# Fighting Ko and Disturbing Ko / Logical definition

### Formal Definition for Basic Kos

RobertJasiek: For basic kos, a formal definition of disturbing ko and its subtypes is available in the paper Types of Basic Ko.

### Circular definition

Bill: According to Ing rules, a disturbing ko can occur only when life and death are settled. (I. e., the ko does not affect life or death aside from the stones captured when taking the ko.) However, it is not clear in all of Ing's examples of disturbing ko that life and death are settled.

Disturbing ko

Disturbing ko (ii)

Ing calls this a disturbing ko. Under a superko rule White cannot capture the stones with , as it would repeat the original situation. Black threatens to capture White's group. In what sense are life and death settled?

Ing allows White to capture the stones, because this is a disturbing ko. So White (and Black) are alive.

Life and death are settled because this is a disturbing ko and it is a disturbing ko because life and death are settled. Ing's definition is circular.

### Rejection of superko

Ing's first set of rules included a superko rule. However, Ing later rejected a superko rule for two main reasons. First, it may be hard to recognize and administer. Some superko cycles involve dozens of moves, and, even knowing that there is a repetition among those moves, a player or referee may fail to recognize it. Second, some superkos offended Ing's intuition. In particular, two double ko death positions could become a superko in which one of them might live. Ing believed that life and death was already settled in those positions.

In my opinion, Ing attempted to capture that intuition in his rules, but did not quite succeed. That is why his definition is unclear and circular.

Looking at Ing's examples, we might guess that he believed that in disturbing kos, two internal breaths guaranteed life. However, he could not say that, because one of his main principles was that life and death are determined by play:

"Stones live or die according to whether or not they can be removed: stones that can be removed are dead; stones that cannot be removed are alive. There are no exceptions whatsoever to this rule that life and death are determined by removal."

### Hypothetical play

Of course, actual removal cannot be used to define a disturbing ko during the game, because of the circularity of the definition. However, it may be possible to distinguish fighting and disturbing kos by hypothetical play. The question, as Ing says, is whether the stones can be removed, not that they actually are yet removed. And after all, in the example that offended Ing's intution, he had to be able to determine that each double ko death was dead without actual play. I believe that Ing gave a basis for such hypothetical play in the following statement.

"A disturbing ko has no hot stones. Hot stones do not work in a disturbing ko because both sides can remove different stones; they do not have to fight over the removal of hot stones."

By contrast, in a fighting ko the players do fight over hot stones.

To distinguish between a disturbing ko and a fighting ko, then, by hypothetical play, do not let the players take back potentially hot stones. If life and death are settled in a disturbing ko, that will not matter, because they do not have to fight over hot stones. If life and death are not settled in a fighting ko, it will.

OC, there is no guarantee that this hypothetical play will agree with Ing's examples. We are not trying to capture Ing's intuition, but to make a logical distinction based upon his principles.

Disturbing ko life

In our first example, neither player is in immediate danger.

Black disturbs

However, if Black plays White must reply with (or ). puts White's large group in atari, but White saves them with .

Cold stones

Now and are potentially hot stones, but if they cannot be taken back, both Black and White stones are safe.

After a pass or play elsewhere, which would lift ko bans, Black could continue the attack, but would simply return to the original position, making no headway. White is similarly unable to capture or kill Black.

Life and death are settled, with both alive.

Fighting ko

White to play can capture Black's group. But let Black play first.

Black takes ko

After we have this position.

Hot stones

If the and stones cannot be taken back, then the White group is dead. If White passes or plays elsewhere to lift the ko ban, Black can capture White's group. (It is OK to capture a potentially hot stone {} if doing so destroys the potential ko by capturing other stones.)

So in the original position whoever plays first can take the opposing group. Life and death are not settled. This is a fighting ko.

This is the basic idea. More needs to be said to make it precise.

(Later.) I have found a ko rule that produces the same effect as this kind of virtual play, without requiring the fighting/disturbing ko distinction. I think it is preferable to use it. See Ing-Spight ko rule.

Fighting Ko and Disturbing Ko / Logical definition last edited by MrTenuki on December 22, 2011 - 00:39