Cut the side you don't want
Because the enemy must normally capture the cutting stones, one should cut the side one doesn't want.
The logic behind the reasoning is the following: after you cut, your opponent can still choose either side.
- if he captures the cutting stone, he takes the side where you cut
- if he covers the other cutting point, he takes the side where you did not cut.
Capturing the cutting stone gives the opponent a much better shape (ponnuki), and is therefore preferred by him. If you would cut at the direction where you want to play, he can take both advantages (getting the ponnuki and getting the best side), if you cut at the direction where you do not want to play, he will have to choose. 
If Black wants the corner, he should cut at a.
If Black wants the outside, he cuts at . We assume the ladder works.
In neither of the above variations can White afford not to capture the cutting stone.
In this position it is good for Black to cut at before turning at a. is normal since otherwise Black takes the corner.
White really can't play here: a novice's mistake. White should play b, naturally, to keep the corner. Therefore here is the wrong side to cut, because the sequence , White b, Black at , White captures is worse than the previous diagram (a One-Two-Three mistake by Black).
Now after , playing at is the correct idea for Black. Probably White has nothing better than , in which case and make sure White has no eye shape here. Black can continue to attack White's group.
It would be a bad idea to follow Example 1 in this case, by cutting with here. White would be very happy with the ponnuki , and Black cannot even cut White on the left.
In this position you can say that Black wants this outcome, where White decides to capture with , and and (or a) are on the side Black 'wants'. That is, Black's fundamental desire is to cut White's long jump along the third line successfully with .
Here, black can decide to play 3 as a way to trade corner for a white to be outside and a pickup of one stone This is recommended to be done when black has the ladder. (There are issues about this, please see other variation to be completely under control in a real game situation).
: Charles: I can remember discussing this kind of point in general with Tim Hunt. Usually there are four variations like A, A', B, B' where it is easy to see that you prefer A to A' and B to B'. On the other hand your opponent will have the choice of giving you a result out of A or B', or out of B or A'. Somehow the decision is between a worse form of a better result, or a better form of a worse result? But actually this is probably just a basic game theory pattern being applied here.