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”.

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

Spreading vs. Clumping Trends (part 2)

Last time we talked about spreading out over roll numbers or clumping, and how people seem to be pre-disposed towards 5’s and 8’s (in the game I played last night, it sure felt like 5’s hit a lot more than 9’s…hmm). We ended on the next logical question:

What about resources?
The easy answer is this: winners (generally) don’t seem to clump up on resources – they like to make sure they get some of everything.

What’s the difference? Well, the most obvious difference is the way we place value in rolls and resources.
Rolls are given value by the probability of them being rolled. This is a pre-calculated value that doesn’t change. Any person who has taken a probability class knows that 6’s are more likely to be rolled than 5’s, which are more likely to be rolled than 4’s, and so on. Anyone who has played even once knows this by experience. Valuable rolls are based on the normal roll distribution.
Resources are a little trickier. The rate at which they are picked up changes every game. We can’t be certain that ore will be picked up more than wood. Also, these resources are used for different things, and so again we have another variable. If development cards and cities are the best thing to get, are ore and wheat the most valuable? You can see where we hit a roadblock – value of certain resources change depending on the strategy certain players use.

Spreading vs. Clumping Trends (part 1)

My first real post brings me to my first real problem: what should I post about first? I’m still adding games played to my charts (which I’m sure I’ll show you sometime, or at least explain what I look for) so I’m not going to present some sort of groundbreaking strategy that’s a sure-fire win every time. Instead, I’m going to speculate about strategy and trends. I keep stats throughout every single game, but only record the winner’s strategy in my charts – I’m tracking winning strategies to see if any come to the surface as the winning strategy. Throughout this stat-keeping process, I’ve noticed some small trends, that are most likely insignificant, but interesting none-the-less.  Let’s look at the opposing strategies of spreading or clumping.