The Brick-Wood Paradox
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.
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).
So, let’s get to it. Where is wood’s real advantage (or brick’s real downfall)?
If we look at the values of brick and wood throughout “stages” of the game, I think the paradox is solved.
In my report, I looked at Primary and Secondary resources separately. The value of brick and wood can be analysed here, to see where the disparity is. To recap, here are the resource values:
There is a huge drop in value for brick after the game starts, and a huge gain in value for wood after the game starts. Well, the first thing to note is that with 6 or 8 settlements on the board (depending on 3 or 4 players), the good brick places are most likely to be taken up, while there may be a good wood placement still hanging around, since there is one less brick tile. I assume that most players use the majority of their brick and wood near the beginning of the game. They use it to build some roads and settlements to expand their domain first. A play for the longest road would undoubtedly increase brick and wood usage throughout the game, but the most important uses of brick and wood are the immediate Secondary Settlements played. Outside of building these settlements (and the roads to them), brick and wood are used in trading. Players with surpluses of wood and brick trade them for the other 3 resources in order to assist the building of cities and buying of development cards. This is where the extra tile of wood comes into play. Through Primary and Secondary Settlements, the average winner occupies 1.71 brick hexes and 2.42 wood hexes.
The rest disparity comes from looking at the Empty Resources. Winners are more apt to skip settling on brick than wood. It’s fairly obvious from the numbers: 27% of winners start without brick while 13% go the whole game without brick, and only 3% of winners start the game without wood, and the same number ending the game without wood. It’s a risky move to start without wood. If you don’t start on it, you’re not getting to it. It’s a lot less risky to start the game without brick.
Here are my conclusions: players are more willing to trade away their brick to other players. Having the extra wood income makes it valuable for not only 2:1 wood ports, but 3:1 ports. Generally, the brick income is not high enough to use in conjunction with a 3:1 port. So, if a 2:1 brick port is not occupied, the best use of brick is to trade away to other people. This works well, because there are people who start and end games on no brick who will take anyone’s excess at a reasonable price (generally very low from my observations). I make the argument that it is better to trade through a port than to an opponent when possible.
With a higher wood income and less tendency to part with it, it seems that wood is indeed more valuable. The biggest disparity between the two resources is the ability to go the whole game without one of them, and the seeming impossibility of going through the game without the other.