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Winning Ticket to Ride with Network Analysis

I have seen that this blog is filled with posts about video games, but if there is one thing I miss most about quarantine life is the ability to sit down with a small group of friends in-person and play a board game or two. In my opinion, board games are a much more enjoyable social activity than online gaming, not to say that is bad, and comes with a plethora of options to chose from including your traditional most points win to ruining said friendships with deceit. The things I look for in a game when introducing to friends is ease of entrance, because explaining rules for half an hour is not fun, and how good I am at the game, because I like winning. Ticket to Ride ticks off the first checkmark easily and the second is fulfilled by the article I have selected looking at the network of the gameboard to maximize the chances of winning.

The gameboard for Ticket to Ride: Europe, the version of the game discussed

To fully understand the game rules, click here, but for the sake of conciseness, I will only briefly go over scoring in the game. You earn points by completing connections between two cities, completing given routes between two specific cities and having the longest continuous chain of train cars. The article goes on to change the gameboard into a network simply by representing cities as nodes and possible connections as edges.

To build strategy, the article focuses on several aspects. The ones of most interest to this course is node and edge Betweenness and Connectivity. Betweenness is a key part of the game as it allows one to plan routes and occupy territory that is most likely wanted by one’s opponents. Connectivity is important to help prioritize isolated locations that may prove difficult to build towards.

Top 5 edges based on edge betweenness

When looking at betweenness of nodes, high betweenness signifies lots of traffic through that city as many shortest routes run through it, so players should expect a lot of opponents to also want to go there. Cities such as Wien and Frankfurt are examples and are a priority to get early. Edge betweenness shows a similar pattern where lots of routes run through them, so it’s important to grab them before having to take a long detour.

Node connectivity of certain cities

When looking at connectivity of nodes, there are two key cities found, being London and Madrid, as if either of them is blocked, Edinburgh, Cadiz and Libona are all cut off from the board, giving them significantly more value to players who have routes going there. Edge connectivity is also important when looking for completing routes, even thought London-Edinburgh is the only route that disconnects the network. That being said, occupying certain routes makes the shortest paths between some cities much longer, such as Kobenhavn-Essen increasing average shortest path cost by 7.34%.

The article goes into much more detail about which routes to prioritize, alternate scoring strategies and how to block opponents effectively, but even with just barebones network analysis, the strategy of the game is elevated to another level. Understanding where players will tend to go and priorities for building allows one to more thoroughly plan out their route and adds more skill to the overall game. There probably is a whole other layer to this with game theory and common knowledge, but that is for another time.

Overall this article provides good insight into how strategy evolves from network analysis and understanding the importance of connectivity and traffic flow. This example from a board game can be expanded into the real world and establish priorities based on similar facts. Either way, just remember, it’s just a game, having fun is most of the reason to play.

Source:

Chintha, R. (2020). Playing Ticket-to-Ride like a Computer Programmer. Towards Data Science. https://towardsdatascience.com/playing-ticket-to-ride-like-a-computer-programmer-2129ac4909d9.

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