TL;DR: Maybe mathematical modeling techniques could be used in board game design when searching and creating mechanisms or when stuck in a design.

In spring I had a very annoying and frustrating math class about derivative/integral calculus. Normally when I do math, I learn a technique and apply the process, but in this class, for what ever reason, the feeling was very different. You had to be creative about solving limits for example which felt almost like if you had to invent the wheel on your own.

Now from my experience it seems easier to design video games than board games which seems to have more trial/error and some struggling to find the right mechanism for the game. And I have been wondering for year about why I would have an harsh time designing board games compared to their digital cousin, and I think I have found the reason.

It would be that board game design would be more closer to mathematical modeling than video game design and that I am not used to use mathematics creatively. Here is a concrete example, Let say you want to solve this simple problem:

"What are the odds to roll 5 or 6 on a D6"

Before the invention of computers, there was 2 ways to solve this: A) Create a mathematical model to find the answer, B) make many die rolls and sum the stats. The problem with method B is that not only it takes a lot of time, but it would also give an imprecise answer. If you use method A, you would have found that the odds can be found by using a simple formula as: Desired number of faces OVER total number of faces.

There is 2 things to point out here:

- first: The face value is not used in the math formula, which means that the math model allows to solve a reality problem, without using reality exactly as it seems.

- Second: When you know the formula, you can easily apply it. But when you don't know the formula, it's a bit more complicated to solve the problem.

Now how can it be transposed to board game mechanics:

- The mechanics of board games does not always reflect reality accurately. For example, in the android board game, you try to incriminate or innocent people rather than trying to find the murderer. In the ends, it gives a similar feeling to what reality could be like without being a perfect replication.

- Then once you know a mechanism, it's easy to apply it to other game ideas but when you don't know, it's harder to design your own mechanism. So for example, if you know deck building games, it's easy to apply the mechanics to another game, but much harder if deck building have not been invented yet.

But if you asked me, how to find the odds of the math problem above, my reflex would be to roll the die multiple times and count the stats. And I know that ... because I actually did it at least once during my youth. Why would I prefer this method, well possibly because I am a practical person, and therefore have an hard time representing reality abstractly. Which could in the end explain why I can barely design new mechanism in board games.

I do have a fascination for board games which could be comparable to my fascination for math. Like I said to a math teacher (or almost), in computer programming, any problem can be solved, but math allow solving the same problem more efficiently and elegantly. So it's hard in this context not to love math, but it does not mean I am capable of solving problems by creating math models by myself.

So I think this is where my limitation lies, and it would explain why many game designers are very good in math. It's not because they necessarily need to know how they compute odds, it's because the process to design board game mechanism is very close to solving mathematical problems.

So for me, the tips I could give myself is focus on video game design and create board games using only mechanisms that already exists. But still, I am wondering, even if I do not have the flair for abstraction, is there some way I could help myself when I am stuck with a board game idea.

This is where the calculus story comes back into play. The books I used in the class was written by James Stewart who seemed pretty lunatic as he said that derivative calculus was ... beautiful. Now one part of the book explained various methods he used to solve mathematical problems creatively. I thought that maybe those techniques could be transposable to board game design if math and BG mechanics are so close to each other. I googled a bit and found this page:

http://stewartmath.com/media/5_inside_focus.php#

which shows some example where he use his problem solving techniques. I'll list what's on the page bellow, but I think there was more techniques originally found in his book. Still, it would be interesting to see how those techniques could be used to design board game mechanics.

- Recognizing something familiar/patterns

- Taking Cases

- Analogy

- Introduce something extra

- Indirect reasoning

- Drawing a diagram

- Working Backwards

- Establishing subgoals

- Mathematical induction

I can see a few application in board games, for example: recognition of patterns could try to map a reality behavior with a game behavior. Introducing something extra consist in adding component to the game to allow expanding the possible mechanics or allowing new interactions. Drawing a diagram can sometimes make reality be seen in a different way (Reminds me of rummy-kub which was displayed in a video game as a 4 by 13 grid for tiles played).

What do you think?

Have you used similar techniques when designing board games?

Do you think the board game design is related to math problem solving?

I know math is used a lot in game design, but here what I am trying to state is that game design process is math. If I have problems using math creatively, those difficulties would transpose to board game design.

For a comparison, you could say that board game use art, but the design of a game itself could also be a piece of art even if no art is used in the game.