4-4 Point 3-3 Invasion, Double Hane, Atari Up, Capture

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The 4-4 point 3-3 invasion, double hane, atari up, capture is part of the main sequence of the double hane joseki.

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Moves are listed by frequency in professional games^[1], which is sensitive to whole-board position. Bolded moves are commonly considered joseki.

3-3 invasion  

• a, 4-4 Point 3-3 Invasion Territorial Double Hane Joseki - (joseki) (common) (beginner) (AI favorite)
• b, 4-4 Point 3-3 Invasion, Double Hane, Atari Up, Capture, Atari Sideways - (situational)

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Overview of Joseki

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Take Corner

See main article: 4-4 Point 3-3 Invasion Territorial Double Hane Joseki

Taking the corner with the counter atari at a is the normal move and generally preferred by professionals and strong AI programs.

Build Thickness

Thickness Variations
Avoid Ko	Ko Variation

• Historically, it was possible for Black to atari sideways with to build thickness while threatening a ko. This move has almost entirely disappeared at the professional level of play ever since the AI Revolution. Jiang Weijie calls it a "very bad move" in the AI Weiqi Joseki Dictionary^[2].
• The best outcome for Black is if White connects with (Diagram 1), and this is generally what Black hopes for when they play the sideways atari. White may connect with to avoid fighting a ko. However, strong AI programs generally believe White should generally counteratari with (Diagram 2) to welcome a ko irregardless of whether there are ko threats on the board. White does not need to fear the ko because it takes multiple multiple moves for Black to open the close the ko, which is generally too slow if Black attempts to resolve the ko immediately. In professional games, the players will often start the ko but leave it alone for dozens of moves at a time because it isn't the largest move on the board.
• There are two cuts that Black could pursue in the ko: x and z.
• Both players have methods to lighten the ko. Black's solid connection at b lightens the ko for Black. White can extend at s or play the tiger's mouth at t to lighten the ko for White. When these moves are played, the ko becomes less urgent and the playing the ko isn't as interesting for the time being.

Discussion

Should Black ever play the atari sideways?

yuzukitea: I was unable to find a game where AI agreed with the professional usage of the sideways atari. If anyone finds a validated example, please feel free to share.

From a big picture perspective, the double hane joseki is unlikely to be the appropriate move for Black to develop thickness.

Don't connect after the side atari

Bad for White  

Extending at is a mistake. If White completes the regular joseki, the - exchange is good for Black.

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References

• [1] Frequency statistics were obtained from Waltheri's Go Pattern Search using the full database restrained to a local search (accessed September 2022).
• [2] AI Weiqi Joseki Dictionary - Jiang Weijie (2021)