Games usually consist of interconnected and repeating patterns of play which group together to form larger movements. Some designers take this idea further by saying that smaller and larger patterns have much the same shape. So a loop generated from a single action such as hitting an opponent and a movement of play (such as killing a boss) are basically the same thing. One is just a larger version of the other.

Recursion

Tests come in different sizes, from the instantaneous reaction to the long term strategic goal, and some tests are composed of many smaller tests. Smaller wins lead to bigger wins, smaller moments lead to bigger moments and so it goes. A single punch may lead to a combo. A single kick may lead to a series of passes and a goal. A championship point is just a point, but is significant because of all the points that have gone into getting there.

However the statement that 'games are made of games' is about more than that. It suggests that larger tests are diagram-able in the same way as smaller tests, that they are self-similar. If so then each button press is a game, each puzzle a game, each level a game and so on. A tennis point could be described as a game and so could a whole set. So could a whole match.

This is called recursion. A recursive pattern can extend into infinity in at least one direction. To be able to do so requires two properties:

A simple base case A set of rules which reduce all other cases toward the base case

A classic example is this shape:

Called the Sierpinski Triangle, it shows the replication of the same triangle by connecting the mid points of larger triangle sides in black space. It forms smaller and smaller triangles with the same shape as the first one, creating a pattern. Two mirrors facing each other and endlessly reflecting the same image is another example of recursion, as is the Mandelbrot Set. If you zoom into any part of it, you will eventually encounter another version of the same shape.

If games are recursive then the simple base case of a verb should scale to up the action, the loop, the dynamic, the task, the scenario, the campaign and the epic. The epic game would have the same shape as the smallest part and scale toward infinity. The smallest verb would set the rules by which all larger structures could be reduced. So the serving of an ace, the winning of a set, a match, a championship and so on would all just be bigger versions of the same basic verb.

It’s an awesome idea. However it’s not true. Here’s why.

#1 Magic Circles

Johan Huizinga observed that humans create special spaces within which they apply rules of their own invention and regard as sacred. A football pitch is a magic circle, as are a courtroom or a church, and we allow or disallow certain actions within the setting of each.

A key aspect of the magic circle is that the moderation of its rules is self-contained. The priest in the temple, the judge in the courtroom and the referee on the football pitch all enforce the rules of the space in-situ. If the rules of the circle change while the prayer meeting, case or match are in session then this causes schism and some form of reset.

One of the primary examples of a magic circle is a game. A tennis court is a magic circle, as is the World of Warcraft or the World of Goo. Each is moderated in-situ, in videogames by software, and each allows or disallows certain actions within their setting. We also treat them as sacred, special and sometimes even thaumatic places. So if games are made of games then it follows that each is its own circle and each has rules which are self contained.

This is demonstrably not true.

For example: The verbs of soccer are mostly kick, run and head. If we use the recursive model then each verb is a game, meaning each kick, each run and each head is its own little game. The win or loss condition of that game becomes ‘Did I kick well?’ or similar.

However in soccer you may make a great kick (win) but score an own goal (lose). You may make a bad kick (lose) but it turns out to be a lucky pass and gives your teammate a golden opportunity to score (win).

The determination of whether a kick results in a goal, an own goal, a throw, a corner or a pass all come from constraints and conditions of the soccer magic circle, not a kick magic circle. They are outside the base case. At smaller levels moderation is no longer self-contained. It becomes inherited, which breaks the second condition of recursion (A set of rules which reduce all other cases toward the base case).

In Scrabble, placing a word is only judged as ‘good’ with reference to the board so a clever action of ‘make word’ may actually turn out to be poorly positioned or illegal. In Quake, jumping on a spring while firing a rail gun might be an impressive action, but not if it doesn’t result in a kill. That kill is only determined by the circle of the game, not a circle of your action.

So what I see in games is not a recursive, self-replicating structure. Instead I see a structure of actions from below meeting rules from above within a magic circle, forming a dynamic.

#2 Dynamic Tests

Fun and learning, as Raph Koster correctly observed, are closely related if not the same thing. This explains why players rarely finish games: the game system is mastered, becoming predictable, or the player feels that he has gone about as far in it (from a learning perspective) as he ever will.

This happens more quickly for some games than others. Depending on the player’s age and aptitude, some games are played only once or twice, others become fascinations for a week, and a few for a life time. While production values, story and other joys play some part in lengthening play time, the most common effector of longevity is a game’s core dynamic. As long as the dynamic remains fascinating and not quite mastered, the game is fun.

In a sense this means that tests need a certain amount of dimensionality for them to be considered fun, and I would argue a game at all. Though many games consist of simple activities executed well (for example: most athletic events), they have a layer of scoring, time pressures or interplay between players that makes it dynamic, and thus fascinating. This presents a problem for the recursive model, because often what defines the dynamic is a rule outside an individual verb or loop.

In professional tennis that rule is that a player must win by two. He must score four times to win a game, but also win by two points. He must win six games to win a set, but also win the set by two games. So a game can go on and on. A set can run for six games, go as long as twelve plus a tie breaker or in some competitions it can continue indefinitely. The final set in Wimbledon, for example, has run to 50 games or more on occasion.

The win-by-two rule obliges each player to create pressure on his opponent in order to break him to get that extra point and game. So he plays tennis as a match, not a series of individual services. He builds toward key decisions, defending his position while attacking his opponent and trying to conserve energy for crucial pivots.

The win-by-two rule is why tennis is a great sport of struggle and overcoming, and also great to watch, however it is not a recursive rule. The player does not have to win a point by two strokes, a match by two sets or a championship by two matches. It does not exist in the simple base case, nor reduce to it.

Recursive game theory essentially says tests and games are the same thing, but excellent forehands by themselves do not make tennis exciting. The test of ‘tennis’ and the test of ‘forehand’ are not bigger or smaller versions of one another. One contributes to the other, but their shape is different. Without the dynamic there is no pressure, nothing to aim for and no reason to win.

Tennis only becomes a game because of that rule.

#3 Strategy and Tactics

There is a difference between tactics and strategy.

A tactic is a short pattern of optimal actions that the player attempts to master and use repeatedly to win. Finding racing lines, special moves, key map positions, simple feints on the chess board and so on are all tactics. Strategy, on the other hand, develops when the player finds optimal tactics which achieve wins, but do not guarantee a win every time. He starts to figure out more complex combinations.

In recursion a strategy would be a larger form of the same basic tactic, but that’s rarely true. One example is Triple Town. Designed by Dan Cook (a strong advocate of recursion) the idea behind the game is to match increasing orders of three or more identical items to produce ever more complicated structures and greater rewards. So three grass objects give you a bush, three bushes give you a tree, three trees a hut and so on.

However that’s not all. There are four constraints that influence the game:

The objects you receive are random You may have to place Bears or Ninja Bears, which impede placement You can store one item for later use You earn currency between sessions, which you can use to buy pieces you need

Tactically Triple Town is all about good placement, but because of Bears there is a strategic layer to setting up enclosures in order to keep your play area clear. Tactically it often makes sense to use a wild-card piece to clear many trees, but strategically they earn more coins if you group three temples together, even though it may kill your current session. Tactically it makes more sense to avoid orphan squares, but strategically you start to figure that the random distribution of objects will eventually grant you the one you need.

In other words, Triple Town is not actually about recursively creating patterns of three. It’s about manageable chaos where the tactic and the strategy are often at odds. Indeed, in games where one tactic proves to have mass applicability the result is usually dull. So while tactics are smaller patterns of play, by themselves they do not scale as good strategies.

Strategic play requires larger understanding, and often a different kind of perception of goals than tactical play. The nature of strategic and tactical decisions tends to be quite different, and this does not reduce or increase recursively. A move in chess may be well timed but there is no way to make the actual action of that move strategic through recursion. You just move the piece. A superb ace in tennis may well swing the match, but the excellent skill of that action does not translate to the win of a whole set. Many are the tennis players who serve powerful aces but play the overall match poorly.

The tactics of lower order goals are not well described by the strategies of higher order goals. Success is an important part of the experience at all stages and lines up with tests. However success does not look the same at all levels of play. Once again, that’s simply not recursive.

Atomic or Chaotic?

One popular model of describing games recursively characterises them as ‘atomic’, showing diagrammatically how they have a self-similar structure. One example is Raph Koster’s mechanic diagram:

The diagram shows an A/B outcome wherein preparation is made, a place is entered, stuff happens and you win or lose. Each of those components can be phrased in big or small terms. Preparing for a match, preparing for an encounter, preparing for a punch all sound like scale versions of the same idea. So does failure, or even place.

However ‘stuff happens’, is where things gets tricky. Exactly how many interactions is that supposed to cover? Does it account for the compound effects of one interaction on top of another? Does context play an equal role? Generally speaking, the answers to all of those questions tend to be vague, making the middle part of the diagram look like a question mark.

So while outward shape is indeed easily scaled, it doesn’t really tell us a whole lot nor satisfy the claim that games are made of games. For a pattern to be considered recursive it needs larger patterns to hold the same shape as smaller versions of itself, both internally and externally.

In games ‘stuff happens’ does no such thing. The shape of the ‘pass the ball’ test in rugby is completely different from the shape of the ‘scrum’ test. The shape of the whole game in fact is a series of modes strung together with many rules that produces an ebb and flow up and down the field. ‘Stuff happens’ in rugby is wildly complicated.

Atomic game design also implies that games can be infinite because their patterns can keep scaling upward. I disagree. There is a necessary simplification and constraint implied in any game that distinguishes it from real life by offering the prospect of finite success. Finite success is why we play games at all: to win, to overcome, to achieve. You can’t do that in an infinite landscape because the levers of the game grow so complicated that they become opaque.

Rather than thinking about games as recursive or ‘atomic’ systems, I find that looking at them as chaotic systems is more useful. In a chaotic system there is much repetition (called iteration) in tightly constrained patterns (called periodic orbits) across a limited space whose composition changes (called topological mixing). The resulting shape can be wildly different to the simple pattern that produced it, particularly if influenced by a strange attractor.

Every tennis match starts with the same basic elements and clear rules of winning, progression and magic circle. The chaotic variation that comes from the tight iterations of racquet and ball leads to endless potential outcomes but the win-by-two rule acts as a strange attractor, making tennis beautiful. Every football match is similar, as is every athletics event, every game of Scrabble, every Halo death match, every Mass Effect mission and every Minecraft map. They are dynamic, fluid, constrained, of endless complexity and yet strangely attracted.

Games are perfect examples of chaos theory. Chaotic systems don’t require simple base cases, nor for all other cases to be reduced to the base case. Plenty of examples show that when games get too complicated the likelihood of exploits emerging grows, but nonetheless a chaotic model allows for it. A chaotic model is also moderated by outside influences. This again is true of games. Football isn’t football without a pitch, halves and goals. For the interesting dynamic to emerge those constraints have to be in place.

The Verb-Epic Model

Buildings are not made of buildings. They're made of bricks, which become rooms, which become buildings. Songs are not made of songs. They’re made of notes and lyrics which become verses, which become songs. Even quantum physicists do not say that atoms are made of atoms for two common sense reasons: it’s confusing, and it gives the wrong impression about what kinds of interaction occur at various orders of magnitude.

Quantum physics uses the Standard Model which describes quarks, bosons and leptons. Those then combine to form hadrons (such as protons and neutrons), which in turn clump into atomic nuclei, then atoms, molecules and compounds. This is the kind of model that we need for games: a Standard Model that captures this chaos more accurately.

I call it the Verb-Epic Model, and will be writing more about it soon.