Ticket to Ride - hledání optimální strategie v deskové hře pomocí teorie grafů

This bachelor thesis deals with the analysis and optimization of strategies in the board game Ticket to Ride. The aim of the thesis is to identify optimal strategies that help players to play more efficiently. The theoretical part introduces the game Ticket to Ride, its history, rules and meaning in the context of graph theory. The practical part is dedicated to the construction of a network graph of the game and its analysis, which allows a deeper understanding of the game structure and supports strategic decision making. Furthermore, two basic strategic approaches are presented: maximizing the score and minimizing the risk of not completing the path. These strategies are expressed using a modified mathematical model based on an integer programming formulation of the well-known travelling salesman problem. The models were solved using the optimization software Lingo, which allowed the identification of optimal paths between cities on the game board. The results of this work offer a new perspective on strategic planning in Ticket to Ride and can serve as a useful tool for players seeking a competitive advantage.