Sorted Affair trick

You display an entire deck of cards, both front and back. The cards are completely mixed in a random order. You remove three red cards and three black cards from the deck and openly mix these together. But, when you spread them face up, the colors have separated! The effect is repeated again and again, each time mixing the cards more fairly than before, yet they still separate! Finally, the deck is spread face up and the entire deck has separated into reds and blacks!

The special cards do all the work, but you'll get all the credit!