Chapter 5: A Theory Of Games

My family had a play structure in our back yard that my brothers and I would use to defend against real and imagined invaders. The structure had two floors. The ground floor was a converted sandbox with with four walls and old carpet for flooring. The upper floor had walls on two sides, a ladder on the third, and a slide on the fourth. I spent a lot of time thinking about how one might defend this structure. The ground floor was a deathtrap; while one of the outer walls was chest high and could be used as cover while lobbing water balloons at invaders, it only had one exit which was easy for larger kids to block and force surrender out of smaller kids through liberal use of the garden hose. The top floor; however, was different. The slide was difficult to get up, especially when wet, but easy to go down, and the ladder required whoever was trying to traverse it to drop their weapons momentarily in order to climb. Even better both the ladder and slide were easy escape routes and even the walls could be vaulted over in case of emergency. Thus it was perfectly defensible.

I have a memory of a game we played once using this structure. My brothers and I were defending the fort against aliens, zombies, or possibly something in between, who were attacking us on all sides. One of us covered the slide while another lobbed invisible explosives indiscriminately over the wall into the yard below. I was responsible for protecting the ladder. Now ammunition, even pretend ammunition, is a limited resource, and if the invaders were going to break into our stronghold it was definitely going to be at the ladder. So, just as the mindless slaughtering of unidentifiable alien zombies was about to get boring, something grabbed my leg. I tried as hard as I could to shake it off, but my Super Soaker was out of both real and pretend ammunition and I eventually succumbed to my injuries. The brother on the slide tried to help, but that only gave the zombie aliens an opportunity to scale the slide and take him out as well. My final brother made a valiant last stand before he too succumbed and declared the game over. There was much fun to be had, but also loss. The joy in an activity like this comes from the interaction with others, and thus that joy ends when your older brother goes inside to clean up. That’s how one losses a game of Calvinball. ¹

I am a gamer. That means that I choose to dedicate a large portion of my time to both playing and thinking about games. Games to me are a pastime, a means of taking in story, and also a lens through which I can see and understand the world around me. Likewise, my relationship with games has grown and changed as I myself have grown and changed. As a child, games were an avenue of wonder; a way to experience things I couldn’t normally experience. As a teen, games were a convenient distraction; a way to establish limited control over my otherwise uncontrollable life. As a young adult games were a way of measuring personal growth; a lens through which I could see my skills develop and improve. Today, games are just a part of who I am and an important lens through which I understand the world around me.

It’s not easy to talk about what a game is because the word means different things to different people. Games are a thing that children play and adults are supposed to grow out of. Ludwig Wittgenstein uses the term “language-game”² as a way of characterizing how we use language. Countries frequently engage in “war games” to train and ready their troops even as other commentaries on the subject explicitly exclude war itself from being a game. ³ I operate primarily in the world of technology and under that umbrella games are primarily a business; they are things, products, nouns, something that one entity designs for other entities to consume. There is a lot of literature around what exactly a game is, especially in the world of commercial video games; however, there is no easy consensus to point to as to what games actually are. If we consider the perspective of a game designer, or games as object, we could come up with a list of attributes that distinguishes a game from some other consumer object like a movie. Jesper Juul in his work “The Game, the Player, the World: Looking for a Heart of Gameness”⁴ summarizes some of this rhetoric by compiling a general list of qualities that appear in most game definitions: rules, variable outcomes, player effort, players attachment to the outcome, negotiable consequences of outcome, etc. However, I believe this approach fails to convey any real insight into what a game truly is, and worse tends to draw the discussion into pointless debates about what is and isn’t a game. As an example, if games must be voluntary and unproductive as Roger Caillois⁵ asserts then Warfare must not be a game. However true this statement might be, it uselessly offers no insight into mathematical game theories fascination with warfare, the game industries obsession with warfare, or the simple fact that we simulate and analysis warfare as if it were a game. Likewise, Juul refers to simulation games like Sim City as being “borderline cases” because they contain no predefined objectives; the game never unambiguously declares the player a winner. However, these simulations are still sold, unambiguously, as computer games in computer game markets and are reviewed as if they were games.

The following definition of a game was given by Bernard Suits in his book “The Grasshopper”:

“…to play a game is to engage in activity directed towards bringing about a specific state of affairs, using only means permitted by rules, where the rules prohibit more efficient in favour of less efficient means, and where such rules are accepted just because they make possible such activity.”

This definition defines two primary components along with one observation. A game, in Suits eyes, requires two things: rules and a desired state of affairs. A player desires a certain outcome, and the rules limit how that player may bring about that outcome. It is important to suits that the rules prohibit the most efficient means of bringing about this outcome. The fastest way to get to the top of a mountain would be to take a helicopter but the sport of mountain climbing prohibits such an act in favour of the less efficient method of climbing via ones own power. A mountain climber engages in the game of mountain climbing if they wish to arrive at the top of the mountain without using a helicopter. The observation Suits makes is that it is this restriction of the most efficient means that makes the game possible. If one wanted to climb a mountain using only ones own power then using a helicopter would not fulfill that desire, so the game of mountain climbing is invented in order to create a structure that encourages one to engage in the activity they wanted to engage in. As another example, the most efficient means of getting a ball into a hole would be to use ones hands to put the ball into the hole, but this is not what the game of golf is all about. Instead we choose to use a stick to hit a ball from a fixed distance away into the hole. Thus we have voluntarily chosen to use less efficient means, the stick, to bring about a desired state of affairs, balls in a hole. In reality, golf is not about getting balls into holes, it is about getting certain balls into certain holes starting from a fixed distance and using only regulation sticks. Thus, we can’t play golf unless we follow the rules of golf and therefore ‘playing golf’ is only made possible by adherence to its rules.

To Suits, “efficient means” implies that a player can use any means available to bring about their desired state of affairs. If two players simply wanted to overpower each other using any and all means at their disposal, then their struggle wouldn’t be a game. However, Suits explores such a scenario and discovers that the simple act of agreeing on a start time qualifies as an agreement to inefficient means and therefore makes it a game. Under this definition suits would have a hard time disqualifying any human activity from being a game because of the pervasiveness of unwritten social norms acting as a limitation of efficient means.

One way to think of the structure of a game is as being an alternate physics. Chess is a good example of this. Chess pieces are only able to move about the board in set ways. An invisible force, the rules of the game, prevent the bishop from moving in any direction except diagonally in much the same way that gravity prevents us from walking anywhere except along the surface of a large object. The thing that separates the physics of chess from the physics of the real world is that we created the rules of chess, we have to enforce them, and we can change them if we so desire; we did not create the laws of gravity and have no say in its enforcement. Assuming inefficient means, all other games contain some form of alternate physics. Softer game systems, like mountain climbing, are subject to both enforceable rules, like the prohibition of flying, and physical rules, like gravity. The allowed ‘moves’ in a game of mountain climbing are governed primarily by the physical world with some restrictions on technologies that we impose on ourselves. The outcomes of the game are a mix of physical results, “Did the player reach the top of the mountain?”, as well as results requiring a human judge, “Did they use only legal means to do so?” Any particular instance of a game is also impossible to reproduce exactly but some formal record of the event, like a recording or an entry in log book, may stick around. The softest game structures are those of make belief and includes the game of Calvinball I detailed in the introduction. These games exist primarily within the human mind and contain no normalized rule systems whatsoever. One might argue that such games have no structure as the rules, dictated by the mind of a child, can change suddenly and without warning. However, a child always knows when an adult has made an illegal move and thus, at least to their own subjective experience, the structure exists even if it can’t be communicated. The outcome of the game is entirely up to the humans, and, much the dismay of my inner child, an instance of a game is impossible to repeat in any form. Once fun has been had once, it can never happen exactly the same way again.

In all these cases the rules of a game act as a sort of simulation running on some sort of medium: a chessboard, physics, or the mind of a child. Video games fit into this model quite well. They are a simulation somewhere between the chess board and the mountain. Video games are simulations that run on the medium of computer hardware. Computer software is a mathematical structure and thus chess can be represented as a video game. However, most computer simulations are complex enough that unintended side effects are common. In chess it is impossible to make an illegal move; however, bugs and exploits that allow the player to act in unintended ways are nearly unavoidable in all sufficiently complex video games or real life simulations. Thus, like the mountain climber, in competitive video games we generally defer to the computer simulation to determine what actions are allowed, and step in sometimes with human judges when the need arises.

The structure of a game exists to moderate our interaction with the game and with each other through the game. However, a structure alone does not make a game. It is possible to follow all of the rules of golf and still not be playing golf. They rules of golf explicitly state that whoever completes every hole with the least number of strokes is the winner, it has no way of enforcing this goal if the player has no interest in winning. There is nothing in the rules that forbid a player from purposefully hitting a ball away from the goal. Worse, the game has no way of forcing a player to even progress through the game short of skipping the remainder of a hole after a set amount of strokes.

Juul attempts to get around this by by claiming that “Player attachment to the outcome” is a necessary part of the game. Suits definition requires a player to want to “bring about a specific state of affairs”. While superficially similar, these two requirements are not the same. Juul is coming at it from the perspective of a game developer. He wants his players to be attached to the outcomes as dictated by the rules of the game, and by extension the game developer. If a game has a celebratory ending sequence, then the player needs to be attracted by the possibility of experiencing it. However, in Suits definition the player themselves dictates the desired state of affairs. The mountain climber wants to reach the top of the mountain, but they might not care if they get there first. So even though the rules state that the winner is the one who gets there first the player may only be attached to the physical act of making it to the top and care substantially less about their placement.

Suits uses the example of ping pong to explore this point. If two professional ping pong players square off against each other in a competitive match, but mutually decide that winning isn’t important they could instead choose to attempt a long rally and hit the ball back and forth indefinitely. If their purpose is to generate the longest rally possible, we might still call what they are doing a game, just not the game the spectators expected them to play. However, it is important to note that this new game, the ping pong rally, exists within the exact same structure as the ping pong match the spectators expected. There is even a judge trying his best to enforce the rules of a game not being played. The thing that makes it a new game is the players expectations, not the structure.

Juul’s definition requires that, “As a player you agree to be happy if you win the game, unhappy if you loose the game.” The ping pong rally could exist under Juul’s definition, but only if we switched the referee out for one who is actively measuring the length of the rally. Juul assumes that a game can only be a game if there is agreement between the game designers and the game player. This is why under his definition simulation games like Sim City are not fully games because the game designer doesn’t prescribe an outcome for the player to valorize.

How a player approaches a game structure dramatically changes how they experience the game. A player could be “playing to win” meaning that they only take actions that purposefully maximizing the probability of achieving an outcome prescribed by the game. They could be “playing for fun” or “playing casually” meaning that they seek to achieve some sort of experience facilitated by, but separate to, the rules of the game itself. I am reminded of a friend in high school who proudly showed me their Elder Scrolls Morrowind save file in which they were in the process of murdering every NPC in the game; a state of affairs certainly allowed by the rules of the game, but not necessarily intended by the developers.

In my view, the separation between Chess which has a goal enshrined in the rules and Sim City which doesn’t isn’t philosophically important. Both are systems of rules, or alternate physics, through which humans can generate a wide variety of experiences. Commercial games, in whatever medium they appear in, are just game structures, and even though these structures may or may not include some prescribed end state, it is only when a player approaches these game structures with purpose do they actually become games. Indeed if we only look at a game in the way rules intend it to be played we frequently miss out on most of what the game becomes as a social phenomenon. Does the rules of chess say anything about chess grand-masters? About chess tournaments? Or chess clocks? Or the social phenomenon of cheating? No. If one wishes to know anything about chess, pure knowledge of its mathematical structure is only partial knowledge of the game itself. If we start by assuming that a game can only be played by people who’s purpose is to play the game as it is designed, then the only knowledge we will ever achieve is of the machines we designed to play them.

So then, what is a game? Well as mentioned above, no single definition will ever suffice. I fully admit that Juul’s and Suits’s definitions are useful when talking about games in their respective fields but fail as a general definition. However, I have nothing definitive to add. The definition I find most useful for my purposes is that games are a metaphor. Games are an attempt to section off some small portion of our lived experience into a much more understandable reality. We limit means because we have no other way of shrinking the enormity of the real world into something we can understand. We humans create games and define the boundary between what is and is not our game, and we do this to fulfill some purpose that is both uniquely personal and uniquely human.

In short games are small worlds; they are miniature universes that humans create and inhabit whenever the real world becomes to large and complex to understand.

1. Bill Waterson, “Calvin and Hobbes”[↩]
2. Ludwig Wittgenstein, “Philosophical Investigations”, (1953)[↩]
3. “I will assume that… traffic, war, hypertext fiction, free-form play and ring-a-ring-a-roses are not games.”

   Jesper Juul, “The Game, the Player, the World: Looking for a Heart of Gameness”, 2003[↩]

4. https://www.jesperjuul.net/text/gameplayerworld/[↩]
5. ”…. to be defined as an activity which is essentially:
   • Free: in which playing is not obligatory; if it were, it would at once lose its attractive and joyous quality as diversion; …
   • Unproductive: creating neither goods, nor wealth, nor new elements of any kind; and, except for the exchange of property among the players, ending in a situation identical to that prevail­ing at the beginning of the game;”

   Roger Caillois, “Man, Play, and Games”, 2001[↩]