Open Access Senior Thesis
Bachelor of Science
Francis E. Su
Arthur T. Benjamin
2021 Kailee Lin
This report details my adventures exploring the Game of Cycles in search of winning strategies. I started by studying combinatorial game theory with hopes to use the Sprague-Grundy Theorem and the structure of Nimbers to gain insight for the Game of Cycles. In the second semester, I pivoted to studying specific types of boards instead. In this thesis I show that variations of the mirror-reverse strategy developed by Alvarado et al. in the original Game of Cycles paper can be used to win on additional game boards with special structure, such as lollipops, steering wheel locks, and 3-spoke trees. Additionally I propose a new "working conjecture" that the player with the winning strategy is always determined by the parity of the number of markable edges on the board at the start of the game.
Lin, Kailee, "Exploring Winning Strategies for the Game of Cycles" (2021). HMC Senior Theses. 253.
Applied Mathematics Commons, Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons