Double Hane Followup

From one stone  

White can connect, since Black threatens a double atari. White can also atari then connect at one of the points a, making a full triangle. If White plays one of the points b Black can atari at the other and force White into an empty triangle.

From two stones (i)  

White can stretch (nobi) at 1 or double hane at a. At b makes an empty triangle. The hanging connection at c invites the atari at 1. Again White can play atari before playing one of those options.

From two stones (ii)  

With the marked stone in place, answering at a invites a double atari at b. White 1 and c are possible defenses. Both invite another atari by Black leaving many cutting points. White b would be bad shape.

From three stones (i)  

Three stones is often the threshold for the effectiveness of the double hane.

From three stones (ii)  

Three is also the threshold for the double hane as a response being possible. The loss of three stones outweighs the ponnuki.