Molasses Ko

  Difficulty: Advanced   Keywords: Life & Death, Ko, Shape, Rules

The Molasses Ko is a strange position, which behaves differently under different rules and might slow the game down to 20% of the normal pace by making it mandatory to exchange four moves after every regular move.

[Diagram]
Molasses ko (Black to play)  

Assuming that there are no ko threats big enough, this situation will repeat as long as there are valid moves on the board.

After the moves a-b-c-d the original situation is reversed (next diagram):

[Diagram]
Black plays elsewhere  

It's still Black's turn, and he uses it to make an ordinary move somewhere else. If that move was not a huge ko threat, White must reset the position (next diagram):

[Diagram]
White continues (5 elsewhere)  

After 1 to 4 it's White's turn to move, and she will play elsewhere. (for example, White could answer the move Black made after a-b-c-d in the first diagram.)

Now the local situation is exactly the same as it was in the first diagram, and the cycle repeats.


Omitting the exchange

Both players must make this exchange after every move played elsewhere, or his/her stones are captured.

[Diagram]
Black omits the exchange after White played elsewhere and loses his stones  

If Black omits the exchange, White can play 1. Now the situation is a real ko, and as was stated above, there are no ko threats big enough, so the black stones are lost.


Status?

Santo: I think the result of this position (*if both players play correctly*) would be (Assuming as always that there are no ko threats bigger than the Molasses ko, so that it cannot be immediately resolved during the game):

1) Basic ko (Japanese Rules) : Antiseki (Unless there is another source of infinite moves like a double-ko seki, in which case it may become a no result).(Explanation: At the game's end, the Ko is asymmetric. One player's big string is uncapturable, but the other player's big string can be captured immediately in hypothetical play since there are no ko threats to save him. HOWEVER, the (four) intermediate ko-stones of both players are dead (they are not even uncapturable-2). Thus, even though one big string is deemed alive and the other dead, the situation becomes an antiseki and scores 0 points locally for both players, with no stones removed. The losing player (the one which will lose if the game is scored as an antiseki) would like not to pass at this point, instead taking the molasses ko and reversing the situation. But then, after his opponent passes, he will be forced to find a move somewhere else in order not to pass and end the game. Since it is always the losing player that tries the game not to end who is forced to find a move somewhere else, he will eventually run out of moves (unless double-ko seki or similar somewhere else) or lose enough points by filling his own territory / playing losing moves. If jigo is the result of antiseki (when integer komi is used), then both players could cooperate to void the game by continuing to play on the molasses ko. It seems strange though that none of them would prefer jigo (which would be achieved by any of the players passing)).

2) Positional superko (Simplified Ing) : At the game's end, a player cannot pass without losing the molasses ko (because he will repeat the board position when trying to save it from immediate opponent attack). So whenever it is game-deciding at the end, first player to pass loses, and so a pass fight begins, so that players are essentially playing No Pass Go now.

3) Situational superko (AGA, New Zealand) : At the game's end, no player can force capture of the molasses ko. Passing is now safe: if the opponent attacks the ko, recapturing is possible since the board position is repeated, but with a different player to play. It is now the opponent who will be unable to capture and lose by superko rule if he tries to capture. So at the end players will have to pass, and in the molasses ko both groups live.

4) Chinese superko (Chinese Rules): Seki-like life, or void if double-ko seki somewhere else or similar. The analysis is just like the japanese case, since chinese specific superko (for sending two - returning one) does not apply here. So for the same reasons, the groups would end up alive (antiseki does not exist in chinese rules), unless there were an infinity of ko threats so that the referee would void the game.

If anybody can confirm that my analysis is correct, it will serve as a quick reference of the (typical) result according to ruleset for future readers.

Robert Jasiek: Compare the section Examples for Molasses Ko in the paper [ext] Types of Basic Ko.

Santo: I have edited my original analysis after finding a mistake in the japanese-rules analysis. It now seems an antiseki. I have to go now, I may check later.

Santo: I have read your examples, but all I seem to find is that for Japanese rules, this is a "semi-stable ko", for positional superko it is a "molasses closed kill" and for situational superko a "molasses life". However those definitions given are not clear enough to me regarding the strategic result of who would (at least typically) win / lose, or if it is a seki, or if it results in a pass fight. The term "molasses life" for situational superko seems to suggest that my seki-like life result analysis is correct. It would be nice if somebody could think about it and validate the analysis I've done for the molasses ko under the major rulesets, so that it stays here as a quick-summary. I've also added the chinese-rules situation, which is analogous to the japanese case (except the result is a seki instead of an antiseki, but the net difference in scores should be identical as far as the molasses ko is concerned, since both players have two points of territory in this case).

---

Anonymous:

What is the status of the groups involved in a molasses ko? I really have no idea whatsoever :-) My first guess would be seki, since neither player can capture the other.

On the other hand, it could be a no-result, since after either of the players passes, the other will take this ko. This will of course depend on the wording of the ko rules used.

If superko rules are used, the game will be decided by "who has most valid moves" (since you always have to play elsewhere or lose). Number of valid moves can be counted by adding up every distinct eye, and then subtracting 2 for every separate group.

Bill: It's more complicated than that. See No Pass Go.
walleye: Also, should that be "if positional superko is used"? There will be no pass fight if situational superko is used, right?
Bill: The first version of the superko rule that was adopted for play was a positional superko rule, so that is the default meaning.

In this situation, the effect of komi is nullified, since the counting system reverts to stone scoring. :-)

Go figure :-)

Bootmii: Neither player is willing to pass, so this is an anti-seki and tedomari wins. So on top of slowing the game down, a molasses ko prolongs it!

~srn347: Looks to me more like a seki, assuming there is a superko rule (otherwise, infinite loop). This is, of course, assuming there are no threats bigger than the size of the group.

RobertJasiek: The status question has been mostly answered: A molasses ko can be black death, white death, seki or - under rules yet to be found - a fighting ko: See the paper [ext] ko types for a proof. So, ~srn347, knowledge has advanced far beyond personal belief like "looks like a seki".


Origin

The first known molasses ko was played in game between British player T. Mark Hall and a chinese player called Zhao Zhengren in a friendly game in a London Go club. GoGoD has an article on it. There is some dispute about who first named it 'molasses ko' - so called because Molasses are very sticky and this situation slows the game down.


Molasses Ko last edited by 190.229.157.221 on November 20, 2014 - 20:51
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