In the olden days, you explain, you could buy quirky novelties from the backs of comics - X Ray specs, electric handshake buzzers, sea monkeys, etc. These were all bitterly disappointing, but collectors of such things occasionally speak of one thing that wasn't - a novelty sold for just one year that worked EVERY time, and which no-one ever found out how it worked. That item was The Psychic Game.
The effect is simple and bizarre - five cards are mixed, a dice rolled and a random card counted to - this sets off a chain of actions that leads to an impossible prediction that they will be utterly unable to explain. The Psychic Game is perfect for presenting a real mystery that seems totally self-contained.