The Magic Numbers
DISCLAIMER: You’ll need an understanding of how to play Stoicheion: Elemental Clash to fully enjoy this article. And probably math too.
As an Engineer, I have a tendency to focus on the math. When this crosses into my role as a game designer, I’m all too comfortable getting into the nitty gritty of calculating the likelihood of different scores, the maximum values certain effects can add to cards, the efficiencies of defenders based on hit points vs average attack values, and other nerd stuff like that. I won’t shy away from admitting I’ve calculated mana curves by hand for some of my magic decks.
So, when it was decided that Stoicheion would be a point-taking/collectible game with multiple elemental “suits”, I knew that my control of numbers was going to be a big part of how I balanced out the viability of each element. In fact, the very first thing I did after coming up with each of their effects and how the Leyline was arranged was to open Google Sheets and create a table of values for every card in the game. Now, there were some LARGE flaws in my initial methodology for doing this. The alpha version of Stoicheion had wild balancing issues, mostly due to the poor implementation of the End-of-Game effects. Giving each element a unique way to add points meant the cards needed to reflect almost entirely different games.
For example, Torrent gave you 4 extra points each time you shifted in the game. Ignition gave you points for half the cards in the discard. Absence had a weird multiplicative effect based around removing cards from the game. Each Firmament in your hand increased in value by 1 for every OTHER Firmament in your hand.
Once I figured out this wasn’t going to work, I axed the EOG effects and standardized the maximum scores of each element. Given that most things about the game were designed around multiples of 3, nine cards of an element with an average of 6 points gave me 54 points for collecting an entire element in your hand. This was a good start, and my point distribution looked like this:
The Original Distribution: Wack.
The idea was that these distributions could serve as another way of imparting the flavor of each element. Moment’s values were the first nine numbers of the Fibonacci sequence (starting from 0), a mathematical visualization of increasing acceleration. Firmament was a solid wall of sixes. Ray showed a spectrum of numbers from 2 to 10. Torrent was in the middle of the Leyline had thus used balanced even numbers. These distributions also helped balance each suit’s effects too. Catalyst was a unique discard recovery, so most of it had a lot of low-scoring cards that could be thrown away for their abilities, while its middle position plus concentrated high-value cards made it an easier pivot for scoring. Ignition had generally balanced values so that, for over half of its cards, you’d need to throw away a sizable chunk of your score to burn someone else’s card.
This worked for a long time, but during one playtest at the Mana Games cafe in Lincoln, the players raised issue with the uneven distribution. One player sitting on Torrent grabbed a hand something like this:
You couldn’t ask for a better hand.
When the end of the game came, no one could really do any thing to stop him, because no matter which cards we discarded from his hand, he could easily pivot to the other two neighboring elements. It was his first time playing too, and almost inadvertent because he was just going for the highest value cards he could see. Which it just so happened, were concentrated in elements two spaces away from each other. It was too easy for one person to hold an extraordinary amount of points in their hand while everyone else concentrated on building at other points on the Leyline. So, I needed to readjust, and I thought it would be a total makeover.
A longtime play tester on our Discord named MonarchMan called the result “Implementing Elemental Communism.” I flatted the curves and normalized the scores for every element. The ceiling would be closer to the floor, and most cards would be worth the same as most other cards. No longer would anyone stockpile cards worth up to 20x the scores of other cards. I produced a number of potential distributions and started testing.
Strange Ideas, man.
You see, while I was also trying the game fairer to play, I wanted to also test how players would react to the numbers themselves. One of the Mana café testers pointed out that picking up a 2 or a 4 of an Element felt unrewarding, despite some games coming down to such minor score differences. I tried scoring multiples of 5. Of 10. I made the lowest card a 5 and the highest a 35. Some distributions still added to 54, others to 270. It was mostly cosmetic, some even ENTIRELY equal in spread, save for the digits appearing on the cards. But after testing, everything just fell flat. There was so little excitement at the table, because you were always seeing cards that were basically worth the same thing. Someone described it as “measurably sucking the charm out of the deck.” And what’s worse, making the numbers bigger just meant some people had harder times holding those numbers in their heads during the game. Adding 10s and 20s and 30s might technical be easier, but they’re bloated compared to adding 1 and 2 and 3.
So, I reverted it all. I went back to the old unique distributions, minus a change to catalyst. It’s two 20’s and seven 2’s became three 10’s and six 4’s. Mostly this was because 02 and 20 look too similar, but also because it was just WAY too much value concentrated in two 20-value cards. So that’s where we sit at this time. I get to keep my funny numbers that almost no one else cares about, and the players keep the excitement of grabbing a 21 of Moment from the Mana Pool.
Peep the Scatter-Plot, Bro.
With various Lines-of-Best-Fit you might not care about.
That said, I’m still unsure this is ultimately the best answer. Can you think of a more optimal way of passing out scores to each card? And can you think of any distributions that would be more ‘flavorful’ for certain elements? Leave a comment below, I’d love to talk math with you.
