More Graph Theory, Not Any Results Yet

I just got a new (small) whiteboard, which is forcing me to come back to my graph theory approach to movement in Catan. Here’s my initial drawing, looking at the centre nodes and their paths to the edges. I’ve got a hunch as to where people move, but we’ll see what happens as I sketch out the 15 games I’ve observed. This board is about the get messy!

So, thoughts on what I’ll find?

 

Google+… Not Even Slightly Related to Catan

So this post isn’t even slightly related to Catan, but I figured I’d post it anyways.

I got into Google+. If you don’t know what that is, it’s Google’s new social networking site, and it’s getting a lot of press. I don’t want to be the guy that reviews it on my non-social-media related blog, so go read what Mashable has to say about it.

Anyways, the point of this post is to say that Developing Catan is in. Add me to a circle to get updates on there if you’re in. I’m looking forward to having a lot of social interaction there. It’s a little more social than wordpress is, and I’d love to work with it more!

The Brick-Wood Paradox

When I first started letting people see some of the research I had done (by showing friends and posting here mainly), it was received with a lot of encouragement, and some follow-up questions, the most prominent of which I have dubbed the “Brick-Wood Paradox”. As quoted from a commenter:

Why [are] brick and wood so different in their value? They are used for the same things, they should be similar.

This is a tricky question. It’s a great observation – one that I missed in my first analysis. Brick and wood are used together in building roads and in building settlements, and neither are used for anything else. As demand for roads and/or settlements changes, the demands for brick and wood should change together, giving them the same “price” or value. At least, that is the intuitive comment made by many. My analysis holds to wildly different values for brick and wood. I believe that my analysis is not completely wrong (I’m not going to claim that it is the “God’s Word” of Settler’s strategy, though). These two facts led me to investigate this paradox.

The first observation (and most elementary – other people have made it since) is that the difference in value must come from the difference in number of tiles. There is no difference between wood and brick in their use, so the difference in value must come from their only difference in the game. This scared me at first. If the problem is that there is a difference between number of tiles, did I not equalize the resources correctly, independent of how many tiles there were? If there was any disparity between them, wouldn’t supply/demand say that the lesser available one is worth more? Is my analysis of ore wrong (since it is the other resource with only 3 tiles)? I hope not (and I don’t think it is).

Profile on Catan Online World

I love playing Settlers with my friends. It’s a great social game, and I don’t have to convince anybody who is actually taking the time to read a blog about Settlers strategy why. I also play Settlers online. If you go to PlayCatan.com and sign up for an account, you can download a little application that hosts Settlers games. The Basic Game is free, and there is an option to pay for the Seafarers and Cities & Knights expansions.

So here’s the deal: I’ve recently dedicated a new profile for playing games for the blog. I like playing personal games under my own username, but I decided that it would be a good idea to separate my own play from the games I play for observation here. This way, I can attach some fun screenshots, and maybe even interact with some of you that frequent the Catan Online World.

So, if you haven’t already downloaded the Catan Online World and registered for an account, go ahead and do that here.

If you’re already on there (or once you sign up), add me as a friend. My name is DevelopingCatan (I believe that it’s case sensitive), and if you see me online, let’s play!

Fluctuating Incomes and Cool Graphs

So this post is going to be a better explanation and answering of the questions posed in “Spreading Vs. Clumping” (part1 and part 2). I asked a lot of questions in these, and even I wasn’t satisfied with the answers that I gave. I think it’s time to attack the beast, with a little help from Paul Gebel. Here’s the story:

When I began my look into Settlers of Catan through my math-lenses, I tweeted about it. Paul somehow found it, and has been a great encouragement since then. The other day, he tweeted something about the “resource curse”, which sounded extremely Catanish. Upon reading it, I found that it was exactly relating to how I wanted to describe fluctuating income.

So, that brings us here. I’m going to follow the format I did last time with introducing my analysis with one of my tweets:

So, there’s a couple of jobs to do. First, the definition of “resource curse” needs to be applied to a Catan setting. Then, sine curves need to be used to help model incomes in Catan. Let’s start with “resource curse”.