Why Do So Many Games Have Five Resources?
While playing a lot of board games and card games over the past few months, I started noticing a trend: most games that include resources have five of them. Since being able to count all of the colors on one hand didn’t seem like a good enough reason for this, I started looking into whether there was some deeper meaning behind what seems to be almost an industry standard of five resources (almost always represented by five colors, so I’ll be using “colors” and “resources” interchangeably in this article).
The Games
Before diving deep, I decided to focus on three of my favorite games, all of which followed this rule. There are probably many more games out there that fit this pattern (if you know of any, let me know!), but these are what I’ll be focusing on for now. Check out their relevant Wiki pages if you want to learn more about them, but I’ve included a super-succinct summary of their rules, and how they use resources, below each one.
Catan (formerly Settlers of Catan)
The five resources: Bricks, Lumber, Wool, Grain, and Ore.
In Catan, you gather resources each turn (if the dice roll is in your favor), and then use a combination of those resources to build various items (roads, settlements, cities, and development cards). These items are worth points, and the first person to 10 points wins, so you’re essentially trying to collect the right combination of resources more quickly than your opponents.
The five gems: Emerald, Diamond, Sapphire, Onyx, and Ruby. The Gold on the right is effectively a wildcard, rather than its own color.
In Splendor, you spend your turn either collecting gems or spending them on cards, which give you some combination of points and reusable gems. There is a limited pool of gems and each player can only hold 10 at one time, so your goal is to get to 15 points first by strategically acquiring and saving gems, then using them to buy more cards which accelerate your buying power.
The five mana: White, Blue, Black, Red, and Green.
In Magic, resources come in five different colors, and you play cards that are one or more colors in order to attack your opponents and get them down to 0 points first. Some cards provide you with resources, and others use those resources to produce effects that help you or hurt your opponent. Unlike the other two games, you assemble your deck (of 60 cards) beforehand, and decks can include a single color or any combination of the five. The various colors interact in interesting ways, with some decks having advantages over others, like an incredibly complicated game of Rock-Paper-Scissors with a lot more skill thrown in.
They all use resources very differently, but what they have in common is that there are five of them, with Magic & Splendor even choosing the same colors — white, black, blue, red, and green. Since it has the biggest and nerdiest fanbase (including myself), there have been some good discussions about why Magic has five colors, but I was curious to see if there were any underlying reasons that could be behind each game making the same choice.
The Gameplay
My first thought was that the primary reason must be balance: game designers always want to balance resources so that no one is too dominant, or else people would always play the “best” strategy or focus solely on collecting the “best” resource, which gets boring fast. Three strategies, like in Rock-Paper-Scissors, is perfectly balanced but not very interesting. With four or five options, there are many more one-on-one interactions, but not an overwhelming amount like when you reach six or seven. When represented visually, it’s clear how complicated things get as the number of points grows:
Each additional point adds more 1:1 connections than the point before it. Balancing a 7-resource game is more than twice as complicated as balancing a 5-resource game.
That was a start, but among these three games, Magic is the only one where you can successfully play a single-resource strategy. In Catan, everything you can build involves at least two resources, and some use three or four. In Splendor, cards can use anywhere from one to four of the gems, and you can’t avoid drawing gems of multiple colors. And while you can play Magic with a mono-colored deck, a central joy of the game comes in using multiple colors in one deck in order to combine their strategies and abilities.
Splendor cards cost gems, and the price (bottom-left of each card) can include multiples of one gem, or combinations of multiple gems.
In Catan, if you only gathered one resource, you would never be able to build anything.
Many Magic cards require more than one color of mana, like this card that requires both Blue and Red.
Because color interactions are so important, game designers must also consider the number of possible combinations, and whether to limit them in any way. Since Catan is designed to be very simple, there are only four combinations: two involving two resources, one involving three resources, and one involving four resources. This makes the game accessible for beginners, and generally requires players to use all of the resources (because some development cards allow you to build roads, it is possible to win without using any brick, but it’s very difficult to pull off).
On the extreme end of complexity, Magic allows every possible color combination, from single-color cards and decks, to ones that use two, three, four, or all five colors. When this full range of interaction is allowed, the number of combinations shoots up quickly, and started to require a bit more math than I could do in my head.
The Math
To see how many combinations would be possible with different numbers of resources, I created this table (with the help of this handy online calculator for the bigger numbers):
Two-color combinations are the simplest, and with five colors you get 10 possible pairs. There are only six pairings when you have four colors, and 15 when you have six. With seven colors you have 21 pairings, more than double the number of pairings with five colors. Going beyond that, it gets so complicated that it would be difficult for game designers (let alone players) to manage.
All of these games include combinations of three colors, which you’d think would make things even more complicated. But with five colors, the number of three-color combinations is the same as the number of two-color combinations: 10. This makes intuitive sense, since a combination of two colors is really just the exclusion of the other three colors.
Magic actually has names for each of the possible color combinations, and capping the maximum number of combinations at 10 makes this a much simpler task.
If there were seven colors with 35 possible three-color combinations, this simple chart would not be possible. Image credit.
But when you go up to six colors, there are 20 three-color combinations, double the highest number of combinations with only five colors. For seven colors, the number of three-color combinations jumps to 35. Whether it’s the number of buildings in Catan, or cards in Splendor or Magic, 35 combinations would make for an overwhelming number of options.
While looking at this table, I noticed that each column was symmetrical, for example six colors including a pattern of 6/15/20/15/6. Since this was a pattern I noticed after doing some math, I was sure that someone already had a name for this, and some quick Googling showed me I was right.
This table is essentially the “binomial coefficient,” which is mathematics jargon for “combinations of two numbers.” The binomial coefficient can also be represented by something called Pascal’s Triangle, a pyramid of numbers where each number is the sum of the two numbers directly above it. Seeing this gave me flashbacks to a long-forgotten highschool math textbook:
Pascal’s Triangle.
As you can see, these are the same number from my table above, with each row representing a certain number of colors, and each row listing the number of 0-, 1-, 2-, 3-, etc.-point connections that are possible. Again, getting beyond five numbers (the 6th row in Pascal’s Triangle) drastically accelerates the complexity.
The total number of combinations (the final column in my table) is also worth considering, and again, five resources seems like a happy medium. It roughly doubles each time, with five colors having a total of 31 combinations. You could still have a robust four-color game with 15 combinations, or a more complicated six-color game with 63 combinations, but getting up to a seven-color game with 127 possible combinations seems like too much for the human brain to handle (or at least while having fun).
There aren’t any universal truths here, and I’m sure more casual players would enjoy games with three or four resources, while more intense players would enjoy games with six or more. But since the most successful games try to please both casual and intense players (something called “lenticular design”), five resources appears to be the best way to strike that balance.
The Conclusions
I hope you’ve enjoyed this deep dive into the underlying math of board game design as much as I have. Of course, there is much more digging to do, and I hope to dive even deeper sometime soon.
I also admit that there are many games that don’t fit this model. For me, the most notable is the Civilization series, with Civilization VI having seven or eight resources, depending on how you count them. But that level of complexity only really works for computer games where a machine is doing all of the calculating and tracking for you. Board games, where humans are doing all of the deck-shuffling and transaction accounting, generally need to be simpler to stay fun.
Five does seem to be a perfect number of resources for all of these reasons: balancing strategies, ease of design, and pleasing both casual and intense gamers. If you know of any more games that fit this mold — or any that blow my theory out of the water — I’d love to hear about them, so please let me know.