For fun, I examined the values of the different resources in Settlers of Catan in terms of how much they can buy you in Victory Points. I determined that Stone and Wheat are generally the most valuable resources and Wood and Brick are the least valuable.

The actual ranking is:

Stone>Wheat>Sheep>Brick>Wood

The “cheapest” winning end state you can get is 4 cities and longest road, which will cost 40 resource cards beyond your start.

The most “expensive” end state is 4 settlements, 5 victory points from Development Cards, and Largest Army, which will cost 95 resources.

Premise:

I began by calculating the total number of end states that can be achieved by a player based on all of the combinations of settlements, cities, and development cards that can be built, and whether they have Longest Road. This resulted in 432 combinations.

I then reduced this to the number that have 10 or 11 Victory Points. (It is possible to end with 11, if you achieve Largest Army or Longest Road after getting 9 points some other way.) This left a total of 81 winning end states.

I then calculated how many of each resource would be necessary to get to each of these.

Assumptions:

In order to simplify the math, I have made a number of assumptions.

You will play a perfect game and there will be exactly two road segments between any of your cities/settlements. There will be no extra road segments built, unless it is to achieve Longest Road.

Development Cards are each worth 7/25ths of a Victory Point, because there are 5 One Victory Point Cards and the possibility of getting Largest Army, worth 2 Victory Points, and there are 25 total cards in the deck. I am disregarding the benefits of the other cards and the robbing ability of the knight card, since these do not gain Victory Points directly.

You start with the equivalent of 4 wood, 4 brick, 2 wheat, and 2 sheep in the 2 settlements and 2 roads in the beginning. This has been deducted from the total resources necessary to achieve each end state.

All resources are equally likely to be gained through rolling or trade. This is a big assumption, especially for any single game, but works out in the long run. Note that there are 4 sheep, wood, and wheat tiles on the board, but only 3 brick and stone tiles. This will be addressed later, since it will not average out over multiple games.

The robber is discounted, since everyone has an equal likelihood of rolling 7.

The benefits of extra resource collection from cities, trading ports, and other strategic placement are disregarded.

Remember that cities cost a total of 1 wood, 1 brick, 1 sheep, 3 wheat, and 3 stone, since you must have a settlement first.

Results:

From this basic breakdown, you will need an average of the following resources to achieve one of the winning end states:

8.7 wood

8.7 brick

18.2 stone

15 sheep

18.6 wheat

The high bias towards stone, wheat, and sheep is due to the number of outcomes that can be achieved with Development Cards. However, it is unlikely that you would actually be able to get to some of the states like, for example, 2 settlements, 5 Development Card victory points, Largest Army, and Longest Road.

When I reduce the maximum number of victory points that you are likely to gain from Development Cards to only 4, the average resources needed becomes:

10.5 wood

10.5 brick

15.2 stone

11.2 sheep

15.8 wheat

This still supports the same hierarchy of the resources.

Distribution curves of the number of each resource needed for each win condition further illustrate this.

The least number of wood, brick, and sheep that it is possible to win with is 2 of each. However, the least number of stone you can have to win is 6 and the least number of wheat is 8.

The most wood and brick that you will ever need is 17 of each, and most condditions only need about half this. More stone, sheep, and wheat than this are needed in most of the possible end states.

As mentioned, the tiles are not evenly divided between the resources. When you take that into account by dividing the average brick and stone needed by ¾ (since they only appear 3 times on the board and the rest appear 4 times), you get the following relative values for each:

8.7 wood

11.6 brick

24.3 stone

15 sheep

18.6 wheat

This makes stone and wheat switch places for top position, and makes the final ranking of resources:

Stone>Wheat>Sheep>Brick>Wood

(Thanks for reading! I’m an amateur at this, so if you have any thoughts, additions, or critiques, please let me know.)