Thursday, August 21, 2014

Math in Board Game Design — Quick notes on Gen Con 2014

We returned home last night from Gen Con... exhausted but with huge smiles on our faces. Our experience was largely shaped by the fact that I was there primarily intent on doing research that consisted mostly of interviews with board game designers. And indeed I was able to interview 10 designers as well as make quite a number of incredible connections and continued to build some great relationships. Some of the designers we were able to meet with were names that almost any gamer would recognize and all of the interviews and other goings on were awesome.

One interesting event we attended was a seminar called "The Basics of Tabletop Game Design." A question asked by someone in the audience was regarding whether or not they should consider hiring a mathematician to help develop their game. Nearly every one of the five designers on the panel enthusiastically agreed... "screw the math! Do not worry about the math... Math should never be a primary consideration!" My impression from their comments is that, while math might... sometimes... eventually... need to be considered, it is far towards the bottom of the list for the design process.

This has caused me to reflect quite a bit on not just board game design but on other types of design and on research as well. Now, as I reflect on this it occurs to me that, if design is fundamentally the creation of a system, that this non- or  anti-math philosophy works rather well. Get the framework in place first. If we use basic systems thinking as described by Donella Meadows in her book "Thinking in Systems," we can create a system framework. We can work on that framework, refining and adjusting and designing the complete system before we may or may not need to introduce any mathematical considerations.

We can design the structure of the system and represent that structure using visual diagrams — this may require little or even no math. I often think of these diagrams as system maps or concept maps. Then when we begin to examine the behavior of the system we introduce math or perhaps in some cases not even math but rather numerical elements. The behavior of a system over time may be represented using visual graphs. So you can think of it in this way — we design the system using system maps. We can then if we choose to do so or if we need to do so reflect on the behavior of the system mathematically, possibly by using graphs as behavior is over time and graphs provided a useful tool for examining behavior over time.

Throughout my interviews and observations I have encountered many comments similar to those of the aforementioned Gen Con panel about math in the design of tabletop games. For example in one of my previous posts I quoted a designer as saying, "I was thinking about why we are here play-testing. It's not so much to work out the mechanics because you can do that very mathematically or through easily testable means. What we are actually play-testing here is ..." These comments by board game designers that down play the mathmatics has lead me to be very curious and desirous to one day interview Reiner Knizia. Knizia, a full-time board game designer (an extremely rare thing), has a PhD in mathmatics and is widely know for his smooth but extremely mathematical game mechanisms. I wonder where in his design process mathematics begins to play a role?


  1. Great post, Gary. Got me thinking about a few things.

    I think some of this discussion ought to include definitions of what folks are thinking of when they talk about the math inherent in a game design.

    A rigorous formula that is inflexibly applied to a routine mechanism of the game can be dangerous because it runs the risk of sucking out some of the variability of that mechanism, thus suppressing the apparent fun of that mechanism. That said, there are some times when a set, predictable formula is just what's needed (a scoring ladder, for example--get (n) resources, get (x) points, get (n+1) resources, get (x+y) points, etc.

    But if we look at the math part of game design for the other things that mathematics is, beyond formulae and statistics--patterns, relationships, and geometry--then I think we can add sensitivity toward the role that mathematics plays in game design and perhaps its priority will incrase on our appreciation scale.

    I'm thinking this especially after reading mention of Reiner Knizia in this post. What I have noticed in many (not all) of Reiner's designs is two-dimensional, orthagonal patterns inherent in his scoring, where the "multiple paths to victory" can be achieved, in part, through skillful planning of scoring points across both a (vertical) hierarchy and a (horizontal) taxonomy.

    That's a fancy way to basically say you have two ways to score. You score (n) points if you build something of (x) value/quality/extent/level, but you score *more* points if the value/quality/extent/level is greater than (x). That's the hierarchy, the vertical dimension.

    But, guess what! You *also* score if you have (n) *kinds* or *types* of things across (x) possible categories. That's the taxonomy, the horizontal dimension.

    So, using patterns and simple orthagonal geometry, Reiner gets players to think on multiple dimensions if they want to win the game. For example: "Hey, in this sailing regatta game, it's not just the *number* of boats I get to cross the finish line (hierarchy), but it's also about getting as many boats of *different colors* across the finish line (taxonomy)." Or, "Hey in this crazy game about planting orchards, it's not just about if I am the winner in the most amount of apples I produce (hierarchy), it's also about did I plant apple trees in as many different orchards as I could (taxonomy)."

    So maybe we need to shed light on the math inherent in the game design, but also look at math beyond simple numeracy.

    1. Hey Phil — Thanks for the great response. Indeed I think that most of what I've been hear with regards to the mathematics in tabletop games is directed at variability. There have been more than a few designers that have commented on the notions that a game can be too balanced. This is the direction I believe these warnings against math are aimed. I believe that there is somewhat of an irrational attraction towards the notion of balance. Can a game be too balanced? I strongly suspect that it can. I further believe that an obsession towards mathematically refining a game is a dangerous path towards a game that is too balanced.

  2. Great post.

    Games are not about math, games are about emotions. But math can be a powerful tool in creating a progression of emotions.

    By the way, Richard Garfield is also a mathematician by training.