# Graph Theory Concepts and Strategies with Ticket to Ride Essay

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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.…show more content…
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 has two or fewer train tokens left and then everyone still has one more turn. The points earned from building a train connecting two adjacent cities are based on the length of the route with the longer routes earning more points per train token. Routes of length one and two earn only one point per token while a route of length three earns a total of four