How to Beat the Cut
In the first way demonstrated, I may not have made it perfectly clear that I am actually picking up the packets in the opposite order you're supposed to. This restores the deck to its original order. It's best to do this late in the game when most everyone has been drinking. Chances are no one will notice, and if they do, blame it on the fact that you've been drinking too. Just be confident about it, at all times. If it looks like you know what you're doing, few people will question you.
The second version is actually a pretty common sleight that I like to rely on if no one is sitting too close to me. Its simplier that a pass, and the less that can go wrong, the less that will go wrong.
Another simple method to beat the cut is by palming a card and re-introducing it into game. This lesson is available in the "Palming Cards" section.