How the Calculator Works
CatanRobberCalculator.com is designed to help you beat your friends in Catan by revealing unique ways to utilize the Robber. So often do I find myself with 7 cards in hand and strong resource production capability debating if I should accept an otherwise unfair 2-for-1. My only reason, to protect against the pesky robber. When faced with this predicament, I am forced to make a gut-call, losing out on potential alpha. That’s where CatanRobberCalculator.com comes in. By comparing your expected loss due to the Robber (ELR) between differing scenarios, you optimize your decision making. For example, if you notice that building a road lowers your ELR by 2+ cards, you should always build that road. The same applies to any trade where a player gives more cards than they receive and lowers their ELR by more than that difference. Other times, it's comforting to know how many cards you can expect next turn.
Tackling Robber Optimization
The Math
I began by breaking down each cycle, the amount of time between a player going twice, into 4 discrete rolls. On each roll (regardless of if it’s yours), you have a calculable probability to earn resources. By taking a weighted average of the potential resource gains, I was able to gauge expected card count in one cycle into the future. Then, I calculated the expected card count discounting the robber by treating “7s” as any other number that doesn’t yield resources. Finally, I took the difference between these two numbers, illustrating the ELR.
The Implementation
My first attempt to carry this protocol was to utilize Google Sheets. I created two 1300+ row sheets where I manually noted every possibility of every roll. While it was by no means pretty, it worked. However, it was not compatible with HTML, the coding language used to make websites like this one. So, I started self-teaching. And after many hours of Khan Academy and YouTube, I figured out how to systemize my unwieldy behemoth of a sheet into a neat and efficient chunk of code.
Who Am I?
Hi, my name is Liam Brooks and I am a 17-year-old from Los Angeles, CA. Similar to you, I like Catan. And I love being the first to 10 VPs. Over the summer, I decided to see how I can leverage game theory to optimize my Catan strategy. I started by doing research to see what’s already out there. Immediately, I was struck by how all the literature discounted one crucial element of Catan: The Robber. For this reason, I decided to explore this niche and develop a practical algorithm to solve this aspect of the game. If you’re curious about the behind-the-scenes work or anything else relating to this website, don’t hesitate to reach out; I’m be psyched to hear any criticism or queries. The best way to contact me is via email: iamliambrooks@gmail.com
Thank you for taking the time to read this and have a nice day!