An interesting option  

What is the purpose of ? How should White react?

• with a White has been tricked
• with b White tries to resist - but needs a favorable ladder
• White c was played several times by professional players
• White d is another option worth mentioning
• White e and f are discussed here

Tricked  

If White takes the bait as in the diagram, we can say that she has been effectively tricked, as not only she is shut in, but also a and b are sente for Black.

An interesting option  

can be played only when the ladder is favourable for Black, otherwise White can crush black with the sort-of-easy-to-understand sequence.

If White resists with . Then sets up a double threat ladder maker.

An interesting option (continuation)  

If this ladder isn't favorable for black, black has to give up either the corner or the stones, so the initial inside cut looks doubtful.

More discussion to be found here

Hane, inside cut, hane again  

How about ? This move aims at the cutting point at a. Black cannot take the white stone on the left.

The pro continuation  

As found through Jansteen's GoBase. Which means my "new" move isn't a new move after all. Hm... Should I be happy or sad? GoranSiska

dnerra: Be happy, Goran! :)

The strongest path  

The "only" continuation would be , . Then is an attempt to control , as well as defending the cut. But cuts there anyway as this brings the aji of back to life. As I see it - Black is in trouble.

Extending  

If I have missed something, it seems that is the only move we haven't discussed yet. seems like the natural answer, after which and follow.

Follow-up  

This shows the follow-up from the previous diagram. White is locked up in the corner, but the marked stone still has quite some aji. Exchanging White a for Black b would decrease this aji.

An alternative for Black 3  

I like Andre's . It has the feeling of a true refutation of a trick move. One question is whether Black can resist more strongly with than in the original diagram. Considering only the corner it does not seem possible. However, there may be a problem...

Black strong outside  

Remembering that the premise behind the 3-3 invasion is that Black has already played on the outside, can White afford to fight hard here or not? Black a now leaves White without two eyes.

Gregory Since the Black at a is a killer, wouldn't be better at leaving many more options of play? Am I misisng the obvious?

unkx80: Actually could be played at b, Black c, White d, no?

Black fails?  

Therefore, after , White turns back to . However, after it does not look like Black is going to able to contain White. --DaveSigaty

For comparison  

But what can White do if the ladder does not work for her? Setting up the double threat is clearly bad for her in that case. My first intuition was to play at without the atari at a, leading to this variation.

I do however get the impression that this is good for Black: because the three white stones have only two liberties, White b is not sente, and White will have to play one of the circled points to use the aji of these stones.

tapir: That is the same with a well known joseki. But, the white ponnuki is weaker than the formation and white has an additional peep at c later. Only disadvantage is that the black wall is one stone higher. I would not mind playing this as white (if it suits me overall)

The simple way  

Could this be good enough sometimes? White is more confined than usual, but Black will have to add one more stone to take off.

(Anyway, Goran's move at a definitely looks more stylish!:)

The difference  

A very good suggestion. The value of a sacrifice depends on the wholeboard position. When Black takes the stone, his shape is much stronger (naturally ). Black a threatens the corner with ko while White a ends in gote. Therefore Black will most likely get to play a in sente.

The difference 2  

In this diagram or are double sente plays and this situation is likely to be played out fairly early. White is left with a as an endgame move since Black a can be ignored. Note that if is one point lower, Black a is sente.

Required reading  

Depending on outside strength Black may play . Because of the strong shape of the black stones White cannot continue with the usual move at a.

It's quite surprising how quickly the whole board considerations come into play.