Graph Theory and Game Theory in Ticket to Ride
http://www.cs.xu.edu/csci390/13s/p367-lim.pdf
http://gametheoryblog.blogspot.com/2010/04/east-coast-west-coast-which-is-best.html
Most of us have played a board game before, and they tend to be simple enough: roll the dice, move your token, buy or sell some stuff. However, outside of negotiating with other players, there doesn’t tend to be a whole lot of strategy or analysis to these games. Enter modern board games: titles lauded by hobbyists for their deep strategy. These games draw upon all sorts “real-world topics”. These two articles address Ticket to Ride.
Ticket to Ride is a game based in graph theory. The board consists of cities across the US. The goal of the game is to score points by completing your own secret “tickets”: cards marking two cities that you must connect with your train routes. The parallels to graph theory are immediately apparent; the cities are nodes that you aim to connect via creating edges between various nodes. Your goal is to construct the most efficient tree (or set of trees) spanning across the cities that you need to connect.
The game also heavily draws upon game theory, due to the fact that there are a limitations on how edges can be formed. Each city can only connect to nearby cities, and can only form one or two routes between the two. If another player claims that route, then you have to find another way to get wherever you are going. This creates the need to approximate payoffs for claiming a route now before someone else takes it versus waiting until later to avoid giving away your plans. The second article also discusses the possible existence of a dominant strategy, in regards to focusing on locations in the west coast versus the east coast.