When he cuts the stack, he puts part of the stack on top of the adjacent pile, and the bottom half of the deck comprises the remaining cards in the stack of 15. When you stack those to piles together you guarantee 15 cards between adjacent aces.
16 is a large power of 2, so if your cards are in the right phase of the sequence, you can divide the deck (modulo 2) a few times without revealing your cards.
When he cuts the stack, he puts part of the stack on top of the adjacent pile, and the bottom half of the deck comprises the remaining cards in the stack of 15. When you stack those to piles together you guarantee 15 cards between adjacent aces.
16 is a large power of 2, so if your cards are in the right phase of the sequence, you can divide the deck (modulo 2) a few times without revealing your cards.