Basic Ko Anomalies

    Keywords: Ko, Rules


The basic-ko rule leads to anomalies.

The most important anomaly is the possibility of long cycles.

Another anomaly lets ko positions of the type Pendulum Ko, which feel like a fighting ko if only one of them is on the board, be anti-sekis. Anti-sekis were supposed not to exist until I discovered them in the position below, where successive passes provide the shortest perfect play under most rulesets.

wrong diagram for stable anti-sekis  
correct diagram for stable anti-sekis  

If you question superko for its anomalies, you should do the same for the basic-ko rule or every other ko ruleset.

I think a more important anomaly of basic ko is the possibility of MoonshineLife, which is ruled out only by special means in most rulesets.

WillerZ: Please explain what an anti-seki is.

Robert Pauli: Guess he means a both dead situation.

WillerZ Okay, maybe I'm being a bit dense, but I don't see what's special about the above diagram. If it is unresolved at the end of the game, you can either say that the six points to either side of the H groups are all in seki, so it's 2-2 on the board. Or you could say that the 2 stones in the lower-left and the 2 stones in the lower-right are capturable and thus the score is 9-9. Or you can say that the 2 bunches of 7 stones are dead, and the score is 19-19. But the point is that the result of the game has remained constant, there is no advantage to either player for playing first, and therefore (while it may not be mathematically elegant) it does not, in any real sense, matter.

Robert Pauli: Sorry, I neither know what the heck he means, especially not how this demonstrates that the basic ko rule leads to anomalies (besides not stopping cylces). I'm as puzzled as you.

WillerZ: Last night at my local go club we tried to find something strange about the above diagram which could fit the term anti-seki. The best we could come up with was that if either player plays it will either lose him points (if he captures the 2 stones) or cause a cycle. But this doesn't seem to be fundamentally any different from a whole-board seki position containing a double-ko seki.

Robert Pauli: Before we can discuss anything, we have to know what ruleset he's using.

RobertJasiek: Any ruleset with the basic ko rule. The above position is an anomaly because it is perfect play to end the game with all those both sides are dead shapes still on the board while common go sense suggests that such could never exist in the scoring position. - Was it me to put up the diagram in the current shape?! I wanted to have pendulum kos, not double kos. So however that diagram concept mistake was created, I correct it now.

Bill: The first diagram simply shows a couple of double ko death positions. The second shows two hot kos that are miai. Sure, it's unusual to leave a miai on the board instead of playing it out before scoring, but I do not think most people would regard it as anomalous. Anyway, the ko aspect is not essential. It is easy to construct non-ko miai antisekis.

RobertJasiek: Yes, the anomaly is not restricted to kos. No, most people I know would regard it as anomalous.


Bill: Is this anti-seki position anomalous or just weird?

RobertJasiek: Both.

Anomaly? Anti-seki? Simply hot but miai?  

Tas: Here's one with no ko's at all. I still dont get what is so anomalous about this. The only plays left are miai, so neither player can gain more by playing than by passing, so what?

Basic Ko Anomalies last edited by on April 24, 2008 - 09:28
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