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”.

Trading – People, Ports, or Production?

Settlers has a lot of trading in it. What’s the best way to do it? I’ve played with people who swear that it’s more advantageous to not trade with anyone until you have 5 points(relying on their own production), and I’ve played with people who only ever used the set rates of 4:1 or the 3:1/2:1 ports to trade.

From an economics standpoint, it is not advantageous to cut yourself off from trading with other players. The main reasoning that I have heard to discourage trading with opponents is the fact that you are directly giving an opponent a resource that he/she deems valuable. Why not keep it for yourself and not help them? The fact is that whether you participate in the trading or not, there is a market available to trade resources at a changing price, and your opponents will participate in it whether you do or not. In fact, the maximum participation in the market will give the most stability and fairness to the pricing of each resources. My advice is then to participate in the trading between players, but with the correct knowledge and foresight. A beneficial trade is one where each player is receiving resources that help him/her the same as the other. Trades need to be mutually beneficial and to the same degree of benefit.

Resources vs. Rolls

On this note, I will make a claim that I’m up for examining closely and testing later:
Numbers don’t matter (as much) when you spread to a new resource.

This was a statement I made near the end of Spreading vs. Clumping Trends (part 2), and since thinking of it, I knew that the comparison of resources to rolls would be an important one. I’ve been looking forward to investigating the relationship between rolls and resources, and I feel that I finally have sufficient data and reasoning to delve into the discussion.

Resources: When we examined resources last time, we found a less than easy way to order the resources by order of importance. When we looked at the demand for resources throughout the different stages of the game (starting resources, secondary resources, and city development), there didn’t seem to be too much difference. Some resources increased in value later (ore) while others decreased in value later (brick). But generally, there was a fairly set importance structure:

1. Wheat
2. Wood
3. Ore
4. Sheep
5. Brick