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Posts Tagged ‘Relative Advantage’

The Brick-Wood Paradox

22/05/2011 5 comments

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.

@DevelopingCatan

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). 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…

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