Utility of Development Cards
This is a much debated topic in Settlers. There is obviously some value in them, but how much?
Overestimating that value is sure to end up in wasting resources buying more than you need.
Underestimating that value is sure to end up in wasting resources buying things you need less.
This is called opportunity cost. Again, this should remind you of any “Introduction to Macroeconomics” class. So, how do we decide how valuable Development Cards are?
Let’s start off with figuring out what Development Cards we’re dealing with before we judge value. In the original Settlers game, there are 25 development cards:
- 14 Soldiers/Knights (I’ll call them Knights from now on)
- 5 Victory Points
- 2 Road Building Cards
- 2 Monopoly Cards
- 2 Year of Plenty Cards
Knights obviously have some value. Aside from warding the robber off of your land or moving the robber to control prices, you can get the 2 extra points for largest army. I’ll discuss how worthwhile attempting to obtain the largest army is later. Road Building Cards are basically a trade of the resources necessary to buy the Development Card for 2 Roads. Year of Plenty is a worse deal, trading the 3 resources in for only 2 back. Monopoly has a high value if played well, but just as often it ends up being a dud. The Victory Points are the most valuable, as they directly further your quest towards 10 points.
Buying Development Cards is like playing games at the carnival – you spend some money (in this case resources) to buy a chance at something awesome (Victory Points) that you have a low probability of getting (20%). More often than not (56% of the time), you’ll get a decent prize (a Knight). The rest of the time (24%), you get screwed (Road Building, Year of Plenty, Monopoly).
I reason with development cards pretty simply: I buy 4 of them throughout the game. If nobody else buys any cards, I’m most likely going to end up with 2 Knights, a Victory Point, and any one of the other 3 types (let’s hope for a Monopoly; I love the control). If I’m lucky, I might get 3 Knights and a Victory Point, for a grand total of 3 points from Development Cards. I try to only expect one point from Development Cards – that way, anything more is just an added bonus. This is all good and well, but let’s be real – everyone is going to be buying Development Cards, so I can’t rely on those probabilities. This is where I channel my inner blackjack player and count cards. If I see people are generally playing their Development Cards (meaning they aren’t Victory Points) then that tells me the chance of me buying a Victory Point is going to go up. I’ll try and buy 2 or 3 quickly. If I see there’s Development Cards face-down for 3 rounds or more, I’ll assume that they are Victory Points, figure out my new probability of drawing a Victory Point, and decide whether I’ll buy one or not based on that. Buying more than 4 Development Cards in one game feels too much like chasing rabbits to me – it’s a fairly inefficient way to gather more than 1 or 2 points.
So what do the stats say? [SIDE NOTE: This is the first time I’m actually introducing a statistic. Notice that it’s a fairly simple one to analyze.]
Winners buy 3.7 – 3.9 Development Cards per game.
Winners hold 1.0 – 1.1 “Hidden Points” (Development Cards that are Victory Points) per game.
This is by no means a hard fact of optimization, but you can use these numbers to analyze your own strategy:
- If you’re buying 1 or 2 Development Cards per game, you’re probably not using them to their full potential.
- If you’re buying more than 5 Development Cards per game, you’re probably wasting your Sheep, Wheat, and Ore.
I’ll admit, I used to think that Development Cards were key, and would regularly end the game with 6 or 7. Where do you fall in this spectrum?
Developing Catan 
I’ve been on C&K for so long, I forgot what Development cards were, but I definitely remember holding 5+ at the end of a game… that I lost.
Ever since writing this post, I’ve found myself going too far in the opposite direction – I continually find myself with only 1 or 2 cards at the end of games. I really have to consciously pace myself in buying them throughout the game.
I would like to commend you on an amazing catan blog. I have lots of these catan statistics/theories but this is the first time I have seen someone getting into really good calculated nuances! I am excited to read more of your posts, but since this is the first one I have run across I am going to throw my hat in the ring.
Development cards are undervalued. Each one of them, even the “dreaded” year of plenty has the potential to be a game winning play.
I think when people are first understanding the world of basic catan they tend to approach the development cards as the I have too many cards in my hand so I need to spend resources. More experienced players no when development cards are going to be important from their first 2 picks.
At the end of the day each development card has game winning potential as someones last play and that makes each one of them have infinite value, because you are no longer specifically relying on dice roles.
I find that in a game of catan often one person can run away with largest army if they are invested, and moving the robber is a good reason to be invested especially if you hope on wining. If your not being competed against that unturned Dcard can be the third knight! road building, has come into play in both scenarios where a player takes longest road, or where these roads are used for someone to nab on last settlement. Year of Plenty although is a loss of resources, could be the last 2 resources you need to win! I often use it to make a city, but it can be held onto as the game winning play. Which of course brings us to monopoly, which if you are watching what resource people are picking up on the one turn around the born, has tons of potential to be the last play of a game (especially at the end when everyone has cities, and are constantly picking up resources. Then there is the VP point, which holds the most value (although I hate drawing it in the beginning of a game), and you probably will only get 1-2 in a game. However thats 1-2 points that people not invested in Dcards are less likely to draw.
My point is that once people hit 6-7 points, watching the Dcards are super important, and buying Dcards will not be a waste.
It should also be noted that many people will be playing with the 5-6 player expansion Development Cards included in their deck- even when only playing a 4 person game. I have yet to meet someone who owns the 5-6 person expansion and keeps the extra dcards separate.
The notable aspect of this being the 5-6 person expansion does not increase the number of victory point cards. The probability of drawing knight/monopoly/road builder/year of plenty all increase, but remain more or less the same, the probability of the first draw being a victory point drops from 20% to 14.7%.
For those who think about such things, the following table expresses the change in starting draw probability for each development card type.
Knights: 56% -> 58.8%
Victory Points: 20% -> 14.7%
Road Building Cards: 8% -> 8.8%
Monopoly Cards: 8% -> 8.8%
Year of Plenty Cards: 8% -> 8.8%
If we use the “rule” of purchasing 4 development cards throughout the game, in the original deck, the probability of one of those 4 being a victory point is 45.1%, but in the expansion deck, the probability of one of those 4 being a victory point is 39.4%.
*This is the probability using a hypergeometric distribution, which calculates based on one card being removed from the set inbetween events across 4 events. Certainly in a real game, other people will be drawing cards in between your turns, and in the also likely event that some of these cards are known to you as knights or road builders, you could calculate this differently with assumptions of draws and reveals between events. Not going to take up space here to work through analysis beyond the ideal probabilities.
corr. above shows exactly 1 in 4, should be at least 1 in 4:
*the probability of at least one of those 4 being a victory point is 61.7%, but in the expansion deck, the probability at least of one of those 4 being a victory point is 48.8%
Came here searching for material for an argument that development cards take less skill than the other ways to earn VP. In recent games I have won/ benefited greatly from dev cards. One game I bought 9 4 VP 3 knights and monopoly and year of plenty (got trapped). We play another game and took the VP out, I also won with largest army of 3 and road building. I know I bought way to many, but my friends undervalue dev cards severely I believe.
If you count how many total resource cards it takes to get to 10 victory points through every possible combination of settlements, cities, largest army, victory point cards, etc. the total number of cards is generally lower for any development card route.
For instance, one of the lowest resource intensity winning combinations would be 4 settlements, 4 victory point cards, and longest road, this would only require 24 total resource cards if you pulled the 4 victory point cards without pulling non-VP development cards (as unlikely as that is). Compare that with a more common 3 cities 4 settlements win, which would require 51 resource cards.
Of course there are differences in the likelihood of having the diversity of cards you need to do each development decision, and differences in the amount of cards you will pick up per turn as the game goes on, but in general, pursuing development card victory points is much lower cost and can allow a win in fewer turns than the more common risk-averse strategy of building cities and settlements to get to 10VP.
Surely though, a big part of the trade-off between settlements/cities or Development cards is that whilst settlements are more resource intensive, they also produce resources of their own. Assuming a reasonable spot for a settlement (9 dots), you would expect it to produce 0.25 res/turn for the rest of the game.
This would surely suggest that the optimal route is weighted in favour of settlements/cities early on and gradually shifts in favour of cards as the game progresses?
Just played a game relying on development cards and bought 10, I ended up with only 8 points.
Damien: Relying on cards, the best case scenario can only net you 9 points. You HAVE to build something on the board to win