4433 enclosure
This enclosure appears quite often in the games of Takemiya, to defend against the 3-3 point invasion.
If you want to shock a stronger player who is giving you a handicap, you can answer the usual kakari of with the surprising kosumi at
. Many players don't know that this is actually a joseki listed on page 1084 of "Joseki Daijiten" (Big Joseki Lexikon) Volume 1, Tokyo, Nihon Kiin, 1986, as Diagram 9257. However, in that book black has a stone on the 3-3 point first and answers the kakari at
with a kosumi outwards to the star point.
Jesse: This would not surprise me at all. It actually seems to be quite common in handicap games at the kyu level, sometimes even without a White kakari. Personally, I don't think it is a good way to develop a 4-4 stone. I'll leave it to stronger players to comment further, though.
The continuation in that diagram is shown below:
Whatever happens after the answer on 3-3 in the diagram above, white can't trade the white stone on the outside for the corner. So this is actually an attack on the kakari stone and should be played aiming at that attack, not in a defensive state of mind.
Klaus: Trying out stuff like this can be fun, and one can learn a lot about attacking baseless stones by using this enclosure.