Leiden University Student Repository

Fitzgerald, Kaitlyn (2026)

Cylindrical Hex and its Strategies: Introducing an Optimal Strategy for Red on m×n (m>n) Boards, and an Improved Strategy for 5×n Boards

Master thesis | Mathematics (MSc)

In this thesis, we discuss the board game Hex and some of its variations, largely focusing on Cylindrical Hex. In addition to discussing the games themselves and providing an overview of what is known about the winners and winning strategies, we focus on two new strategies for Cylindrical Hex. We provide a rigorous proof of the optimality of the Gardner strategy for asymmetrical boards in Hex, and then show that Red can even continue to use this strategy on Cylindrical Hex boards with m>n. We also look at how to improve a sub-optimal strategy for the 5xn Cylindrical Hex board. While the resulting strategy is also not optimal, it does perform noticeably better than its predecessor in simulated games. Some suggestions for future improvements are also made based on the lost games.

Author

Fitzgerald, Kaitlyn

Faculty

Faculty of Science

Supervisors

Spieksma, F.M.

ECTS Credits

40

Language

en