Settlers of Catan Analysis

22/02/2011 14 comments

I completed my actual school project on this, and presented it to the Math faculty here – they seemed to enjoy it.

I thought you might all enjoy it as well, so below is a link to download the .pdf file of this guy.

Just click the page for some light Settlers reading material.

Advertisements
Categories: Settlers of Catan

Trading – People, Ports, or Production?

29/11/2010 1 comment

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. 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…

Understanding What To Settle

16/11/2010 11 comments

We know the difference between rolls, as we can look at the graph of the roll distribution. But what’s the difference between the 5 different resources? This is a lot harder to figure out, since we don’t have a nice graph charting what is most important. We can look at what we use the resources for, and the value of those things though. We know that there are only 4 different things to spend our resources on (or 5 if we’re playing Seafarers):

  • Roads (or Ships)
  • Settlements
  • Cities
  • Development Cards

Settlements: The most settlements that can possibly be built by a single player in Settlers is 5 – upgrading the original 2 settlements to cities and building 5 settlements gives 9 points, and no more settlements before a city us built, in which case 10 points is reached. Read more…

Armies and Roads (Or Maybe Not)

04/11/2010 2 comments

I’ve mentioned the longest road and largest army before on here, and undoubtedly anyone visiting this blog knows what they are – 2 points for owning the longest trading route of roads (and/or ships if we’re playing the Seafarers expansion) as well as 2 points for having the largest army of knights (from Development Cards). A couple of questions jump to mind:

  1. What is the main role of each of these outside of the 2 points they give?
  2. How useful are these two extra ways of gathering points?

The main role of road building is to develop settlements. The rules of Settlers state that two roads need to separate every connected settlement. Roads are necessary for any development past the original two settlements of each player. We can then say that roads are really the most fundamental way of expanding spatially (no roads are necessary to upgrade a settlement to a city). This is an inherit part of our overall strategy, as it is next to impossible to win with only the original settlement spaces (I suppose that one could do it by upgrading both to cities, obtaining the largest army, and purchasing their remaining 4 points in development cards, but that’s quite the challenge). 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…

Utility of Development Cards

22/10/2010 14 comments

This is a much debated topic in Settlers. There is obviously some value in them, but how much?
Overestimating that value is sure to end up in wasting resources buying more than you need.
Underestimating that value is sure to end up in wasting resources buying things you need less.

This is called opportunity cost. Again, this should remind you of any “Introduction to Macroeconomics” class. So, how do we decide how valuable Development Cards are?

Let’s start off with figuring out what Development Cards we’re dealing with before we judge value. In the original Settlers game, there are 25 development cards:

  • 14 Soldiers/Knights (I’ll call them Knights from now on)
  • 5 Victory Points
  • 2 Road Building Cards
  • 2 Monopoly Cards
  • 2 Year of Plenty Cards Read more…
%d bloggers like this: