Campus Only Senior Thesis
Bachelor of Arts
2020 Sarah E Groh
Combinatorial games are finite games where players are aware of all plays at all times and there is no element of chance. Some combinatorial games can be "solved" and with the right math, a player can beat their opponent every game. This thesis investigates combinatorial games from a mathematical and philosophical perspective. For the mathematical portion of this thesis, we present two proofs and discuss their importance to combinatorial game theory and how they can be applied to games. We then explore how small changes to the game of NIM affect winning strategies and present and prove new winning strategies. Following the mathematical portion of this thesis is a philosophical discussion of combinatorial games. In that section, we aim to tackle what a game is, how deceit is involved in winning strategies, and if using math to win games is a moral or fair way to play games.
Groh, Sarah E., "Winning Moves: Mathematical strategies behind certain games and their philosophical implications" (2020). Scripps Senior Theses. 1570.
This thesis is restricted to the Claremont Colleges current faculty, students, and staff.