Look for double threats
This article is from one of my insei games in Japan. I am playing White, and in Diagram 1 Black has just cut with 1 and 3. This is an overplay for Black, but as it is the case with overplays, if we don't find a sharp response they turn out well for the player who overplayed.
There is no hard rule about how to punish an overplay; actually it's the postmortem analysis that may prove something an overplay; during the game it is best to just concentrate on looking for weaknesses in the opponent's formation, and ideally we may be able to find a double threat. When I start by telling myself "My opponent has just made an overplay... Have to punish him... Have to punish him..." I normally lose focus and make mistakes.
First of all, the most straightforward way to capture, the ladder, doesn't work, as Diagram 2 shows.
Since White cannot capture Black's cutting stone, then it's time for White to think about defending his own isolated stone on the left side. This is a good approach, and White 4 in Diagram 3 is what I played in the game - except that this is too mild and it's missing a nice opportunity: Black can play A next, for instance, and given that he has the nozoki at B to take advantage of White's weakness, Black is in good shape to fight in the center.
Can you find a better alternative for White 4 in Diagram 3?
The answer is for White to descend with 4 in Diagram 4, which makes A and B miai for White next. This is better for White than Diagram 3, where White 4 was only creating one threat (that of capturing Black's cutting stone in a net).
Let's see next why White A and B in Diagram 4 are both very unpleasant for Black.
First of all, if Black defends with 5 in Diagram 5, White can capture in a net with 6.
On the other hand, if Black defends against the net with 5 in Diagram 6, White will aim for the cutting point in Black's keima and push with 6. If Black 7 in Diagram 6, White 8 captures the two triangle-marked Black stones.
Black can try to resist with 7 in Diagram 7 instead of Diagram 6, but White resolutely pushes and cuts, taking advantage of Black's two cutting points. Diagram 7 doesn't end up too pretty for Black, since his corner stones are captured. If Black connected at 12 instead of 11 in Diagram 7, White captures a stone with A and Black's position in the lower-left corner becomes very thin.