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The goal of a game designer is very similar to that of a sculptor- chip away at all the excess until only elegant beauty remains. Here are 5 simple rules to make your designs more elegant.

1. Have as few rules as possible.

 
The pleasure that comes from seeing a depth of strategy emerge from simple premises is at the heart of great game design.  Scrutinize each rule in your game closely. Cut away any excess  to let the core mechanic shine through.
Perhaps the greatest example of elegant design is the classic strategy game Go. Go rules are stunningly simple:

Black goes first.
Take turns placing stones.
Surround the most territory.

There are a few more rules to deal with special situations that arise, but there is hardly an easier game to explain. And yet, Go has far more depth and permutations than even complex games like chess.[note] Computers still can’t beat the best Go masters [/note]  This depth of play is astonishing for a system of so few rules.
Digital games can accomplish this same goal. In the game Katamari Damacy, you roll a ball around, trying to absorb things smaller than you and avoid things bigger than you. You explore the game beginning at the size of a mouse, but eventually find yourself rolling up the whole world. This sense of relative growth and advancement creates an engaging experience almost by itself.
Similarly, in the game Portal, the player has one basic innovative tool that allows you to create portals from one area to another by shooting first one location, then the second location. Portal succeeds as an elegant game because it takes its one core mechanic and presents it in a variety of contexts. Through a creative exploration of the various uses of that device (moving objects, using gravity to generate velocity and change directions, trapping potential threats, etc.) the game creates a series of fascinating puzzles for the player to solve. This illustrates one of the key tricks to making elegant games- look closely at the core mechanic you have for ways to “context shift” and get more value out of the same mechanic. What properties does your core mechanic have that can be utilized in other ways?
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2. Have as few components as necessary

 
Have you ever opened up a boxed game and dumped out dozens of pieces, tokens, tiles, etc. that then had to be organized and sorted before play could begin? Not fun. Similarly, in a digital game, a screen presenting an overwhelming number of units and options can immediately turn off a player and prevent them from being able to meaningfully engage with the game. For each additional piece, button, or board, ask yourself whether this needs to exist. Is there a way to do more with less?
You can use the same strategy of “context shifting” to help use your game pieces to their greatest effectiveness. For example, the Star Wars Customizable Card Game  uses cards for a variety of purposes beyond shuffling and drawing.  Cards in the deck are used to represent a resource you can spend to play other cards[note] Set aside as a separate “Force” pile [/note], as a victory condition, [note] you lose the game when you run out of cards [/note] and a as combat randomization mechanic. [note] each card has a “Destiny” rating that influences combat when flipped off the top of the deck [/note]  Similarly, the card game for Eve Online uses card orientation to indicate the “build time” for a ship. [note] rotating the card once each turn until the ship is built [/note] Compress more play into less things.

3. Have an uncluttered and intuitive User Interface

 
The core goals that every good User Interface (UI) must accomplish are:
– Make it obvious what options a user has
– Make it easy to find the option a user wants
– Make a user want to interact with it
Building a simple and intuitive user interface is a complex and time consuming design task, requiring its own Core Design Loop. Take the time to iterate and learn what works and what doesn’t.
To help develop your intuition for good UI, pay attention to interactions you have throughout your life- not just in digital and physical games, but also interfaces in your kitchen, car, work, etc. Notice how some things seem obvious and direct, but others require learning and training before they become clear. Some interfaces draw you to them while others subtly repel you. Ask yourself why things are designed the way they are to help train your instincts for making your own beautiful and intuitive interfaces.

4. Find ways to “chunk” information

 
Often, very complex concepts can be combined or “chunked” in ways that make them feel like a cohesive whole. This serves the purpose of making your game more elegant, more intuitive, and easier to learn. If you have a desire to make complex games with lots of mechanics, chunking information needs to be your go to strategy to maintain elegance. The key is to understand what the player is already likely to believe and use that to your advantage.
Often in games, the theme or story is one of the best tools to help chunk information. For example, calling a character in a game a Wizard will automatically create associations for the player that can help them. A player may expect this character to cast spells, have a mana resource, have little to no armor, etc. You can use these preconceived notions to your advantage to make a variety of mechanics feel like a unified whole.
Beyond story and theme, information can be chunked based on how it is presented. In most first person shooter games, players understand that they can get a variety of weapons and each one will have slight variations. All of them, however, will typically have range, damage, ammunition, etc. And are usually controlled by the same button. Thus, when I encounter new information (a new gun) I can understand it more easily in the context of the information I already have. Similarly, if I see this disk icon:

I likely already assume that if I push that button, I can save the game. [note] I am amused that this association holds despite the fact that most modern gamers have never used the actual disk this icon represents [/note]
Think carefully about the associations your players already have to make complex systems elegant.

5. Teach information in steps

 
The human brain is capable of incredible things, but if you throw too much at it at once, it will become overwhelmed and shut down. The best games have a smooth ramp up where new skills and information are slowly acquired and mastered.
Compare the following World of Warcraft level 1 player screen:

To a typical top level player screen:
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If you began the game with all the options of a top level player, the game would quickly become overwhelming. But because each skill is gained one or two at a time, a new player is able to process a relatively complex set of information. Great game tutorials are crucial for more complex games.  Often, removing pieces of your game until later stages can help with the learning process and increase perceived elegance.

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Elegance comes down to a simple principle: Do more with less. Think of your games like a well crafted poem. Calibrate every word choice, every rule, and every component for maximum impact and mercilessly remove anything unnecessary to let your core vision shine.