# Graph Theory Concepts and Strategies with Ticket to Ride

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Ticket to Ride is a board game created by Alan R. Moon that has been growing in popularity since its first release in 2004 by Days of Wonder. The game components include a map with cities and defined train routes, sets of 45 colored, plastic train car tokens for up to five players, destination tickets, and colored train cards. The premise of the game involves collecting enough of the colored train cards to claim or build train routes to connect various major cities in the United States and southern Canada to earn points as well as completing routes designated on the destination tickets. The game itself is not only a fun way to spend hours playing but it is also a good tool to showcase various concepts in graph theory and combinatorics. Graph theory may also be useful in creating or enhancing game play strategies. Set Up and Game Play The original version of the game has a map of the United States and southern Canada with 30 destination tickets. An expansion to the original game features larger sized card sets as well as 39 additional destination tickets for what is referred to as the “Mega Game” variant. Throughout this analysis, I will assume all features of the “Mega Game” will be used unless otherwise stated. Since the first release, maps of Europe, Switzerland, Germany, Scandinavia, Asia, India, Africa, and the Netherlands have been added as well as a card game, a dice expansion, and additional destination ticket expansions have been created with the same basic game play. The original map is shown in Figure 1.The set up for the game begins with each player selecting his/her set of color train tokens. Next each player is dealt four of the colored train cards that players can later use to build or purchase train routes... ... middle of paper ... ...the game. Other plays could be going for the same tickets and routes or they could be attempting to block other players from completing a strategy. Graph theory can be used to help but does little to account for these unknowns. Even without a winning strategy, Ticket to Ride is a good medium to showcase different definitions and theorems within graph theory in accessible terms that can be understandable to more people while still being an enjoyable game to play. Works Cited Days of Wonder, "Game Rules - Ticket to Ride." Last modified 2013. Accessed November 29, 2013. http://cdn0.daysofwonder.com/tickettoride/en/img/tt_rules_2013_en.pdf. Harris, John M., Jeffry L. Hirst, and Michael J. Mossinghoff. Combinatorics and Graph Theory. New York: Springer, 2008. Rosen, Kenneth H. Discrete Mathematics and Its Applications. New York: McGraw Hill Higher Education, 2007.