This diagram shows an occurrence of a double ko. (From Large Avalanche Turn Inward). The black group has one liberty (the marked eye) and two kos, giving him always two liberties. If White takes away a liberty by taking the ko at a, Black can take the ko at b. It is then up to White to find a ko threat. Black can answer the ko threat, and when White recaptures at b, Black takes at a. It is again White who has to play a ko threat, which Black can answer.
It should be clear that White cannot win in this situation - Black is alive in double ko.
Velobici: The middle group (black with marked eye in the diagram), surrounding an opponent's inside group, is itself surrounded by an outside group. In order for such a group to live in double ko, these conditions must be met:
Bill: Velobici, I have edited your paragraph and made it less sweeping. I think that in this particular kind of double ko life (not seki), one of the surrounding groups must die. At the end, the opponent fills one of the kos and the other is resolved by taking the other stones (in this case, the White stones in the corner). But there are many kinds of double kos.
Here the double ko will normally be resolved into a single (two stage) ko, but the White stones that need to die are not part of any ko mouth.
I don't know if this is a counter-example to your idea or not. Anyway, you certainly describe some double ko life situations. :-)
A point worth mentioning is that a double ko can serve as an infinite supply of ko-threats to the player at a disadvantage (in this case, White). This is because White a does require Black to answer at b and vice versa. This means that White will win any ko on the board which is worth less than the double ko.
-- Morten Pahle
TakeNGive (11k): Wow. What happens to this kind of shape (first diagram) under the Ing Ko Rules?
unkx80: White is dead, and if I'm not wrong, White has only two ko-threats under the Ing Ko Rules, not an infinite number. See Disturbing Kos for more information.
TakeNGive: Thanks unkx. A double ko recently came up in my tournament game. Luckily for me, we were not using Ing rules; but I'm curious whether this was a disturbing or fighting ko, and whether the line of play would have been legal under Ing rules. Please have a look at my Double Ko Question.
This situation would be like a double ko for both sides, so both sides would have infinite ko threats. Wouldn't any additional ko that is worth less than this corner then lead to a TripleKo?
-- Harleqin
Charles There are also connections that work because of double ko, as well as groups that have two eyes thanks to a pair of kos.
Bill: There are double ko death, seki, and life positions. As Charles indicates, there are other double kos, as well.