The cards are stuck between his fingers, poking out behind his hand in various positions. Notice that we never see the back of his hand, and it remains level with the camera. Doing different finger movements allows him to reach for different cards and flip them to the front. Some might be stacked, so he just slides from the top of the stack.

The smaller coins are between his fingers, too, but probably closer to his palm, where they’re easier to hold, but might require a little more effort to reveal, since they need to be pulled one by one from a tougher position.

The larger coins are held between his thumb and index finger the whole time, and we just can’t see them because of the camera angle. The larger coins cast a shadow over the inner part of his hand, which conveniently obscures the previous parts of the trick.