A twelve-card packet, dealt into piles as often as you like, then a reverse perfect shuffle and a Monge shuffle. Cut anywhere, take the top card, and let the down-under deal eliminate the rest: the last card left is your card's mate.
Packet, top first · 12
Twelve cards: ace to six of spades, then six down to ace of clubs. Deal them into piles as often as you like.
Piles: