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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.
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.
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.
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.
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).
The game ends with two cycles of consecutive passes of all players.
Published by Wilton Kee on 18-Aug-2007.
Dedicated to Wing.
Kee Rules have been tested against:
Desired result: The player who can have further action after winning the ko shall win the game.
Knowing that Black would all be captured if losing the ko, chooses to take the ko even with no hope to win. Since there is no other intersection to place,
can only pass.
does the same.
Under traditional positional superko rule White can never recapture without changing the board position. But now under Kee Rules can because of the pass. As the superko rule has been broken once,
cannot follow suit before he/she makes his/her own another pass.
White wins the game with under Kee Rules.
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.
Under traditional superko rule Black can never recapture. But now under Kee Rules 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.
Black wins the game with under Kee Rules.
Desired result: The player who sends two and returns one shall not be able to prolong the game.
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.
After , White cannot recapture under traditional superko rule (both positional and situational). Kee Rules, however, allow
to recapture because
is a pass.
Notice that under Kee Rules is prohibited instead because another pass of Black is required to break the superko rule again. White wins the game with
.
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.
recaptures. The is the first board situation which breaks the superko rule. Both White and Black pass because of superko rule.
recaptures. The is the second board situation which breaks the superko rule. Both Black and White pass because of superko rule.
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.
This temptation arises because White may think that on
would repeat the board position. However, this is actually a trap that Black can actually pass first to lift the ban.
does not have meaningful move to follow and can only pass.
can now capture 3 White stones because of the pass in
. Unfortunately, just after breaking the superko rule,
cannot immediately be placed on
and Black would win the game by getting the lower-right corner. So the correct response of
is to pass.
can pass as now Black is having 1 point advantage (under Chinese area scoring). Inevitably,
has to capture to avoid such board position as scoring position. Notice that the resulting board situation of
has been repeated.
After Black 11 (), White 12 is good to pass. Black 13 would pass as well to create recapture opportunity.
With White 14 passes, Black 15 () 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).
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.
It is worth to note that White 22 can capture the two Black stones, despite that same board situation (after ) has been breaking the superko rule, because a board position produced afterwards (by Black 11) is new.
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).
If Black is patient as well so that Black 13 and Black 15 are passes. has broken the superko rule but allowed under Kee Rules.
Black 19 () makes the game start over again. White 20 passes and Black 21 (
) 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 (
) has broken the superko rule but allowed under Kee Rules.
After , 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 (
) has broken the superko rule but allowed under Kee Rules.
White 28 and Black 29 would pass because White 26 () has broken the superko rule. White 30 (
) has broken the superko rule but allowed under Kee Rules.