The standard way to mix a deck of playing cards—the one used everywhere from casinos to rec rooms—is what is known as a riffle (or "dovetail") shuffle. You begin by splitting the deck into two roughly equal stacks. Then you flick the cards with your thumbs off the bottoms of the piles in alternating fashion, interleaving the two stacks.

For games like blackjack or poker to be truly fair, the order of the cards must be completely random when the game begins. Otherwise a skilled...