Telling Fibs
One of the most frequently asked questions on game design forums is how to pick numbers for your design: How much should cards cost? What should the hand size be? How many victory points do you need to win?
The canonical answer is to just pick something, try it out, and see how it feels. Then change as needed. Or if you’re trying to cost a set of cards with different abilities, for example, just pick an arbitrary cost for a basic card, and scale everything around that. If a basic attack costs 3, how much should this enhanced attack cost?
There are other approaches, of course, and an interesting one was chosen by Henry Audubon, the designer of the new game Cosmoctopus. Henry is also the designer of the wildly popular PARKS (and in the interests of full disclosure a friend).
We had the opportunity to grab lunch at Gencon and he revealed to me that Cosmoctopus leans heavily on the Fibonacci Sequence for all of its numbers.
For those of you unfamiliar with the Fibonacci Sequence, it is formed by starting with the numbers 0 and 1. Then the next number is the sum of the two prior numbers. So it goes:
0, 1, 1, 2, 3, 5, 8, 13, 21, …
Each term is the sum of the two before it. So the next term will be 13+21, or 34.
The Fibonacci sequence frequently arises in nature, from flower petals to seashells. It naturally forms spirals, which can also be seen in, well, octopus tentacles.
The central character in Cosmoctopus is “The Great Inky One”, an elder god that bears a striking resemblance to a certain earthly mollusk. So the number ‘8’ being in the sequence was a natural draw for the designer.
Everything in Cosmoctopus is keyed off of these numbers. At the start you get eight cards and five resources (a total of 13 things!). The goal is to get eight tentacles (of course). Max hand size is 8.
The card costs all stick to this sequence:
Note the use of 1, 2, 3, 5, 8 in the upper left corner.
The maximum resources you can keep from turn to turn is 8. However, if you manage to accumulate 13 before the end of your turn you gain a special bonus.
Other than pleasing math geeks such as myself, what does using the Fibonacci sequence accomplish? A lot, in my opinion.
The repetition of the same numbers makes it easy for players to internalize and remember. While the ‘scale’ goes up to 13, only 1, 2, 3, 5, 8, and 13 are used. So just six key numbers to remember. The fewer things your players need to learn, the better.
It makes the design process simpler, as everything needs to be scaled to fit into those slots. No agonizing over whether a cost should be 5 or 6. It needs to be 5, or jump up to 8.
The second one dovetails with a recommendation I make to designers, and a dirty little secret.
First, the recommendation: When changing values, don’t make tiny little changes. Try big jumps first. If you go too far, at least you have the problem bracketed. If something costs 3, but it feels too cheap, don’t increase the cost to 4 for your next play. Jump up to 6 or even more. If it’s now too expensive, at least you have the values bracketed. And more often than not, having very high or low cost items opens up new design space. Cosmoctopus’s Fibonacci Sequence forces the designer to do that. If 3 is too cheap, your next options are 5 or 8.
The dirty little secret is that a lot of these numbers don’t really matter all that much. Hand size is a good example. Should the hand size in your game be five, six, or seven? Honestly, it probably doesn’t really matter. When I first started designing, I figured there would be a huge period of A/B testing, where I play several games with six card hands, and then several with seven, and see how it works.
The reality is that most of these decisions don’t actually make that much of a difference. As the designer you need to specify something, just so the players know what to do. But often it’s an arbitrary choice.
By locking your design into a sequence like this, you naturally force where these little things end up. It makes decisions like how many starting resources players should get much simpler.
There are other number sequences you might consider designing around:
Triangular Numbers: 1, 3, 6, 10, 15, 21
Powers of 2: 1, 2, 4, 8, 16, 32
Prime Numbers: 1, 2, 3, 5, 7, 11
All of these have their own flavor and would be interesting to explore.
If there are expansions to Cosmoctopus, will they blow past 13 and go all the way to 21, the next Fibonacci number? We will have to wait and see.
What games have you played that are based on the Fibonacci or other numeric sequences? Let me know in the comments!
I’m working on a game and there is a bit of adding and subtracting for each player every turn. First iteration had numbers 1-10. Next iteration 3 and 7 are gone which makes it a bit easier.
Sometimes I find power-of-two grows too quickly, so I use what I call half power of 2, which (if you're also a camera buff) is what a cameras use for their f-stops. The sequence on a camera is 1.4, 2.0, 2.8, 4.0, 5.6, 8.0, 11, 16, 22, 32. You may notice that it doubles with every other number instead of every number. Mathematically, this works by starting with 1, then multiplying the previous number by the square root of 2. These get rounded down.
For a simple, clean implementation that doesn't stray from the sequence due to rounding errors, I start with 1 (or any power of 2). Call that n. The next two numbers are round((root 2) * n) and 2*n.