A Projective Set card has six binary attributes, or
bits, generally represented by colored dots. For each color of dot, each card either has that dot or does not. There is one card for each possible combination of dots except the combination of no dots at all, making 2^6 - 1 = 63 cards total. Three cards are said to form a "set" if the total number of dots of each color is either 0 or 2. Similarly, four or more cards form a "set" if the number of dots of each color is an even number. A card and itself could be said to form a two-card set, but as the cards in the deck are all distinct, this does not arise in actual gameplay.
Original Version In the original version, as in
Set, 12 cards are laid out on the table. The first player to find three cards which form a set and call out "set" takes the three cards. Three new cards are then dealt and the play continues until the deck is depleted. If at any time the players agree there is no set among the cards, three new cards can be dealt, bringing the total number of cards on the table to 15. Other than this, new cards are not dealt out unless the number of cards on the table goes below 12. The game ends when the deck is depleted and no more sets can be found among the cards on the table. The player who captured the most sets is the winner.
7-card Version A variation of the game, more popular than the original, allows sets of any size, rather than just sets of size three. 7 cards are put out on the table at a time, and when a set is found (with anywhere from 3-7 cards), all the cards from the set are taken and then replaced. Points are generally given at the end according to how many cards each player captured rather than how many sets. It turns out that among any 7 cards there is a set, under these rules, so there is no extra rule necessary for the case that no set can be found. == Mathematics ==