Minding the Gap
Math and language work in reverse fashion from one another, resulting in a gap. Try as we might, we cannot fully span the chasm that separates the two. For many, this is a nonissue as the two work well enough as is that there is no need to examine the issue. Then again, they rarely need to mix the two. For simulationists and game designers, this gap cannot be ignored. It informs the decisions we need to make when developing a new project.
While some people may see using math and language hand-in-hand as a marriage in hell, it is the stock-in-trade for designers of simulations, models, and games. Our goal is to make an attempt to span the gap so there are no discrepancies between the intent of the procedural elements defining the rules and the equations that accept the variables from the rules. This might seem easy, but it is not. The worst part is the audacity we have in believing or leading our clients and consumers to believe we have succeeded. If this were true, there would be few to no arguments over our efforts. We do our best to cover our tracks, but we leave you holding the bag and hope you never notice.
How do we do this and get away with it for as long as we can? Show me an experience. Go ahead, point out one to me. Not someone’s expression, I mean an outright experience. Through the use of language, I get you to buy into a contract to suspend the social order at minimum and most of reality at maximum. While you enact the rules supplanting part of reality, I tell the rules how to process your inputs through the structures I created beforehand. What you get back from those rules causes a state of change. You experience and react to this change, but the math and language never interact. You do. In effect, I turn you into an organic computer.
You experience the gap. Nothing happens without a player’s involvement and it has to be thus if you want the experience to be termed as a game. Herein lays one of the secrets of game design: you as the player have to enact the rules and follow the results the rules stipulate. How do you do this without arguing what specifically is being asked of you? Therein lays the mystery of the gap. Rules do not inform you how to read the equations, they only tell you what to input and what to do with the results. Somehow you bridged the gap long enough to extract some data.
The procedures to get the outcome mean nothing to the math. Likewise, the value returned means nothing to the language. The results are either applied to a game piece, meaning it moves, or it is compared to a table that then tells you which procedure is executed. “Oh, you got an 8, see Rule X. Next.” Unlike meters and yards, there is no unit of measure here. The values have already been accounted for and sorted for you. This seems a bit clinical, so how do we extrapolate fun out of this?
The general qualities of the experience are conceptually encoded in the rules and supported by the math. The trip around a Monopoly board takes 44 spaces. You roll two dice and are as likely to roll a total of 7 as you are doubles. This averages out to roughly six throws of the dice to make a complete circuit around the board. The experience is not measured in throws of the dice, it is measured in turns, and the actions of those turns are subject to cash flow and conditions imposed by the square landed upon. While you are juggling the bookkeeping math, the game is using its slightly-greater-than-six-turns value to govern cash infusions that feed into the acquisition process to tip the game even further into an imbalance that favors one player over another. Your only way to mitigate these processes is by leveraging the procedures that call upon you to negotiate with your fellow players.
So, while you are engaged deeply in the experiential elements of the procedural side of the game, the dice mechanic is the clock that works against any attempts to shore up equilibrium. Prices of property, regardless of development, do not change in relationship to your cash total. They are proportional to distance around the board, however. Thus, the prices work in tandem with the dice mechanic to drain players of money before passing Go. The rules are unconcerned with how much money you have at any point and the potential dilemmas they may place you in. The two elements that compose the game force you to make choices to interact with the math or not, or even to choose how you will respond to it (pay to get out of jail or try rolling doubles; or buy or pass on a property; sell assets, mortgage properties, or pay cash for rent costs; etc.). Each action triggers a different mathematical function that interacts with others in the game.
Notice that while the rules provide options for handling transactions, there are no procedures interacting with actual computations. That is the result of the gap. You can also see this in games like Risk. Now, there is a rule that has you earn a card if you conquer at least one territory during a turn, but that is also a state you changed to trigger that procedure. Another rule governing the cards states you cannot hold onto those cards once you have at least five. You must turn in sets of three until you have fewer than five cards. Each set consists of three-of-a-kind or one each of infantry, cavalry, or artillery icons on a card. The rules cannot (and do not) explain that it is statistically impossible to not meet the conditions to make a set of three with five cards, neither do they explain the progression for the number of reinforcements earned or that the procedure triggered by gaining cards as the game progresses are all designed to create an imbalance mathematically, just like in Monopoly, but none of that is reflected in the language because it is outside the scope of language’s role in games and its function in general.
One of the choices we have to make as designers is how much of an explanation is needed for players to enjoy an experience, something language and math can describe but cannot communicate. Neither medium can point to one, but they can observe and prepare the space for an experience to occur. Hence, we lie about how well we can make language and math link up and span the gap. See, by having rules that trigger mathematical functions and vice versa, we give the illusion weight. Think of it as so much smoke in mirrors. What is really going on in tabletop games is that designers tell you when to do math. The rules do not speak to the math and the math likewise with language. That is where tables and lists come into play. In Risk, it is a simple greater-than/less-than function to see who wins with ties going to the defender. The rules tell you to roll dice to attack. The math is completely inherent in the random function of the dice, just like the cards in the draw pile. There is no math in the rules of Risk. To be sure, there are numbers listed, but no actual math despite how it appears (See “Modifiers” for a more detailed look at Risk’s mechanics).
As designers, we start with one of three things: a premise, a rule, or a mechanic and then start adding the other two. This early prototype lets us experience the game and gives a sense of what needs to be adjusted in order to fine tune the experience as we have envisioned it. We are aware of the math and the rules needed to replicate the experience for others. When we fail to make the two sides appear seamless, we expose the gap. This is what playtesting is supposed to catch. Unfortunately nobody can account for every condition, one of the things covered under “House Rules.” There is supposed to be a slight gap between the written rules to allow for creativity in skill usage, which makes players better with those skills the game is designed around. When the language and math do not match up according to the way the rules claim the game is supposed to work, the players are led to several options: exploit the gap, try to interpret the rules to make them work, patch the game’s broken span, or abandon it. Some may try to ignore it, but such a breach often creates too much friction to be ignored for long.
What happens when people begin to abandon a game after such breaks are exposed well after the fact? The designers often work on a new edition or errata that work to fix the issue or they make a new game if they feel the problem is too deeply rooted in the system to be changed. After all, the exposure of the gap is the disruption of the suspension of belief that sustains the magic circle. If the game was playable up until that point when the exposure occurred, the cause is often a result of the skills the game hones exceeding the framework of the game’s challenge. That is less a failure of the game as it is a result of the phenomenon covered in “Driven Towards Extinction.”
Once you learn how an illusion works you are no longer entertained by it as you once were. That is all a game is: an illusion that allows you to improve real-world skills in a safe manner. You have several options available at that point: find a new game, abandon the genre of games honing those skills, develop your own game, or to even admire the artistry used to hide the gap. There is something to be said about the admiration of technique as a form of entertainment. After all, illusion is an art form, and it is how we mind the gap between language and math by stepping around it, just like you would when stepping from the platform onto a train.
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Anatomy of Game Design: An Unbridgeable Divide, Part 4
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Anatomy of Game Design: An Unbridgeable Divide, Part 6