses to take the ko even with no hope to win. Since there is no other intersection to place, W2 can only pass. B3 does the same.

[Diagram]

White recaptures in compliance with Kee Rules

Under traditional positional superko rule White can never recapture without changing the board position. But now under Kee Rules W4 can because of the pass. As the superko rule has been broken once, B5 cannot follow suit before he/she makes his/her own another pass.

[Diagram]

White wins

White wins the game with W6 under Kee Rules.



2. Simple ko between 2 players in a 3-player game while the 3rd player is trying to help the weaker ko-player.

[Diagram]

Initial board position

[Diagram]

Black obviously in advantage

Black wishes to capture White. Seems to be an easy task. W2 can only pass.

[Diagram]

Red's intervention

Now the third player, say Red, captures the ko to help White (maybe due to non-local consideration). Now Black cannot immediately recapture because of superko rule. Black, White and Red then pass.

[Diagram]

Black recaptures

Under traditional superko rule Black can never recapture. But now under Kee Rules B7 can because of the pass. As the superko rule has been broken once, White and Red cannot follow suit before they make their own another passes.

[Diagram]

Black wins

Black wins the game with B10 under Kee Rules.



B. Sending two returning one in a bent-5-corner of a fully occupied board

Desired result: The player who sends two and returns one shall not be able to prolong the game.

1. Sending two first

[Diagram]

Initial board position

[Diagram]

Black tries to prolong the game

Black tries to prolong the game by B1 and White has to respond by W2.

[Diagram]

Black 3 is always prohibited

B3 is prohibited under both traditional positional superko rule and Kee Rules. Notice that situational superko rule is slightly different here but we are not going to go into details.



2. Returning one first

[Diagram]

Initial board position

What if the game starts from here?

[Diagram]

Black does the same

Black does the same by B1 and W2 can only pass.

[Diagram]

Can White recapture?

After B3, White cannot recapture under traditional superko rule (both positional and situational). Kee Rules, however, allow W4 to recapture because W2 is a pass.

[Diagram]

Black is prohibited instead

Notice that under Kee Rules B5 is prohibited instead because another pass of Black is required to break the superko rule again. White wins the game with W6.



C. 2xX boards

Desired result: The player who plays first (Black) shall not win the game given the opponent can always capture the greedy Black cyclically in these small boards.

1. 2x1 board

[Diagram]

Initial board position

[Diagram]

Black tries to open the game

B1 tries to open the game but W2 immediately captures. Both Black and White pass because of superko rule.

[Diagram]

Black recaptures

B5 recaptures. The is the first board situation which breaks the superko rule. Both White and Black pass because of superko rule.

[Diagram]

White recaptures

W8 recaptures. The is the second board situation which breaks the superko rule. Both Black and White pass because of superko rule.

[Diagram]

Black 11 is prohibited

Notice that Black 11 is prohibited even under Kee Rules because this is the same board situation breaking superko rule but without any new board position since the last occurrence of such board situation. This rule is important in Kee Rules to disallow recurrent cyclic moves. This means White shall have won the game under Kee Rules.



2. 2x2 board

[Diagram]

Initial board position

[Diagram]

Greedy Black

Black would try to take 1 more point under Chinese area scoring.

[Diagram]

A trap to White

It might be tempting for W6 to capture B5...

[Diagram]

Scenario 1: B7 prohibited

This temptation arises because White may think that B7 on B5 would repeat the board position. However, this is actually a trap that Black can actually pass first to lift the ban. W8 does not have meaningful move to follow and can only pass.

[Diagram]

Scenario 1: B9 not prohibited

B9 can now capture 3 White stones because of the pass in B7. Unfortunately, just after breaking the superko rule, W10 cannot immediately be placed on W2 and Black would win the game by getting the lower-right corner. So the correct response of W6 is to pass.

[Diagram]

Scenario 2: W6 passes

Now W6 passes and B7 captures.

[Diagram]

Scenario 2: Inevitable move of White

B9 can pass as now Black is having 1 point advantage (under Chinese area scoring). Inevitably, W10 has to capture to avoid such board position as scoring position. Notice that the resulting board situation of W10 has been repeated.

[Diagram]

Scenario 2: White 12 is good to pass

After Black 11 (B1), White 12 is good to pass. Black 13 would pass as well to create recapture opportunity.

[Diagram]

Scenario 2: Black recaptures

With White 14 passes, Black 15 (B5) can break the superko rule and capture the two White stones (of course repeating the board situation, but that's fine for the first time).

[Diagram]

Scenario 2: Passes to lift the ban

White 16, Black 17, Black 19, White 20 and Black 21 are all passes to lift the superko ban. Black is unwilling to capture the single White stone because it leads to a situation that White would get the opposite corner if Black continues to be greedy.

[Diagram]

Scenario 2: Can White 22 recapture?

It is worth to note that White 22 can capture the two Black stones, despite that same board situation (after W10) has been breaking the superko rule, because a board position produced afterwards (by Black 11) is new.

[Diagram]

Scenario 2: Black cannot recapture after Black 25

However, Black cannot recapture no matter how many passes made, because no new board position is produced since Black 15 (the last play to produce such board situation). Therefore, the optimal score for 2x2 board is draw (no greedy Black).



3. 2x3 board

[Diagram]

Initial board position

[Diagram]

Greedy Black again

B5 is greedy, trying to get one more point from White.

[Diagram]

Patient White

White would be patient enough so that W8 and W10 would be passes. Black 11 (B1) captures the 3 White stones.

[Diagram]

Scenario 1: If Black is patient as well

If Black is patient as well so that Black 13 and Black 15 are passes. W6 has broken the superko rule but allowed under Kee Rules.

[Diagram]

Scenario 1: White would win the game

White would win the game because B7 cannot immediately break the superko rule again.

[Diagram]

Scenario 2: If Black becomes impatient

If Black is patient at the first time (B3) but not at the second time (B5)...

[Diagram]

Scenario 2.1: Black may choose to capture

And if B7 chooses to capture...

[Diagram]

Scenario 2.1: White recaptures

W8 recaptures.

[Diagram]

Scenario 2.1: Black tries from another direction

Black 19 (B9) makes the game start over again. White 20 passes and Black 21 (B1) tries another direction to attack. Black 23 and White 24 pass and superko is temporarily lifted. White 26 and Black 27 pass and superko temporarily lifted. White 28 (W8) has broken the superko rule but allowed under Kee Rules.

[Diagram]

Scenario 2.1: White would win the game

Similarly Black 29 cannot get to the middle because White 28 has just broken the superko rule.

[Diagram]

Scenario 2.2: Now Black 17 passes

White 18 would capture.

[Diagram]

Scenario 2.2: White always passes

After B9, White (moves 20 and 22) would pass all along until Black occupied the whole upper column. White 24 and Black 25 pass and superko temporarily lifted. White 26 (W6) has broken the superko rule but allowed under Kee Rules.

[Diagram]

Scenario 2.2: White wins the game

Similarly Black 27 cannot get to the middle because White 26 has just broken the superko rule.

[Diagram]

Scenario 3: If Black is always impatient

White 14 would capture.

[Diagram]

Scenario 3: Black 15 (B5) to Black 19 (B9)

Passes are necessary because of traditional superko rule inherited in Kee Rules.

[Diagram]

Scenario 3: Black 23 (B3) breaks the superko rule

White 24 cannot capture immediately because Black 23 (B3) has just broken the superko rule.

[Diagram]

Scenario 3.1: From White 26 (W6), if Black 27 (B7) passes...

White 28 and Black 29 would pass because White 26 (W6) has broken the superko rule. White 30 (W10) has broken the superko rule but allowed under Kee Rules.

[Diagram]

Scenario 3.1: White would win the game

Black 31 can only pass because White 30 has just broken the superko rule.

[Diagram]

Scenario 3.2: From White 26, if Black 27 (B7) captures...

Alternatively if Black 27 captures...

[Diagram]

Scenario 3.2: White 28 recaptures to break the superko rule

Black 29 can only pass because superko rule has just been broken.

[Diagram]

Scenario 3.1: White would win the game

White 30 (W10) wins the game.



D. Conclusion

It is found that all the above board positions give desired results and are all free from anomaly.


This is a copy of the living page "Kee Rules Of Go/v Aug 2007" at Sensei's Library.
(OC) 2009 the Authors, published under the OpenContent License V1.0.
[Welcome to Sensei's Library!]
StartingPoints
ReferenceSection
About