Graph Theory Concepts And Strategies With Ticket To Ride

3768 words - 15 pages

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 between adjacent cities. The colored cards come in eight different colors (red, orange, yellow, green, blue, purple, white and black) which correspond to specific routes on the map and are also include a unique symbol and train car for those that may have color blindness. There are also multi-colored locomotive that are used like wild cards. The colored train cards are shown in Figure 2. The second part of the set up to deal out five destination tickets (three, if not playing with the “Mega Game” expansion) a minimum of three which must be retained. Any destination tickets not kept by a player are returned to draw pile for later in the game. Note that some versions of the game remove any discarded tickets from play for the rest of the game. An example of a destination ticket is shown in Figure 3.
On a player’s turn, he/she chooses one of three options: Build a train connecting two adjacent cities using sets of colored train cards to earn points immediately, draw up to two additional colored train cards to be used later to build a train, or draw three additional destination tickets keeping a minimum of one to earn points at the end of the game. Play continues in this fashion for each player until one player...

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