Written by Wilton Kee on 12-May-2009.
Based on principles set up on 14-Mar-2009.
Dedicated to Wing.
Homepage: http://www.geocities.com/kee_rules/kee_rules_of_go.html
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.
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.
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).
Ans: This is to draw consistency between a non-fully-occupied board and a fully-occupied board. In a non-fully-occupied board, to a player who has just occupied a ko position but actually hopeless to take further step on it, an irrelevant play on elsewhere on the board by his opponent can already be treated as a effective ko-threat to him because the board position has been altered. As the hopeless player finds no way to take further step on it, the opponent can take back the ko position and win the ko.
However, in a fully-occupied board, no where on the board is available for the opponent to make such a irrelevant ko-threat play. If cyclic prohibition cannot be lifted by a pass, i.e. a pass is not assumed to have altered the board position or treated as the weakest ko-threat, the ko position would be forever occupied by the hopeless player and the game would be halted there. This is inconsistent with the non-fully-occupied board and undesirable.
As an example, consider this simple ko on a fully occupied board. If the cyclic prohibition is not lifted, no opportunity can be given to White when Black has nothing to do after capturing the ko.
Also consider this "sending two returning one" situation where Black keeps playing as a cycle after White has already passed (in White 2). If the cyclic prohibition is not lifted, wrong timing of cycle (White 4 instead of Black 5) would be prohibited.
After a pass play, the player is free from any previous cyclic prohibition. If the same player passes on the same board position again, there is actually no change in both board position and prohibition status (i.e. free from any previous cyclic prohibition) from the previous identical pass play. The game can end without any complaint because any desired possibility should have already been be tried out after the previous identical pass play.
Ans: If there is any stone play after the initial scoring play, the result of the game is cyclic in nature. Instead of putting all weights to the single final board position which is just one within a cycle of many board positions, it is reasonable to allow certain board positions within the cycle to be used for scoring.
It is easy to understand that board positions which are not consecutively passed by all players should not be used for scoring. It is because there is at least one player does not agree on such board position to be used for scoring by successfully making stone play on it.
On the other hand, a player passes on a board position either because he agrees on such board position to be used for scoring, or is forced to pass because of cyclic prohibition. As the end of a game means the desired possibility has been tried out, a player forced to pass will still be forced to pass next time even if the game continues. In such case, the player cannot say he does not agree if situation does not allow. Therefore, all the board positions consecutively passed by all players can be considered as the scoring board positions.
1. Game ends in finite plays on all types of finite boards.
2. Game ends with a definite score.
3. Applicable to any number of players (even 3 or more).
4. Compatible no matter whether suicide is allowed (suicide is not allowed in the following rules as default).
5. Compatible with both area and territory scoring systems (area scoring is chosen in the following rules as default).
1. A board consists of intersections, where intersections are adjacent to some of the others in a pre-defined way. In usual circumstances, a board is marked with 19 parallel vertical lines and 19 parallel horizontal lines, making 361 intersections.
2. The number of stones shall be sufficient to end a game. In a two-player game, usually lens-shaped black and white stones are used.
3. During a game, each player possesses one color of stones.
4. In usual circumstances, a game starts with an empty board, where all intersections on the board are unoccupied.
5. Each player makes a play by alternately placing one stone on an unoccupied intersection of the board ("stone play") to occupy such intersection. In a two-player game, usually black player makes the first play, then white player, and then black player again and so on in alternation until the end of the game.
6. After a stone has been placed on the board, it cannot be moved to any other intersection.
7. A stone play is the right of a player. In any play, a player can give up the right of a stone play and choose to pass instead ("pass play").
8. An unoccupied intersection which is adjacent to a stone on the board is called the liberty of such stone.
9. When a stone is adjacent to another stone of the same color, these two stones are connected and belong to a single stone unit, and the liberty of any one of these stones is considered to be the liberty of the whole stone unit.
10. For any stone unit, when an opponent stone is placed adjacent to it, such opponent stone takes a liberty away from it. When all the liberties of a stone unit have been taken away and no liberties are left, such stone unit has to be removed from the board.
11. A stone unit without liberties is removed from the board. There are two cases:
(a) When a stone is played so as to take the last remaining liberty of any opponent stone unit(s), all those opponent stone unit(s) is/are immediately removed from the board.
(b) When a stone is played so as to take the last remaining liberty of any opponent stone unit but would also leave the newly formed stone unit with no liberties, only all those opponent stone unit(s) is/are immediately removed from the board and the newly formed stone unit is not removed.
12. A forbidden intersection of a player is an unoccupied intersection on the board which, if occupied by a stone of such player, would leave the newly formed stone unit with no liberties but fail to take the last remaining liberty of any opponent stone unit(s). A player may not place a stone on a forbidden intersection.
13. A player may not make a stone play to produce a board position which would be identical to a previous board position unless a pass play has ever been made by any player after the last such previous board position.
14. The game ends when the ranking can be agreed by all players.
15. The game also ends when a player makes a pass play on a board position which he has previously made a pass play on. The series of plays after but not including such previous pass play is called the "scoring cycle".
16. At the end of a game where ranking cannot be agreed by all players, the ranking would be determined by scoring.
17. For the scoring cycle, if any stone play exists, the series of all pass play(s) before the first such stone play, if any, is repositioned to follow the last play. A board position which has been consecutively passed by all players in the scoring cycle after such reposition, if any, is called a “scoring board position”.
18. For each scoring board position:
(a) Stone(s) is/are removed from the board if all players agree.
(b) With respect to each player, the intersection(s) occupied by the stone(s) of such player on the board, as well as the unoccupied intersection(s) which is/are fully enclosed by such stone(s), is/are counted towards the point(s) of such player.
(c) Unoccupied intersection(s) which is/are enclosed by stones of different players on the board are not counted towards the point(s) of any player.
19. If there are no scoring board positions after the game has ended, the game is draw.
20. The ranking is determined according to the average of total point(s) earned by each player from each of the scoring board position(s). The higher the point(s) earned by a player, the higher is the ranking.
Examples: Boards with 3-ko, 4-ko or chosei
Type 1 can be solved using traditional superko.
Examples: 2x1 board, 2x2 board, 2x3 board, some players disturbing on a fully occupied board, 1x8 board (see below)
Type 2 can be concluded with a definite score under "cyclic scoring" in Kee Rules which considers the board positions passed by all players during the cycle.
Too weak to disallow all kinds of long cycles (all long cycles concluded as "no result").
Too strong to turn type 2 to anomaly. "No result" would be eliminated.
Spight Rules give scores to type 2 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.
Kee Rules give scores to all types. Type 2 is given a definite score by "cyclic scoring" which considers the board positions passed by all players during the cycle.
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 the cyclic 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.
Black has nothing else to do and Black 3 passes as well.
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 the cyclic prohibition has been lifted.
With the cyclic prohibition 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 going to see whether stronger Black can capture all white stones.
With the cyclic 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.
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 the cyclic prohibition. Black 4, White 5 and Red 6 then pass.
Under traditional superko rule, Black 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 the cyclic prohibition has been lifted.
Now can snap back. This is not prohibited because the pass of Black 4 has lifted the cyclic prohibition. Red 9 also passes.
Now can snap back. This is not prohibited because the pass of Red 9 has lifted the cyclic prohibition.
Like White 2, with the cyclic prohibition in place, White 11 cannot immediately snap back. Therefore White 11 passes.
The game ends here. In other words, Black cannot capture the White stones if the third party (Red) offers help. This board position is the only one consecutively passed by all players, and therefore it is the scoring board position.
is prohibited under both traditional positional superko rule and Kee Rules (with the cyclic prohibition). 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 the cyclic prohibition in place, White 2 can only pass.
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 with the pass of White 2 the cyclic prohibition has been lifted.
is not prohibited because White 2 pass has lifted the cyclic prohibition. However, as White 6 would pass again, the 3 intersections would become neutral.
Such result would be less favourable to Black as compared to the score Black can obtain if allowing usual seki (2 points less now).
With the cyclic 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.
White has nothing else to do and White 4 passes as well.
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 the cyclic prohibition has been lifted.
With the cyclic 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 6 can only pass.
Black has nothing else to do and Black 7 passes as well.
(unlike White 6) can now snap back because with the pass of Black 7 the cyclic prohibition has been lifted.
Black 9 cannot immediately snap back and can only pass, which leads the game to "cyclic scoring". During the cycle, since both board positions have been consecutively passed by both players, the game (2x1 board) would therefore be scored as a draw.
Black puts one stone back. The outcome is the same no matter is on the upper or lower corner. Readers may verify by themselves.
The board position is favorable to White for scoring even if White 6 passes. So White 6 passes.
White puts one stone back. The outcome is the same no matter is on the upper or lower corner. Readers may verify by themselves.
The board position is favorable to Black for scoring even if Black 9 passes. So Black 9 passes.
Black puts one stone back. If Black 11 is on the lower corner, it would lead to more steps, but the result is the same. Readers may verify by themselves.
When White 12 passes, it is identical to White 6. The game ends here. Since there is no scoring board position formed, the game is draw.
This is the only choice for .
The board position is favorable to White for scoring even if White 8 passes. So White 8 passes.
Black puts one stone back. The outcome is the same no matter is on the left or right corner. Readers may verify by themselves.
The board position is favorable to White for scoring even if White 10 passes. So White 10 passes.
This is the only choice for White 12.
The board position is favorable to Black for scoring even if Black 13 passes. So White 13 passes.