Standard sequence  

Previously considered a crude move, is part of the standard sequence today

bugcat: For a few years I've been under the impression that extending with (5) is an error, and that the double hane is pretty much always the best move. I looked up this sequence in Waltheri, and only one professional game (and that from 1960) had as the extension. In comparison, nineteen had as the double hane. So isn't the double hane variation the standard sequence and the extension the sideline?

PS. In my book the 3-3 is an invasion, not an approach. There's no "3-3 approach to the 4-4."

Alternative  

can also be played as a double hane. Black can locally continue at a but is more likely to play elsewhere.

White resists  

White can capture but suffers forcing moves at and , even . This is inefficient for White

White resists (2)  

is even worse than in the previous diagram. Even if the ladder doesn't work, Black can squeeze.

Attach

Previous standard  

used to be this immediate contact play leaving Black to choose a or b.

Hane  

If blocks at we revert to the standard sequence. This time however, Black can choose to atari at and force White into bad shape. This option to play on both sides depends heavily on the circumstances at the sides.

bugcat: I only found one instance of anything like this in Waltheri, being used by Shusaku in a two stone handicap game in 1851. In that game, was a solid connection and was a solid extension. Did you source this sequence from professional play?

Crosscut  

The crosscut leads to a long one way street where Black crawls to have enough liberties to capture the corner, while White gets outside influence by pressuring White. The variation may even depend on who has a stone in the bottom left.

Stretch  

here leads to territory in sente for White and influence for Black.