As any competitive Catan player will tell you, the beginning of the game is crucial. The first settlements usually having a major impact on the rest of the game.
A good starting position will offer a good variety of high-paying resources. But how do you know which resources to get?
For a while now, I’ve been working on an in-depth article about Catan islands board fairness, and to make sure boards give a relatively good chance to all players, I had to determine the relative values of the different resources.
So today I decided to dedicate a post to this:
Can we determine the strategic values of each resource?
The short answer is approximately, but yes!
Now… I’m pretty sure everyone will find some ways to disagree with my results, but my hope is that we can still agree on parts of the answer!
And if we cannot agree on a definitive answer, at least we will be able to discuss the methodology, and get sone insights in the overall game strategy for the future!
Will I be able to use this to easily find the best settlement location?
That is the whole idea!
The goal is to give a different value to each resource type, and use those values in conjunction with the roll numbers to obtain a score for each location on the board.
In the above example, the chance of obtaining resource cards are the same for both central location….
But the strategic value of both is not the same….
How should we evaluate this? Let’s have a look….
How did this idea got started?
The whole idea of resources relative values originated for me when I started this blog, quite a long time ago. While doing research for my first post, I happened to read an interesting Catan analysis by someone name Peter Keep, addressing this exact point of resource value.
For the curious, you can visit his website, it has not been updated in 10 years, but can be interesting to read nonetheless:
- Settlers of Catan analysis (pdf)
- Developing Catan – Blog
So let’s go with my take on this, using his work as a starting point…
Raw resources needed to win a Catan game
One interesting take he had on resource values was to count how many resource cards of each type are needed to win the game.
A quick reminder of the cost or each item
No matter what is your strategy, the maximum you can buy during the game should be about the following:
- 5 settlements (5 bricks, 5 wood, 5 wheat, 5 sheep)
- 4 cities (8 wheat, 12 ore)
- 11 roads (approximation of most roads) (11 bricks, 11 wood)
- 7 development cards (approximation for the biggest army) (7 sheep, 7 ore, 7 wheat)
So a upper bound on spending could be: 19 ore, 20 wheat,12 sheep, 16 wood, 16 bricks
This is a quick, if rather simple way to measure resource relative importance. But it’s good to see that it supports the intuition that wheat and ore are often considered the most important resources in Catan.
Typical spending during a Catan game
However, you would never spend that much during a real game…
If we go for a more typical game spending, we would get:
- 3 settlements (3 bricks, 3 wood, 3 wheat, 3 sheep)
- 2 cities (4 wheat, 6 ore)
- 5 roads (5 bricks, 5 wood)
- 3 development cards (3 sheep, 3 ore, 3 wheat)
Which would be: 9 ores, 10 wheat, 6 sheep, 8 woods, 8 bricks
Getting values we can compare…
Trying to compare the last 2 approaches (and the ones that follow) simply by looking at the number of resources is not very practical: they vary too much in their range.
And more so, how would you use this during a real game, when trying to decide if it’s better to build next to a Wheat location with the roll number 5 or building next to the brick location with the number 6… This simply won’t do.
If we want a usable metric, we need values that can be used to help our decision process.
To transform the raw card numbers into something easy to compare with, we can use a simple trick called normalization.
Or more simply: Dividing each value by the average of all values.
Take our first maximum spending values of:
- 19 Ore
- 20 Wheat
- 12 Sheep
- 16 Woods
- 16 Bricks
Their average is: (19+20+12+16+16) / 5
or 83 / 5 = 16.6
Dividing each value by the average (16.6) we get:
Now all values are close to 1.0 and indicate relative value to each other:
- Of two values, the higher one is the more valuable
- Values above 1.0 indicate above average
- Values below 1.0 being below average.
More importantly, if you do the same thing with the second set of values (the typical spending in a game), this time you will divide the resource initial values (9 ore, 10 wheat, 6 sheep, 8 woods, 8 bricks) by 8.2 (their average), to get the following:
Suddenly, it becomes really easy to compare both sets of numbers.
The values we end up with for each resource here are not that different one from one another.
(Which is good! At least for the moment.)
Comparing the two sets of values we can see that:
- In both cases, Wood and Brick have the same values.
- The order of importance is the same (Wheat > Ore > Wood – Brick > Sheep
- In the first Ore is slightly more valuable than in the second approach (1.1446 instead of 1.0976)
- In the first, wheat and ore are much closer in how valuable they are than in the second approach.
How to use those value in the game ?
And now, for the real magic.
Let’s say you decided than the second set of values is the right one to use, how could you use them in a real game situation?
For this, we will need to use the roll number associated with each tile.
Remember, in Catan, each time a player rolls the dice, everyone with a settlement around a tile with this number will receive a resource card.
But the real interesting piece of information is the number of dots underneath each number. To simplify things, they represent how many times on average a number will come up for each 36 dice roll.
So basically, two-dots numbers should come up twice as often than one-dot numbers, and so on.
Knowing this, let’s compare the value of two hexes:
So to take our latest value:
Bricks: 0.9756 multiplied by 4-dots (under the number 5): 0.9756 x 4 = 3.9024
Ore: 1.0976 multiplied by 3-dots (under the number 4) : 1.0976 * 3 = 3.2928
So here the Brick position would be more valuable than the ore.
But using different values, this could be the inverse…
That is why finding the right numbers is important!
To evaluate a complete position, one could then simply calculate and add the values for all tiles surrounding a settlement position, and see which one is better!
Take a minute to look at the values and to understand what they mean in terms of relative importance, this should make the rest of this article easier to follow.
The importance of the specifics for each victory
One caveat to this is that the resource relative values are highly dependent on the actual victory you are trying to achieve….
For example, if we take the typical game spending from earlier but only make two changes:
- An additional city (+2 wheat +3 ores)
- But one less settlement (-1 brick, -1, wood, -1 wheat, -1 sheep)
This would make the ore the most desired resources for our typical spending victory evaluation…
So how the victory is achieved change the relative evaluation. But this is not to say that any numbers will do!
Nothing you do would make Sheep the most desired resource! (At best, sheep would be equal to wheat in a victory based strictly on settlements and development cards.)
The one thing this approach won’t be good for, is to evaluate specific game resource scarcity.
One could imagine a game where sheep are scarce (Sheep tiles being badly positioned, each with a low roll number on them). In such a game, one could manage to get an effective sheep monopoly and strategically exchange sheep cards to reach a victory.
But for the sake of the present discussion, we will keep to the relative value of equally available resources!
This should at least provide a strategic baseline that can be tweaked when needed.
Evaluating the cost of all possible Catan victories
The best way to think about this I think is to consider all possible victories.
Some readers may remember that in the first series of articles I wrote about Catan, originally titled The 102 ways to win at Catan, I explored all the possible game victories and their individual costs. (There are in fact 143 ways to win at Catan, something I learned after astute readers reminded me you can have 11 or even 12 points victories in the game.)
It certainly would be a waste not to use this information, so I revisited the 143 ways of winning and checked what was their average cost.
- First with the minimal card cost associated with each victory (shown in resource cards)
Once normalized…
- Second, with the realistic expected cost of each victory
This takes into account the number of victory cards needed on average (instead of minimally) to realistically reach each victory. Furthermore, I added one road cost to each victory in order to reflect real game situations.
The realistic approach gives us:
Normalized…
Interestingly, even if the realistic cost is higher on average, the normalized values do not change their order of importance.
However, the value of the wood and bricks gets much lower…
But this is an artefact of looking at all the expected values.
Where the expected value differs from the minimum value, it’s that we calculate how much it will likely cost you to obtain the desired development cards. (Instead of the minimum it could cost if you were infinitely lucky).
If you need 2 victory points from development cards, how many will you have to realistically buy to get them?
Winning with 1 or 2 victory point cards is not unusual. But if you need all the 5 victory point cards, the amount of development cards you will have to buy on average is prohibitive. And since here we consider all possible victories, those very costly victories drive up the average relative value of resources needed to get them (coal, wheat and sheep)….
So we need to take a more realistic approach.
Let’s look at the individual winning conditions, and see what it means for the relative value of each resource.
Different victories, different values
If you already know how you will win, the resources relative values are easier to calculate. And they can be wildly different from one victory to the other…
Let’s say you are landlocked and decide to win without building any roads.
The victory condition, and associated normalize values would be:
Biggest army (2 points), 2 Cities (4 points), 4 victory points cards.
Alternatively, if you are looking for the longest road with the smallest amount of sheep to use, you could consider aiming for the Longest road and 4 cities.
Or if Coal is the scarce resource, you should maybe try for the Longest Road, with a final 2 Cities and 5 Settlements. (For the astute reader, this is an 11-point victory implying you win by getting the longest road being already at 9 victory points).
I have a few ideas, but remember, more specific wins will necessitate using specific resource valuations.
So what should we do? If you are not sure of the exact path for the win, how to get a reasonable overall resource valuation?
The relative value of resources for the fastest victories
One very promising approach is to look at the fastest victories…
So I decided to extract the relative values of the 25 fastest victory, just to see if there are variations per victory not well reflected in the averaged values.
If you would like to know how I decided those were the fastest victories… Well, you will have to take a look at my earlier article: The 143 Ways to win at Catan – Part III (or the whole series… but it may take you a while!)
I think this is an interesting approach, because it automatically filters most of the unrealistic victories, at least the one you should not be aiming at from the beginning… (such as the one involving 4 or 5 victory point from development cards).
First, let’s look at the average cost in resource cards, to give an idea of the total number of cards needed.
And here are their normalize values.
And just because, maybe this is a bit more all encompassing, here are the normalized values for the top 50 victories
>> The top 50 victories <<
Now we enter the crux of the problem.
That is that for my personal approach, I think those are the most appropriate values to use!
At least when it comes to evaluating the fairness of Catan boards. (Something I will explore in detail in the next post.)
However, let’s discuss a few more items before calling it a day, since a general strategy is not the final consideration for real in game strategy.
A look at values for different types of victories
For the sake of completeness, I decided to split the victories according to two general criteria.
- With or without the Longest road
- With or without the Biggest army.
The logic here being that those should be the main difference in Wood/Brick usage.
And to get a better evaluation, I decided to ignore all unrealistic victories implying 4 or 5 victory point from development cards.
Here are the valuation results using those criteria:
Clearly here the relative evaluation is changing. Coal and wheat being 3 times more valuable when aiming only for the biggest army. But fewer than 2 times more valuable when only aiming for the longest road…
Interestingly enough, is that the strict order from most valuable to less valuable always stays the same, with Sheep managing to stay slightly more valuable than the Wood/Brick resources.
Other interesting approaches to consider
One thing I cannot do at the moment is to use real-world game data to see if my valuation correlate with real world winning.
This approach was taken by Peter, in the blog mentioned earlier, but the actual metrics used were not exactly what I would have chosen. Those include:
- Percentage of time winner settle first around certain resources.
- Percentage of time winner did not settle around resources during the whole game
- Number of starting settlements around each resource for winners.
- Number of cities build around each resource for winners.
But the sample is difficult to analyze without the data itself. And it does not take into account the fact that a different number of tiles for forest or brick will change the chance for those to have higher numbers from the get-go.
All this to say that I cannot reliably use those numbers to establish what strategic value we should attribute to each resource, since part of his numbers is more about what ends up being used, not what you should aim for.
So what value should we use?
For the general approach. I believe the top 50 victories is the best evaluation for the resources.
This will guarantee a good basis for a general strategy, . Let’s call it: The open-minded approach.
More strategically planned strategy could make good use of the average victory using (or not) the longest road and biggest army criteria.
Looking at the initial example on how to rank position this would translate into:
For the Left we would have:
Bricks: ( 0.781 x 4) + Sheep: ( 0.760 x 5 ) + Ore: ( 1.329 x 3) = 10.911
For the Right:
Wheat: ( 1.350 x 5) + Wood: (0.781 x 4) + Sheep:(0.760 x 3) = 12.154
So clearly, this would indicate that the right one is the best overall value proposition!
Now imagine doing this for the whole board, and checking if all players have a fair chance at good spots before starting the game…
This is what I propose we do in the next article. In a much more user-friendly way!
And the game simulation generated are quite fun to watch!
I hope you’ll enjoy the next part!
