Hi, I'm Mike Patrick and this is how to do a thumb cut. A thumb cut looks like this. It's easier to do with half the deck. I can do it with an entire deck, but you're going to have to have awfully large hands and stretch a whole lot to do it this way.
So I recommend that you start with half the deck. What you're going to do is you're going to place your thumb over the deck, you're going to stretch and try to catch this entire packet in your hand like that. The middle finger is going to reach in and your other fingers are curled underneath like this. So you have your middle finger going in between the packets and all the other fingers supporting from underneath.
You're going to extend these fingers like so, and then your thumb drops and these come back in. So once again, the thumb comes over, the middle finger pulls the packet off of the thumb, and the other fingers support it as you cut it forward and back on top like this. One more time. You can do this in both hands, and you can do this in conjunction with the one-handed shuffle like this to create a very nice closer for the cut. So that is the thumb cut.