Splendor has become a very popular game recently, likely due to its Spiel des Jahres nomination. Splendor is a card game about using limited resources to build an efficient engine. There are five colored gems, and playing only a few times it might feel like the costs and distribution of the colors are the same. In other words, the colors are different currencies with no other differentiating qualities. If that were true, we’d be able to add up all the costs and find that the colors are evenly distributed. But even with a few plays of Splendor that assumption is difficult to maintain. The rules are simple and there are no exception-based cards, so it’s a great game to analyze by number crunching. I’ve set out some research questions to help guide the analysis. Some of them are basic, but I think they’ll open up other directions for exploring the data.

### Research Questions

RQ1: are color bonuses evenly distributed?

RQ2: are color costs evenly distributed?

RQ3: what is the average point:cost ratio for a level one, two, and three card?

RQ4: what is the percentage of “on color” cards? (Cards that give a bonus for a color that is also in the cost).

### Process

It’s always useful to communication the analysis process, but if you’re interested strictly in results then scroll down to the Results section. The process first involved developing a taxonomy to store the attributes, entering and cleaning the data, then validating the data. Some of this may seem excessive for a small project like this, but there are always unexpected events that a formal procedure can mitigate.

To operate on the card data I input it into Excel. The data entered would consist of the cards and all their attributes, including the bonus, level and cost (see Figure 1). Noble cards would also be input. There was some taxonomic thinking that went into the process: how should I manage the terms used? For example, instead of writing out the word “black,” it’s easier to input “b,” but there’s also “blue” then term management needs to standardize that “blue” becomes “u” instead.

Data validity was also an issue because I was manually uploading the information; I didn’t perform a second check nor have others do it, so I had no reference to determine whether the uploaded data was correct. I did do a card count to ensure I had input the correct number of cards, but nothing beyond that. An auto-incrementing CardID attribute was created to ensure I could individually track each card.

Analysis and data visualization was performed in R Studio.

### Results

#### RQ1: are color bonuses evenly distributed?

Yes. See Table 1.

#### RQ2: are color costs evenly distributed?

No. If you sum all the card’s costs, the colors are relatively equal. But when slicing those costs by level, the distribution becomes uneven.

Table 2 charts the frequency of color cost. That means it counts occurrences of color cost. So the Black row under Level One indicates that White and Blue occur as a cost in four level one black cards. Note that this table does not track intensity of those costs (that’s for later).

In terms of frequency, on-color costs are infrequent (few cards with a color bonus also have that same colored cost). There are some other odd frequency dynamics: level two blue cards feature a blue cost five times, with other colors appearing two times. So each color has a unique frequency of cost, as seen in the figures below.

These figures displays the distributions of White and Red costs among the cards. Because the two figures are different, we can conclude that certain card colors require varying degrees of red and white costs. Because the figures are box plots we can also discern the expected white or red cost depending on the card color. A white card will have a higher red cost on average when compared to a green, red, or blue card.

While each color has a unique frequency of cost, those patterns do not occur from level to level. In other words, investing in white bonuses to buy red cards at level one will not be a reasonable strategy at level two or three because the white cost frequency changes.

Table 3 charts the intensity of color cost, which is where the uneven distribution really comes into perspective. The level three cards are representative of this trend. Like a lot of other games, the expensive cards reward a vertical strategy of investing a lot in a few colors. For example, the sum total of white costs in level three blue cards is 23, with all other colors totaling less than 8. As a proportion of the total costs of all level three blue cards, that’s 70%. So there are clear color affinities, but they change at each level, so white costs won’t always be strongly tied to blue bonuses.

#### RQ3: what is the average point:cost ratio for a level one, two, and three card?

For cards with point values, the average cost of a point goes down as the card level increases. At level three, the average cost a point is 2.7, level two is 3.7, and level one it is 4 (every level one card with a point costs 4). This isn’t too surprising; a lot of games reward big investments by making them more efficient. The trade off, of course, is that they require long-term planning to efficiently buy them, while low-level cards require little.

After a few plays of Splendor you’ll probably notice that some cards cost more for the same point value. Indeed, Figure 4 shows that some cards are just strictly more efficient. However, the cards that cost the most (14) spread the cost among 3-4 colors, while the highest value cards (5 points) are concentrated on high costs of one or two colors. So the design of the costs provides two clear paths to efficient point gain.

#### RQ4: what is the percentage of “on color” cards (Cards that give a bonus for a color also in the cost)?

My playgroup assumed these cards are high value because players have a tendency to collect things they already own. They occur infrequently in level one, but in card levels two and three they’re at least 50% of all cards.

### Conclusions

One important aspect of this analysis is that it’s dealing with static information. This data tells us about the set information of the game, but it doesn’t describe any behaviors. We can infer some behaviors based on the incentives provided by the set rules of the cards, but we should be conservative in those conclusions.

That said, the frequency and intensity of the color costs does validate the potential for a vertical, one or two color strategy. But it seems like those strategies require careful planning, as by level 3 each color is essentially “locked” into buying up one particular color. So if that color is available to buy, well, you might have some problems. At the same time, it may be a viable strategy if every other player is competing for a wider strategy with nobles.

That said, I remain skeptical of a strategy concerned with concentrating on level three high value cards, and remain convinced that Splendor is very much a game of opportunistic, incremental victories that rewards turn-by-turn efficiency rather than grand strategies. Consider for example that the average point value of a level three card is four. To win, you would need to purchase three plus something else or four. That’s a tall order, especially considering the bonus return is the same as a level one or two card. Instead, it seems much more likely that–like all other parts of the game–level three cards are purchases of opportunity. If a player is able to efficiently purchase a level three card, it is because they just happen to have the correct bonuses and gems at hand, rather than a “from turn one” plan. That said, without behavioral data to acknowledge that, I can only speculate.