Synthetic Two Stage Ko
A synthetic two-stage ko consists of two distinct ko mouths that have to be fought consecutively, thus resembling a two-stage ko with regards to gameplay, without, however, meeting the formal criteria of being a proper two-stage ko, "where taking the ko produces another ko mouth."
The groups share a liberty and each has an external simple ko; they do not share the kos. As a result, this plays not like a double ko, but as a two-stage ko determining the status of all inside stones. Having won one ko, neither player can fill, but must instead start the other ko, which then behaves as the next "stage".
We can also form such a position by giving each group an eye, and no shared liberties.
In each case Black needs to first win the ko fight on the left to gain an additional liberty for his group before being able to fight the second ko to the right.
Two-stage mannen ko?
With both an eye each and a shared liberty, the position can be seki or mannenko. This is the only construction of two-stage mannenko I am aware of.
It is, presumably, somewhat less likely to be played than an ordinary mannenko, because a two-stage ko starting in the "unfavourable" position is harder to win than a direct ko from the "unfavourable" position. And of course, there is the double-ko potential too (a 4-move cycle exists) - very complicated!
Note that there is an asymmetry here.
If Black plays first, in ineffective, because at kills.
If White plays first there is a triple ko.
Now, when Black wins the first ko, he can resolve to "double ko capture", the whole position does not behave like a two-stage ko anymore.
In this position White is dead.
Same as in this position.
tapir: Yes, thus "double ko capture".
mainly by karl knechtel