Depth and Complexity

A discussion cropped up the other day at work that prompted me to think more clearly about complexity and depth and why they matter to game design. The topic isn’t new ground, but I’m using this as an exercise to solidify my thoughts and be able to share them.

First, I’d like to propose a general axiom for game design: our goal as game designers is to create the most amount of depth for the least amount of complexity. To talk about this idea properly we need a precise definition for both complexity and depth, so let’s examine them separately and bring them together at the end.

I. Complexity

I’m going to define complexity in two parts: action complexity and information complexity. Action complexity is the number of actions you can take at a given time. On the other hand, information complexity is the amount of information needed to play at the level the game demands. The more actions available, or the more information you need to play, the more complex the game. There’s a lot there, so let’s unpack each part with two examples: Go and Super Mario Bros.

Go board

In Go, you can take one action: place one stone on an open space of the board’s grid. You need to know two things: the board's state, and the rules for taking your opponent’s stones. The basic rule for taking stones is simple -- surround your opponent’s stones on four sides and you earn points. More complexity can be found as you dig deeper into the rules, but as a beginner that’s the scope of what you need to play.

Opening level of Super Mario Bros

In Mario, more is happening. When the game starts, you can move side to side, jump, and hold a button to run. Information complexity evolves as the game progresses (as it does in most games), but right away you need to know that touching the side of an enemy kills you, and that jumping on enemies kills them. Through the first level you need to learn a few more things: falling down pits is fatal, enemies can come out of pipes, and some enemies can’t be jumped on. Most of these are introduced individually and naturally, so the complexity ramp is never too steep for new players to handle. 

This is why complexity is defined by what you need to play at the level the game demands. There’s a lot of information packed into Mario’s first level, and nuance to Go's rules, but when starting out you need to know very little. As you progress, new situations expand your actions and information needed, but if the game allows the player grasp previous complexities, they aren't overwhelmed. Low initial complexity isn’t required for a good game, but will generally open it to more players.

Visibility

A major aspect of information complexity is the information’s visibility. The less visible the information you need or want to know, the more complexity it adds. There are three levels of visibility: clear, observable, and hidden.

• Clear information is immediately seen when the player needs it. In Go, the board’s state is clear. It’s always there, and is understandable without further investigation. The amount of time you have left to complete a level in Mario is also always present.
• Observable information can be inferred but isn’t directly available, such as each player’s current score in Go. Unless a scoreboard is maintained, the point totals of each player can be calculated but aren’t immediately available. In Mario, the location of piranha plants in pipes is observable (you have to watch for them), but not clear. It would be clear information if pipes with enemies were a unique color.

Piranha plant chomps Mario

• Hidden information cannot be seen, only obtained or inferred when actions are taken. Go’s hidden information is what action your opponent will take. This is true of most player vs player interaction. Until you make a move, you cannot know your opponent’s plans. In Mario, the contents of question blocks are hidden, as well as the ability to enter pipes. The player can learn these things, but the game doesn’t provide the information without the player taking action. 

As designers, we must decide the appropriate level of visibility for information, as each has its own benefits and drawbacks.

Complexity Ceiling

The final point on complexity is the fact that players have a complexity ceiling they’re willing to tolerate. This is going to be different for every game, and different for every player of that game. Put another way, games must budget their complexity, or players will be overwhelmed. This will be an important point at the end, when we examine the interaction of complexity and depth.

II. Depth

This leads us to depth. Depth is the number of meaningful and interesting choices available to the player at a given time. This is not the same as action complexity. In Go, remember that there is one action you can take: place a stone. The number of choices you have to place that stone is the foundation of Go’s depth. Note, however, that all choices don’t add depth. You can place a stone anywhere on the board, but the number of meaningful moves you can make is much smaller, especially if your opponent is about to surround one of your pieces and capture them. In such cases, you may have a small number of options to prevent them from doing so.

Illusion of Choice

To break away from Go and Mario, games will often provide the player with multiple dialogue options that all lead to the same outcome. An action game may have a plethora of attacks, but using one or two combos is always the most efficient. In such cases, the game has provided many actions, but little depth. This is often referred to as the illusion of choice. Sometimes, the illusion isn't immediately clear. In earlier versions of World of Warcraft, each class had a talent tree in which the player could place points in a large number of mostly passive abilities.

Old World of Warcraft talent tree

On paper, this should add a tremendous amount of interesting choices. In practice, players determined the most optimal way to spend their talent points, limiting the meaningful choices to a few at best, and one at worst. In this case, the system was moderately complex, but afforded minimal depth. In newer versions of the game, players make fewer choices, but each choice has a larger strategic impact on the player’s class, both reducing complexity and hopefully increasing depth.

Complexity is Not Depth

It is very easy to confuse complexity for depth, and players will commonly do so. Many players see a large number of actions and assume the game is deeper and more interesting. This is often wrong. While actions can add depth, we want to make sure that if we’re adding complexity, that complexity comes with far more depth than the game would have otherwise. This brings us back to our original axiom.

III. Our Goal

To restate, our goal as game designers is to create the most amount of depth for the least amount of complexity. Games and players have a complexity ceiling that we need to respect, so we can’t add an infinite amount of actions and information to a game, even if each adds a little more depth. In addition, the more actions we add, the greater the risk that many or most of the actions are illusions of choice. Each action or piece of information should ideally add a disproportionate number of meaningful and interesting choices to the game. Removing actions or information with a low ratio of choices is a good way to simplify a game and add room for more interesting mechanics.

Complexity generally makes a game harder to play, while depth makes the game more interesting. If players want a more difficult game, they may be looking for more complexity which can be added at the risk of alienating players looking for simplicity, or added to optional sections of the game. 

Depth itself is often optional, but always available. Young children or new players might enjoy playing Go, even if they don’t quite understand its intricacies. As they play more, they can start digging into the depths of the game, finding new and exciting ways to experience it, making depth a fantastic way to improve the game’s longevity and replayability.