d = 0 is impossible, since no two cards are identical.) Thus, 10% of possible sets differ in one feature, 30% in two features, 40% in three features, and 20% in all four features. The number of different 12-card deals is . The odds against there being no Set in 12 cards when playing a game of Set start off at 30:1 for the first round. Then they quickly fall, and after about the 4th round they are 14:1 and for the next 20 rounds, they slowly fall towards 13:1. So for most of the rounds played, the odds are between 14:1 and 13:1. The odds against there being no Set in 15 cards when playing a game are 88:1. (This is different from the odds against there being no Set in any 15 cards (which is 2700:1) since during play, 15 cards are only shown when a group of 12 cards has no Set.) Around 30% of all games always have a Set among the 12 cards, and thus never need to go to 15 cards. The average number of available Sets among 12 cards is and among 15 cards . However, in play the numbers are smaller. If there were 26 sets picked from the deck, the last three cards would necessarily form another 27th set. Complexity Using a natural generalization of Set, where the number of properties and values vary, it was shown that determining whether a set exists from a collection of dealt cards is NP-complete. References External links Set Enterprises website A (2002?) mathematic exploration of the game Set . Including 'How many cards may be laid without creating a set', as well as investigations of different types of set games (some in the Fano plane). The Mathematics of the Card Game Set - Paola Y. Reyes - 2014 - Rhode Island College Honors Projects There is a graphic computer solitaire version of Set written in tcl/Tk. The script can be found in a "tclapps" bundle at ActiveState Ftp://tcl.activestate.com/pub/tcl/nightly-cvs/. Sets, Planets, and Comets. An alternate, extended version of Set Set Daily Puzzle SET Finder Set with Friends Card games introduced in 1991 Dedicated deck card games Mensa Select winners