Expected Value of Development Cards Throughout a Game of Catan

Donny
9 min readJul 10, 2023

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If you’ve ever played a game of Catan, you most likely have heard players say “I just drew the worst (or wrong) development card!”. And chances are, you’ve said that yourself as well.

So, is there such a thing as a bad development card? Or are you and other players just bluffing and downplaying your positions like how any good Catan player should?

As someone who has played over 1,000 games online and over 100 games over the board in some of the most competitive online and over-the-board scenes (e.g. 2022 US Nationals), I can confidently say that there is no such thing as a bad development card but there are definitely poorly timed development cards.

Why should you buy development cards?

As someone who has coached players at all levels, I would say the most common mistake made by newer players is that they do not buy (enough) development cards! And the second most common mistake is that they do not pay (enough) attention to other players with many development cards.

Newer players are very focused on the board in front of them and are always looking to build the next road, settlement, and city. They often overlook development cards since it is off the board. This phenomenon exists in both the online and physical game but it is much more pronounced in the physical version because development cards are more out of sight, placed to the side of each player compared to the centrally located board that is some 30 to 40 times the size of a development card. This in itself already provides a huge advantage because a player with few pieces on the board but many development cards is often perceived by those less experienced as less of a threat than a player with many pieces on the board but no development cards.

But an even greater factor is that development cards provide an information asymmetry advantage. While any player can easily see what everyone has on the board and experienced players will know what resource cards are in each player's hand with 80–90% accuracy, it is a lot harder to correctly guess other players’ development cards (although there are often social cues that can give this away if you pay enough attention).

Experienced players often use hidden development cards to scare away other players from blocking and stealing from them, take away another player’s settlement spot, steal the longest road, shockingly build a city (or two), and even prevent another player from winning on their turn. Development cards offer an additional layer of strategy and players can leverage this favorable information asymmetry to drive the direction of their path to 10 Victory Points.

Aren’t development cards more luck-dependent?

Ah, the age-old question in Catan — luck versus skill.

The general consensus I’ve heard from many experienced players is around 70–80% skill and 20–30% luck. I would add that this ranges significantly depending on who you’re playing against. With a large skill gap, luck barely plays a factor at all. But in highly competitive scenes such as the US Nationals (where all players must’ve won a regional tournament to qualify), luck likely plays a bigger factor than skill. Based on my personal experiences there last year, in all 3 of my games, 3 out of 4 players (including myself) had winning rolls when someone won the game.

So, do development cards add a bigger luck factor to the game since you’re not sure what you’d pick up?

The short answer is NO.

But anyone that has played more than 10 games of Catan has been there. You’re looking for a Knight to take the largest army away from the leading player but you draw a Road Building and Year of Plenty instead. Or you already have the largest army locked down and you’re just looking for anything that will help you get a settlement down but you draw Knights after Knights. Or you have 5 settlements and the longest road and just need to pick up a development card that will help you build a city but you draw a Road Building. Meanwhile, you watch as another player draws 3 back-to-back Victory Point (VP) cards and wins the game.

Development cards can be frustrating. And yes, there is definitely luck involved. But I still think it actually decreases the luck factor to your game because you control when you play your development cards (timing is a skill and matters a lot!) and the more hidden development cards you have, the greater your information asymmetry advantage becomes.

The 80–20 Rule to Development Cards

Before buying a development card, you should always ask yourself this question: “Are 80% or more of the development cards left in the deck beneficial to me?”.

For example, at the beginning of a game when no development cards have been revealed, you can assume that there is a 56% chance (14/25) of drawing a Knight, 20% chance (5/25) of drawing a VP, and 8% chance (2/25) each of drawing the other 3 development cards — Monopoly, Road Building, and Year of Plenty. At this early stage of the game, you find yourself already significantly behind on production and believe drawing a VP is not beneficial at all but drawing any other cards would be. This means you have an 80% chance of drawing something you believe is beneficial so you should go for it.

Now, let’s say in this same exact situation, you realize you have very little shot of getting the largest army and you’re well set up to take the longest road. In addition, because you’re behind, you’re unlikely to have your production blocked by the other players and if you were to rob someone, the cards you are looking for are wheat and ore, the same resources you are using to buy a development card. In this scenario, drawing a Knight will also not be beneficial. This means you now only have a 24% chance of drawing something beneficial and therefore, you should not buy a development card.

Obviously, evaluating the probability of drawing each development card is usually not that easy. As the game progresses, your perceived probability may be far off from the actual probability. For example, you may notice that there are 8 development cards left in the deck, no Monopoly cards have been played, and you don’t have a Monopoly card yourself. Therefore, your perceived probability of drawing a Monopoly may be 25% (2 out of 8). However, in actuality, both the Monopoly cards are hidden by other players who are patiently waiting for the right time to use them.

While the perceived probability of drawing each development card will shift as the game progresses, it is important to remember that the more hidden development cards that you own relative to other players, the closer your perceived probability is to the actual probability. Therefore, by having more hidden development cards and using this information to calculate probabilities more accurately (technical skill), you have more knowledge about the remaining development card deck, minimizing your chances of getting an undesirable draw (luck). In addition, being able to accurately guess other players’ hidden development cards (social skill) can also play a major factor in your knowledge about the development cards left in the deck.

Expected Value of Each Development Card

With all that being said, there is still definitely a 20–30% luck factor (like any other elements to a Catan game) that may work against you at times. So, is there a definitive way to tell if you are truly unlucky with your development card pulls? Not exactly. But there are general assumptions that can be made.

In my analysis, I separated the expected values based on if you are playing a largest army or longest road game (based on stats gathered from over 100 competitive games, only around 1 in 8 games are won without the largest army or longest road).

Army Objective

When playing with the largest army in mind, Knights are a pretty average pull throughout the entire game. Knights are a little weaker in the first half of the game due to fewer resources being blocked by it and go up in value slightly around 70–80% into the game where generally, the largest army is claimed and locked by a player (stealing largest army beyond this is often pretty difficult).

VPs and Monopolies offer lower value early game but steadily increase throughout the game. For a largest army player with high ore, wheat, and sheep (OWS), VPs are likely the worst development card to draw since it may lead to you losing pacing in the largest army race without any production compensation and is less likely to play a big impact even in the late game as long as you have spots where you can city up.

Road Building is generally a gold mine for a largest army player in the early game because it helps tremendously in achieving an OWS setup’s hardest objective — building settlements. An OWS player that can use the Road Building to get 2 settlements down means that they may not have to worry about building any more roads or settlements for the rest of their game. However, this card becomes significantly weakened late game when there are often only low-value spots (or sometimes no spots at all) left for an OWS player to settle on and longest road is impossible.

Finally, Year of Plenty is generally an above-average pull throughout the game because it provides flexibility in achieving any objectives you may need. Year of Plenty has higher value early game because you generally have low flexibility (lack of ports and fewer cards to trade with), lower value mid-game when your ports are unlocked and trades are still abundant, and higher value late game when trading diminishes significantly.

Road Objective

Compared to largest army players, playing with the longest road in mind means that Knights (and development cards in general) provide slightly less value. The difference is not overly significant since Knights still provide the value of unblocking your hex, stealing a resource from another player, and blocking their hex whenever you see fit. However, compared to the value of other development cards for a longest road player, Knights are by far the worst pull overall.

VPs are more valuable for longest road players because it means you need 1 city instead of 2 cities to win (5 settlements, 1 city, longest road) which makes a significant difference because building cities is your hardest objective. Monopolies are also more valuable earlier on in the game because road players are likely to get port settlements earlier (increasing flexibility from monopoly) and playing a monopoly on ore specifically to get the first city up significantly increases your chances of winning the game.

On the other hand, Road Building is much less valuable early game since you likely have no difficulties building roads to get to your settlement spots at all. Generally, you are better off holding onto the Road Building card as if it was a VP until much later in the game when you can use it to solidify the longest road objective.

Finally, Year of Plenty is slightly more valuable for longest road players who will likely use it for ore and/or wheat to build a city. These resources are usually harder to get in trades. Year of Plenty decreases in value slightly around 70–80% into the game where generally, your focus is to solidify the longest road.

Interestingly, this comparison shows that if the probability of draws from the development card deck stays exactly the same during the entire game (e.g. 56% chance of Knights, 20% chance of VPs, etc.), buying development cards is more beneficial for largest army players for most of the game but that changes around 75% into the game where it becomes more beneficial for longest road players. This is due to the generally decreasing value of Knights for everyone once largest army is locked down but the rapid increase in value of all other development cards for road players (while a late Road Building may be completely unusable for a largest army player, a late Road Building could easily give a longest road player the ability to steal road to win or solidify longest road forever).

So, what does this mean for you?

If you see a player who is trying to go for the largest army truly agonizing over their development card draw towards the end of the game, chances are, they took the Road Building card that you were looking for.

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In the meantime, have fun popping those development cards!

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