Answer the capping play with a knight's move

Capping play and knight's move  

Why this knight's move played? Probably because it is a double purpose move. Its first purpose is to make territory while connecting, ...

Capping play and knight's move  

... and its second to prepare an attack like in this diagram. For comparison ...

Capping play and knight's move  

If Black defends and connects at , he has no severe follow up so that White can ignore it and treat as a forcing move.

Capping play against the fourth line  

This situation yields quite a different shape. In this case, an extension to is better. It prepares an attack at .

Defending at 3 is standard honte move  

The efficient peep in the previous diagram is the reason why White must defend at . Otherwise he should not play in the first place (and keep other options open).

Search region  

Charles Matthews did a search for a region like this (marked points included), not anchored (so in any position along the side), and symmetrised for left-right reflection. Mostly this formation will arise as White capping Black's stone. The most common answer was Black at a (30%); then Black at b (15%), Black at c (13%), tenuki and White plays d (10%), Black plays e (8%).

In handicap go the answer at a is recommended, and it is also the common play in simple cases like this:

Enclosure framework  

Black does usually react with or the marked point. Of course, this is an artificial position, as the right corner is open. Still, playing seems to leave Black a bit overconcentrated in relation to the left corner. But ...

The other way  

This is from a pro game. now opens up the position in a way Black at a wouldn't. For example Black can attack at b.

Looking at how the cap is handled in pro games, one sees tenuki quite frequently as an answer. As one would expect, if there isn't a local response that is good-looking.