Applications of Graph Theory and Probability in the Board Game Ticket to Ride

Abstract

In the board game Ticket to Ride, players race to claim routes and connect cities on a map of the U.S. In this work, we identify winning strategies for and potential improvements to Ticket to Ride by applying probabilistic and graph-theoretic concepts. We find that longer routes are overvalued, presenting a simple winning strategy for opportunistic players. The scoring scheme we propose—based on indicator random variables—prevents exploitation from this strategy and improves the competitive nature of the game. Using a variety of game data visualizations, we also investigate why players who connect particular pairs of cities perform better than others. In addition, we build a statistical model from the effective resistance of the game’s underlying graph structure to suggest how to choose the best pairs of cities.