Home > Settlers of Catan > The Brick-Wood Paradox

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.

@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).

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:

Primary Resources:

    1. Wheat
    2. Ore/Brick
    3. Sheep
    4. Wood
Secondary Resources:
    1. Wheat
    2. Ore
    3. Wood
    4. Brick
    5. Sheep

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.

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  1. Dean Underhill
    16/01/2012 at 6:24 pm

    I started playing Settlers of Catan last year. It is no doubt the most addictive board game I’ve ever played.

  2. Jehovah's Blitzness
    13/12/2012 at 3:53 pm

    Unfortunately, it IS a fundamental flaw in your analysis. Because the tiles are randomly sorted, but the numbers are more-or-less fixed (the desert adds a little wrinkle, but not much of one), the disparity between wood and brick is magnified beyond a simple 3/18 vs 4/18. Consider:
    1. There are more Wood tiles on the board than Brick
    2. There’s a better chance a Wood tile will have a high-frequency number (6-8 or 5-9)
    3. There’s a better chance a Wood tile will be ADJACENT to a high-frequency number, and would thus be “settled” even though it isn’t the “target.”

    Using the stats behind game outcomes is a dubious business. Just because I happen to start without brick (or happen to win without brick) doesn’t automatically mean brick is less valuable. I would say it’s more indicative that Brick is hard to get. You’re not controlling those outcomes for frequency. Most players would rather have a high-frequency tile in a less-valuable resource than a low-frequency tile of a more-valuable resource. If my choices for Brick are no better than a 4-10 or 3-11, I’m unlikely to bother with it. That’s a very unlikely occurrence for Wood.

    Also, equally weighting primary and secondary settlements is a mistake; a primary settlement is in play for 100% of the game’s rolls. A secondary settlement can be in play for as few as 1, or as many as (N – 2) where N is the total number of rolls.

    I think you touched on these points a bit, but you took your conclusion in a very different direction. I would suggest: First, your attempt to normalize for rarity is incomplete, and understates the value of rare resources (Ore included.) Second, the methodology you’ve used for valuing tiles (based on game outcome data) is NOT normalized for rarity, so it inherently overvalues the common resources (again, the same thing as understating rare resources.)

    Basically, I’m not sure that this “paradox” is as pronounced as described, even probabilisticaly. I wouldn’t go so far as to say that Brick is more valuable than Wood, though given that 13% of winners never settle Brick vs. 3% of winners never settling Wood, I would bet that Brick is about 4x more rare than Wood. Quick, someone do the math!

  3. Ehren
    21/09/2013 at 8:14 pm

    In my experience, everybody wants brick at the very beginning of the game and there isn’t enough to go around, regardless of the level of the players. There is just an absolute brick scarcity. Experienced and “good” (meaning they win more often), players expect the brick scarcity and prepare for it in their placements. Also, very experienced and “good” players trade less often with other players though I think that’s a mistake. Wheat is the scarce resource in the middle of the game and ore at the end of the game. Because there are fewer brick and ore tiles, those tiles are less likely to have commonly rolled numbers assigned to them, which means that there is typically only 0-1 commonly rolled brick or ore, but 1-3 commonly rolled wheat, wood and sheep. .

    So, if you are a good player, the way you prepare for the scarce wheat and brick is to either 1) be lucky and place your settlements on abundant brick and wheat or 2) you set your initial settlements up with a surplus of a particular “throw-away” resource that you can use for non-player trades to get the resources you need. As i said, grain, brick and ore are typically what you are receiving from your non-player trading, while wood and sheep are typically what you are throwing away. So that leaves wood and sheep as throw-away resources. Wood is slightly better than sheep because you can use it to build roads at the beginning of the game, in addition to trading for brick. I go for sheep if I am close to the 2:1 sheep port or if I am on an abundant grain or ore or both tiles, because the sheep is useful for development cards, the grain and ore are useful for cities and cities are attractive targets for putting the robber next to, which means you need knights to kick him off.

    So, the real paradox is that wood and sheep are the most valuable resources because they are not valuable, i.e. you can afford to throw them away in non-player trades.

  4. magnemg
    28/07/2014 at 5:56 pm

    Thanks for an excellent analysis Peter! As the statistics you are basing your analysis on has a lot to say for its worth as general rules, would you mind sharing it? The number of games played to arrive at the statistics is especially important, for the percentages to have any meaning.

    • magnemg
      28/07/2014 at 5:57 pm

      (I’d like to be notified of any follow-up comments.)

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