Abstract
Santorini is a two player combinatorial board game. Santorini bears resemblance to the graph theory game of Geography, a game of moving and deleting vertices on a graph. We explore Santorini with game theory, complexity theory, and artificial intelligence. We present David Lichtenstein’s proof that Geography is PSPACE-hard and adapt the proof for generalized forms of Santorini. Last, we discuss the development of an AI built for a software implementation of Santorini and present a number of improvements to that AI.
Advisor
Fox, Nathan
Department
Mathematics
Recommended Citation
Geissler, Carson Clyde, "A Mathematical Analysis of the Game of Santorini" (2020). Senior Independent Study Theses. Paper 8917.
https://openworks.wooster.edu/independentstudy/8917
Disciplines
Artificial Intelligence and Robotics | Discrete Mathematics and Combinatorics | Other Mathematics | Theory and Algorithms
Keywords
Game Theory, Graph Theory, Santorini, AI, PSPACE, Complexity, Game, Graph, Artificial Intelligence
Publication Date
2020
Degree Granted
Bachelor of Arts
Document Type
Senior Independent Study Thesis Exemplar
External Link
https://github.com/carsongeissler/SantoriniIS
Included in
Artificial Intelligence and Robotics Commons, Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons, Theory and Algorithms Commons
© Copyright 2020 Carson Clyde Geissler