Written by Wilton Kee on 19-Jun-2008. 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: 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.
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.
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.
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.
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.
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.
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, stone play blocked in the Playing Phase due to Secondary Prohibition would be allowed 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 unconditional play (when the board was at its renewal status) 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.
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.
1. The board consists of intersections, where intersections are adjacent to some of the others in pre-determined way. In usual circumstances, the 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 move 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 move, then white player, and then black player again and so on in alternation until the end of the game.
6. After a stone is placed on the board, it cannot be moved to any other intersection.
7. A stone play is the right of a player. In any move, a player can give up the right of a stone play and choose to pass instead ("pass play").
8. The unoccupied intersections which are adjacent to a stone on the board are called the liberties of such stone.
9. When a stone is adjacent to another stone of the same color, these stones are connected and form a single stone unit, and the liberties of any one of these stones are considered to be the liberties 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, all such opposing 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 without liberties, all such opponent stone unit(s) is/are immediately removed from the board.
12. After consecutive pass plays of all opponents, the board attains its renewal status.
13. After a valid stone play, the board loses its renewal status.
14. When the game starts, the game is at playing stage and the board is not at its renewal status.
15. When the board is at its renewal status, if all players have consecutively made a pass play, the game progresses from playing stage to affirming stage.
16. A forbidden intersection of a player is an intersection on the board which, if occupied by a stone of such player, would leave the newly formed stone unit without liberties but fail to take all the liberties of any opponent stone unit. A player may not place a stone on a forbidden intersection.
17. PRIMARY PROHIBITION: A player may not make a stone play to produce a board position which would be identical to a previous board position unless the board has attained its renewal status after the board position has been altered from the last appearance of such previous board position.
18. SECONDARY PROHIBITION: If a player has encountered a board position when the game was at playing stage and the board was at its renewal status, so long as the game is still at playing stage, such player may not make a stone play to produce a board position which would be identical to such previous board position.
19. The game ends when all players agree that there will be no more stone plays.
20. The game ends when all players agree on the ranking of all players during the game.
21. The game ends when all players have consecutively made a pass play when the game is at affirming stage and the board is at its renewal status.
22. Other than the above circumstances, the game ends when the same player encounters the same board position when the game stage is again affirming and the board position is again unconditional, and the game is considered to end "cyclically".
23. At the end of the game, stones which all players agree can be removed are called "dead stones".
24. If the game ends cyclically, intersections which have ever changed during the cycle are called "neutral intersections". If the game does not end cyclically, there are no neutral intersections on the board at all.
25. At the end of the game, stones which are neither dead stones nor placed on neutral intersections are called "living stones".
26. At the end of the game where ranking cannot be agreed by all players, the winner is determined by counting points. After all dead stones are removed from the board, with respect of each player, the intersections occupied by the living stones of such player, as well as the unoccupied and non-neutral intersections enclosed by such living stones, are counted towards the points of such player.
27. Unoccupied intersections situating between the living stones of any two players are not counted towards the points of any player.
28. The ranking is determined according to the total points of each player. The player having higher total points is the winner.
Examples: Boards with 3-ko, 4-ko or chosei
Type 1 can be solved using traditional superko.
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.
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)
"Free local second stone" cannot be utilized if given to type 3, the game should be concluded under "Cyclic Scoring" mechanism (use of definition of neutral intersections).
Too weak to disallow all kinds of long cycles (all long cycles concluded as "no result").
Too strong to turn types 2 and 3 to anomaly. "No result" would be eliminated.
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.
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.
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 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.
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 Primary Prohibition has been erased.
With Secondary Prohibition (even Primary 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 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.
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 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.
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 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.
So 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.
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.
Black wins the game by Black 16.
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.
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 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 such Primary Prohibition has been erased.
As discussed above, with Secondary Prohibition in place, is prohibited. Therefore, Black 5 can only pass.
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.
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 Primary Prohibition has been erased.
As discussed above, with Secondary Prohibition in place, 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.
With Secondary Prohibition still in place during the Playing Phase, White 8 can only pass and the Playing Phase ends with 3 consecutive passes.
In the Affirming Phase, Black 9 passes. is not prohibited because Secondary Prohibition is not applied in the Affirming Phase.
Without Secondary Prohibition, both players would capture opponent's stone once Primary Prohibition is lifted. This leads the game to Cyclic Scoring. Since both intersections have ever changed during the cycle and thus are just neutral points. 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.
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 to capture the two white stones.
The outcome is the same no matter 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.
White captures the two black stones again. This capture is allowed because with pass of White 6 such Primary Prohibition have been erased.
Black is prohibited to place stone on the upper corner with Secondary Prohibition. Black therefore places stone on the lower corner instead.
White 12 passes. After such pass, Black is subject to Secondary Prohibition upon the resulting board position of Black 11.
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.
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.
White captures the two black stones again. This capture is allowed because with pass of White 12 such Primary Prohibition have been erased.
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.
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.
In the Affirming Phase, White 20 passes to ensure a draw (as follows).
Black 21 is not prohibited because Secondary Prohibition does not apply in the Affirming Phase.
Without Secondary Prohibition, both players would capture opponent's stones once Primary Prohibition is lifted. This leads the game to Cyclic Scoring. Since all 4 intersections have ever changed during the "whatever" cycle and thus are just neutral points. The game (2x2 board) would therefore be scored as a draw.
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 .
may be on the opposite corner but it does not matter.
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.
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.
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.
White captures the three black stones again. This capture is allowed because with the pass of White 8 such Primary Prohibition have been erased.