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Posts Tagged ‘Roll Distribution’

Fluctuating Incomes and Cool Graphs

07/03/2011 2 comments

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”. Read more…

Resources vs. Rolls

17/11/2010 1 comment

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 Read more…

Is Getting Robbed a Good Thing?

25/10/2010 4 comments

Well no. It’s not. First, I should clarify my distinction between getting stolen from and robbed.
Getting Robbed is when a 7 is rolled and you have more than 7 cards, forcing you to discard half of them.
Getting Stolen From is when the Robber is put on your hex and the opponent gets to steal a card from you. This isn’t what I’m talking about.

So again: is getting robbed a good thing? No. It means you lose cards. In the strictest sense of the definition, getting robbed is simply spending cards and getting nothing tangible in return. It’s spending resources on nothing. More precisely, it’s spending resources for the convenience of holding those resources. So, in that sense of it, if at any time you find yourself holding more than 7 cards in your hand, you are essentially gambling half of them. We’re gambling against the roll distribution.

Here’s a little math lesson for you. Anyone who has taken some basic probability classes will be able to teach this lesson, so bear with me if this sounds like a class you took freshman year of college. Basically, there’s a set probability of rolling each number, shown by the graph below: Read more…

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