However, one should notice that if the stone (which was ) is at a instead, then White at b can make the second eye and live. This observation leads to the improved sequence below.
If does not play the ko and destroys the eye at the side instead, then is sente, so White has time to live at the vital point of . However, the improved sequence is not yet the solution, since Black takes the ko first.
If Black avoids this ko, White can live, as the variations below show.
goes all out to kill.
takes four stones, but cannot make an eye there because of under the stones play.
But White takes sente and lives.
Since this ko is so large, it is reasonable to assume that neither player has a ko threat, and also that the temperature of the board is not too high, so that there will be no ko exchange. Then the best way for Black to play is to simply capture at , allowing to connect to the group outside.