(Referenced by 230; 231)

However, the matter will change fundamentally if there is a larger eye for Black. Capturing what is inside this larger eye will give Black breathing space. Again, we start the discussion with the case EX = 1.

:
Here, Black can occupy the last shared liberty.

:
After White captures the ko, with , Black takes the two White stones inside his eye.

:
White must play into Black's eye.

:
Black now gives atari on White's group, by capturing the ko in the top left.

The additional ko did not help White. Again, if all other conditions are the same, Black wins, if he has one more ko-threat than White does. t = 1.

///:

EX = 2
If we give White's group another liberty, Black wins, if he has t = ( + + ) - 1 ko-threats more than White, including the internal one.

:
White captures the ko "early".

:
Again, Black can occupy the last shared liberty.

:
White must play into Black's eye.

:
Black finally gives atari on White's group.

Again, the larger eye for Black compensates for the effect of the additional outside ko for White.

, :
However, a special effect must be considered with this formation (if Black lacks further ko-threats).

Black cannot answer locally, so White gets to play a fourth move elsewhere, with . Combined (, , ), she has got the chance to play four moves in a row elsewhere, and none of the first three moves must contain a really "large" threat, compared to the value of the ko-fight. It will be sufficient to prepare a situation, where the fourth move is really destructive.

This seems to give the same result as with EX = 0, but two -liberties less for Black's group.