A set of 81 unique cards, expressing all possible combinations the four attributes:
The object of the game is to find "sets" of three cards, where each attribute is either the same for all three cards, or different for all three cards. The game starts with twelve cards laid out on the table and players pour over them looking for sets. When a set is found, the player declares it and play is suspended as the player indicates the three cards and other players confirm it is a set. The finding player takes those three cards, and three more are dealt out to replace them if there is less than twelve on the table. If all players agree there are no sets, three more cards are added to the table (raising the probability of a set greatly). The game ends when the deck is exhausted, and players agree no more sets can be found in the remaining cards on the table.
It's not a competitive game so much as a collaborative puzzle.
An endgame, told to me by Molly Pottruff of Waterloo, is to take one card out of the deck (I called it "the checksum card") and putting it face down aside before the start of the game. When the deck is exhausted, and no more sets can be found, it's possible to deduce the face down card by examining the remaining cards and counting the modulo 3 of each attribute. IE: for colour, if five red cards remain (5 modulo 3 = 2), two green cards (2 modulo 3 = 2) and only one violet card (1 modulo 3 = 1), then the checksum card must be violet. If all the sets taken during the game were correct, you can determine all four attributes of the checksum card in this fashion. Players usually do their calculations silently, and check the checksum card discretely to allow other players to try to get it correct themselves.