If play on KGS at around 9k, you might have faced this move:
Have you wondered how to refute it? I offer three ideas: A, B and C.
With A, the idea is to progress to this position. You may now be questioning whether you can immediately attempt to kill with X or if you must first prepare your shape with Y.
The purpose of X is to continue to this shape, which seems to make A and B miai; Black reasons that if White makes the southern eye with A, Black takes the northern with B, and vice versa.
However, White has a tesuji here: C, threatening D to capture the two stones. If Black then fixes at X, White can play A and live, the upper eye having been secured.
With that in mind, Black can omit the testing sequence and move immediately to the atari and capture:
B is a less taxing move to implement, if perhaps a few points worse than A.
Note that B can transpose to a shape very similar to Play Go at online-go.com! | OGS (even slightly better for Black due to the wasted southernmost stone not being in the shape), despite that being result being from an enclosure joseki and White having invaded an unenclosed corner.
The least severe refutation, but a refutation nonetheless, is C. This shape is most similar to a regular 3-3 invasion, but White’s shortage of liberties caused by the cut exchange makes his shape painful.
You can now choose between the solid A and the principled B.
The key thing to note about B is that the turn exchange (13)–(14) is sente due to aji at the squared points, giving Black an edge in the fight.
What do you think? Did I miss something, especially in the A line?