This article is #1 of a 5-article series called Felix Felicis. In this series I discuss strategies to win at the board game of Catan. All articles in this series are focused on the standard four-player base game and assume familiarity with the rules of Catan. Each article is focused on a different idea or aspect of the game. The aim of this series is to formalize a theory for playing Catan based on the insights that experienced players intuitively possess but have never explicitly expressed. I hope to make the reader appreciate the nuances of playing Catan at the highest level and to improve their gameplay by introducing them to advanced strategies.
Introduction:
The single most important thing that good Catan players understand better than others is that Catan is a race. The goal of the game is not just to get to 10 victory points, but to do so before anyone else does. This means, every single decision in the game should be made in order to accelerate your score from 0 to 10 points in the shortest amount of time, which in the Catan world, is measured in the units of dice rolls.
Let’s talk about the victory points first – you need to score a total of 10 victory points to win the game. However, there are 5 different ways of scoring points:
- Each Settlement = 1 point
- Each City = 2 points
- Victory Point Card = 1 point
- Longest Road = 2 points
- Largest Army = 2 points
Technically, you can make the 10 points needed for victory through a combination of any of these. For example, I have listed 3 ways of making 10 points below:
- 4 cities + 2 settlements
- Largest Army + 3 cities + 2 settlements
- Longest Road + Largest Army + 3 settlements + 3 Victory Points
While all of the above combinations can get you the victory, it is important to realize that not all victories are created equal. To understand why, we need to discuss a concept that I like to call the Cost of Victory.
Cost of Victory:
The fundamental gameplay in Catan involves collecting resources through dice rolls and utilizing them to score points by building roads, settlements, cities or buying development cards. Each of these actions have a cost associated with them.
Road = 1 wood + 1 brick = 2 res
Settlement = 1 wood + 1 brick + 1 sheep + 1 grain = 4 res
City = 2 grain + 3 ore = 5 res
Development Card = 1 sheep + 1 grain + 1 ore = 3 res
Keeping this in mind, lets calculate the cost of victory for the 3 scenarios discussed above. Cost of Victory (as is perhaps obvious from the title) is defined as the total number of in-game resources needed to achieve a particular win condition. For the sake of simplicity, lets assume ideal road positioning and ideal draw of development cards such that all cards are drawn exactly when needed. Thus, if you sit down and do the math (which I have decided not to include here for the sake of brevity), the cost of victory for each case will be as follows:
- 4 cities + 2 settlements = 46 res
- Largest Army + 3 cities + 2 settlements = 35 res
- Longest Road + Largest Army + 3 settlements + 3 VPs = 24 res
It is clear that by pursuing win condition (iii) over (i), one can attain victory at almost half the cost, and therefore twice the speed, on a balanced map with a normal dice roll distribution. In a game that values speed over anything else, it is easy to imagine that pursuing win condition (iii) over others can give you a significant advantage in the big picture. This is because (iii) needs lesser resources and therefore lesser number of favorable dice rolls, as compared to win conditions (i) or (ii).
Now, astute readers will point out that in the example above I am conveniently ignoring the fact it is well-nigh impossible to get both the longest road and the largest army while also simultaneously and miraculously drawing three victory points from the deck. This just never happens in a typical game. Even if you do get lucky and manage to pull it off once, banking on such a win-condition in every single game is not smart but outright foolish.
I hear ye, I hear ye. While all of that is true, the fundamental point that I am trying to get across here still holds, and that is : Cheaper victories are faster victories and since the goal is to be the first to reach 10 points, it is important that one: always, always, always, pursue the cheapest possible victory on any given board. This, here, really, is the fundamental mantra, the one singular truth, the first principle, the primary axiom (call it what you may), that I use to base all of my in-game decisions.
While what I am saying might sound obvious, new Catan players (and sometimes even veterans) almost never think this way, and this is apparent from the way they go about their game. A lot of people like to fall back on the familiar, comfortable, build order of first making settlements, then upgrading them to cities and only going for dev cards, largest army etc. when it is convenient to do so. This is actually one of the most inefficient ways to go about the game. If you only rely primarily on cities and settlements to get your 10 victory points, then your cost of victory is going to get very expensive and it is going to take you a lot longer (more number of favorable dice rolls) to get the resources that you need for winning. It is critical to understand that actively pursuing longest road, largest army, or victory point cards, gets you towards the same victory in a much, much cheaper and therefore, faster manner. Catan can be entirely reduced down to a cost-of-victory minimization problem.
If I have convinced you that going for the cheapest victory is the answer to all problems in Catan, the next obvious question to ask would be how many possible win conditions are there in Catan? And which of those win conditions are the cheapest?
Fortunately for us, someone has already done the math for that[1]. According to their analysis, there are as many as 143 unique ways of reaching 10 (or more) points in Catan. Table 1 below lists the top 10 cheapest ways (1a) and the top 10 costliest ways (1b) to win at Catan (Check the reference for a full list of 143-win-conditions and their cost of victory). Again, the assumptions of optimal road network and ideal dev card draw have been made to generate the following data.
| Set. | Cities | LR | LA | VP | Cost of Victory |
| 2 | 0 | Yes | yes | 4 | 23 |
| 3 | 0 | Yes | No | 5 | 24 |
| 3 | 0 | Yes | yes | 3 | 24 |
| 1 | 1 | Yes | yes | 3 | 25 |
| 1 | 1 | Yes | No | 5 | 25 |
| 1 | 1 | No | yes | 5 | 26 |
| 4 | 0 | Yes | No | 4 | 26 |
| 2 | 1 | Yes | yes | 2 | 26 |
| 4 | 0 | Yes | yes | 2 | 26 |
| 2 | 0 | Yes | yes | 5 | 26 |
Table 1a: Top 10 cheapest ways to win at Catan.
| Set. | Cities | LR | LA | VP | Cost of Victory |
| 4 | 3 | Yes | no | 0 | 47 |
| 5 | 2 | No | yes | 0 | 46 |
| 2 | 4 | Yes | no | 0 | 46 |
| 5 | 2 | Yes | no | 1 | 45 |
| 4 | 3 | No | no | 0 | 45 |
| 3 | 3 | Yes | no | 1 | 44 |
| 5 | 2 | No | no | 1 | 43 |
| 1 | 4 | No | yes | 0 | 43 |
| 1 | 4 | Yes | no | 1 | 43 |
| 3 | 3 | No | yes | 0 | 43 |
Table 1b: Top 10 costliest ways to win at Catan.
A quick glance through both the tables should make the following things obvious: (a) The costliest victories are almost twice as expensive as the cheapest victories and therefore significantly slower. (b) Drawing multiple victory point cards significantly reduce the cost of victory. (d) Building cities and settlements is expensive and therefore the cost of victory rapidly goes up the more the number of settlements/cities that you are forced to make (c) Almost all of the cheapest victories rely on taking the Longest Road or the Largest Army or Both.
A major problem with the win conditions listed in table 1a is that in real games, one typically cannot depend on drawing multiple victory point cards from a shuffled deck, especially since there are only 5 available VP cards and other players are also fighting for the same. It is also very difficult to take control of both the longest road and the largest army simultaneously, as both of these things require widely differently type of resources. Therefore, I have created a third table that I like to call the top 10 most realistic ways to win at Catan (1c). This table lists the top 10 cheapest ways of winning at Catan without having to draw more than 1 victory point card or simultaneously take both the longest road and the largest army.
| Set. | Cities | LR | LA | VP | Cost of Victory |
| 1 | 3 | yes | no | 1 | 32 |
| 0 | 4 | yes | no | 0 | 34 |
| 5 | 1 | yes | no | 1 | 34 |
| 1 | 3 | no | yes | 1 | 35 |
| 2 | 3 | yes | no | 0 | 35 |
| 5 | 1 | no | yes | 1 | 36 |
| 4 | 2 | yes | no | 0 | 36 |
| 3 | 2 | no | yes | 1 | 36 |
| 0 | 4 | no | yes | 0 | 37 |
| 2 | 3 | no | yes | 0 | 38 |
Table.1c: Top 10 cheapest most realistic ways to win at Catan.
Notice that because we have reduced the dependency of drawing victory point cards, all the cheapest victories now definitely need the 2 victory points that one gets by taking either the Longest Road or the Largest army. Of course, in case you are lucky enough to get the road or army and also draw a few victory points, you will win even faster.
Therefore, my key takeaway from all of these tables is as follows: If the goal of the game is to get to 10 points fastest, then it becomes mandatory to take either the Longest Road or the Largest Army (if not both), as they significantly reduce the cost of victory for any win-condition. Secondly, drawing victory cards also significantly help, however that is not always in our control, but one should atleast attempt to draw as many dev cards as possible in order to maximize their chances of drawing the victory point. This idea gives rise to a natural build order that can consistently lead towards a fast victory.
The Dev Card Strategy is Broken:
I used to think Catan is one of the most balanced board games to play. That was before I stumbled on to the dev card strategy. In the current meta of Catan, a majority of the top-ranking players, including myself, always try to go for the Dev Card strategy in as many games as possible. This is because having a very strong Dev Card build virtually guarantees victory, especially against players who are not aware of it.
This ties in with our previous discussion of minimizing the cost of victory. One of the cheapest and most realistic (and therefore the fastest) ways to win is by simply building 4 cities and taking the largest army. The dev card strategy essentially plays for this win-condition. In order to do so, the player performing this strategy just has to take control of a lot of grain and ore numbers and little bit of sheep through their initial placements. Because building cities and buying dev cards both need grain and ore, this strategy synergizes better with taking the largest army instead of the longest road. The aim of this build is simply to upgrade the 2 existing settlements into cities as fast as possible, then start buying and using development cards every turn, and in doing so build 2 more cities and take the largest army through knights.
Here’s where the true strength of this build lies: Because this strategy relies on getting a lot of grain and ore and quickly upgrading the initial settlements to cities (thereby giving you even more grain and ore), it becomes very easy to snowball and buy a huge number of development cards in a very short time (number of dice rolls) . Now, the dev cards give you flexibility. Firstly, because you have set yourself up in this manner, the largest army is virtually guaranteed as (hopefully) nobody else has the setup to buy as many dev cards as you. Secondly, because you are drawing so many dev cards, along with the knights that help you get the largest army, you will either get victory points (which will make you win even faster), road building or year of plenty (which will help you build the next two settlements that you need to convert later into cities), or you will draw the most broken card in the game: Monopoly (which, if used correctly, is by itself equivalent to drawing two victory points).
Through this strategy, even if you do not produce any wood or brick, it is still fairly easily to build two more roads and settlements through trading, or robbing (with all those knights) or using Road building or Year of Plenty. Upgrading all the settlements to cities is also fairly easy due to your innate abundance of grain and ore. In some situations, it is even possible to take control of the longest road along with the largest army through the correct use of road building and monopoly cards, thereby making you win a LOT faster. Randomly drawing one or two victory points is also very common, and rarely, one can even draw 3 or 4 victory points (although I haven’t had a single game yet where I have drawn all 5).
Having an abundance of knights ensures that your own high-producing tiles remain unblocked and gives you the upper hand in blocking the best tiles of your opponents. The sheer speed through which one can win simply by buying dev cards is second to nothing else. Against newer players, this strategy takes the game away before they even fully realize what’s happening (as victory point cards are hidden and the largest army points are also hidden until you play the third knight). By the time they do come to see you as a threat, you should have already won.
Now, I am afraid I might have made this sound a lot easier than it actually is. Even though the dev card strategy is great, it has some limitations, and a thorough discussion of its merits and weaknesses is a discussion for another day. But very briefly, the key to this strategy is getting access to a large amount of grain and ore and little bit of sheep. This by itself is not possible on a large number of maps on account of low ore or grain numbers on those maps.
Secondly, this strategy is harder to pull against experienced players who will notice what you are up to and start blocking your limiting resource (whichever is lower amongst grain or ore) from the get-go, and start competing with you for largest army. Good catan players will also try to block your path towards building more settlements in a way that you now need more roads to get to the next available settlement point, thereby slowing down your victory.
A note on assumptions:
During the cost of victory analysis early on in the article, I made many assumptions such as having an ideal road network, optimal dev card draw, normal dice roll distribution and a balanced map. All of these assumptions were made in order to simplify the calculations and to make a point. However, none of these assumptions hold true for an actual game. Earlier I made a list of the top 10 most realistic win-conditions to aim for. However, the truth is that the best win-condition will vary significantly with the nature of the map and an important skill to develop in Catan is the ability to read a map and decide which win-conditions are worth going for. Factors such as dice rolls, initial settlement positions and resource variability will also significantly affect the feasibility of different win-conditions. For e.g., on maps where you have low access to bricks relative to others, it will be a harder task getting the longest road as compared to the largest army. All of these factors merit a further in-depth discussion, which will the subject matter for a future article.
The key takeaway from this article is to understand that minimizing cost of victory is essential to win at Catan. In order to do so, it is critical to aim for either the longest road or the largest army, depending on the kind of setup that you have. While it is not impossible to get 10 points without the Road or Army, it does get really hard (and slow) to win without it.
– Starlitknight
References:
The Quintessential Flâneur 