How Many Games of Spider Solitaire are Winnable?
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- combinatorics; computer simulation; fitness function; integer partitions; recreational mathematics; solitaire
thesis / dissertation description
The game of Spider Solitaire is analyzed to determine the number of the 104! initial arrangements of cards that have a winning solution. The game is broken down into its essential characteristics. Five parameters describing a Spider Solitaire game card pack and board configuration are formulated allowing variants of the game, notably smaller ones, to be analyzed. A computer program is developed and used to analyze and simulate the play of the various game variants. A class of Spider solitaire games using an infinite number of cards is then examined and used as a basis for constructing a graph of game positions traversed by a random walk. A suggestion for a new type of Spider game based on the graph construction is presented. A definitive answer is not reached. Areas for continued explorations are suggested.