Solitaire


This page is a mix of recreation, information, and mathematical research. (Yes, folks, math can be fun!) When I was young I had a couple of books describing hundreds of different solitaire games. During the dull parts of family vacations, I tried almost every game in those books and invented several more of my own. More recently, I've become interested in knowing the probability of winning various games, and in discovering the optimal strategy for the games involving skill. (Actually, only a handful of solitaires involve no skill whatsoever.) Listed below are the names of several solitaires; click on a name to get a description of the game and a summary of my statistical investigations of it. Most of the descriptions of new games also describe when the game was invented and how it received its name. I've also included some references and some background information.


New Games

Links marked with an asterisk are incomplete.


Old Games


What is Solitaire?

The family (actually, a large set of families... phylum?) of one-player card games. Multi-player adaptations of several such games exist; these go by the oxymoronic name "double (triple, and even quadruple, if you're really crazy) solitaire." In many other countries, solitaire is more commonly known as Patience. Most of the common solitaires are based on sorting the deck into suits according to some set of rules restricting how the cards may be rearranged.

Classification of Solitaires

No perfect classification scheme exists, but I like the one used by Parlett (1979) pretty well. He divides the games based on two characteristics: how many cards in the deck are exposed at the beginning of the game, and the general pattern of assembling cards into groups during play. This leads to the following categories:

Non-solitaire examples of these categories include chess; stud poker and blackjack; and draw poker and cribbage, respectively.

Obviously, there is some overlap between these varieties, and there are several solitaires that fit none of these three.


References

Brown, Douglas. The Key to Solitaire. Bell, 1966. Descriptions of 150 solitaires, along with numerous illustrations and examples of how to play. No serious analysis of any of the games.

Morehead, Albert, and Geoffrey Mott-Smith. The Complete Book of Patience. Faber & Faber, 1950. Unfortunately, I haven't been able to find a copy of this book, but all subsequent sources cite it extensively. The authors were the inventors of many solitaires.

---. Hoyle's Rules of Games. Signet, 1983. A quick overview of card games of all types. A few dozen of the most popular solitaires are described.

Parlett, David. Solitaire: "Aces Up" and 399 Other Card Games. Pantheon, 1979. A good description and classification of all the common solitaires and most of the uncommon ones, along with (very approximate) chances of winning.


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This page was last updated 02.12.97