So, are you left handed? If you are, you have to do everything mirror-like with respect to a right-handed player. Not only your body is mirrored, but the spin of the top will also be reversed. By the way, Greg's video site had a great feature where there was a button that swapped left and right so you could transform a right-handed player into a virtual lefty and vice versa. I will try to implement that in the future.
For corkscrew, if you are right handed (and wrapped and threw the usual way) the spin and the precession are both counterclockwise. You normally want the top to swing around the arm in the same direction as the precession, so you wrap the string counterclockwise around the right arm. By doing so you can get the top to lean at a constant angle with respect to the arm and do a smooth corkscrew. If you are left handed you would do a clockwise wrap around the left arm. The difficulty for both types of players is, of course, the same.
Note that somebody could do a corkscrew around the non-throwing arm. This will not change the sense of precession or the direction of the wrap (but the top will start by going towards the center of the body instead of going towards the outside).
Pulp breaks this rule on the second corkscrew. He has a top spinning counter-clockwise but makes it turn clockwise around the arm. This is much more difficult than the normal one as the top will try to lean in different directions (with respect to the arm) while doing a revolution. Unless . . . you can keep it very straight.
Did Lao invent (in the US) the trick doing it in the wrong direction? Wow!
I practiced yesterday and today and could finally do a few clean wrong-way corkscrews, even a couple of 4 wraps. It helped that a long time ago I had practiced "wrong-way" MGRs. But it was not easy, even using a throwback (that Italian top must be really good.)
Mmm, we need another name for doing a trick in the reverse direction. There is already a trick named reversible corkscrew. Perhaps "counter-corkscrew" ?