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# How Mathematics Creates Gaming Magic

The gaming industry is easily one of the world’s most technologically-advanced markets. Ever since gaming fully emerged into the mainstream during the latter half of the 20th century, with each new console or game release, the industry has pushed the boundaries of innovation.

At the core of gaming, however, are a series of methodologies that we’ve all learned in some form or another – mathematics. Yes, maths plays a fundamental role in everything that’s involved in games, from their design, to gameplay mechanics and, of course, gaming hardware. From the simplest of games to the most complex, without maths, they simply wouldn’t exist.

In this article, we’ll take a look at just how the application of mathematics creates gaming magic, as well as the types of maths that you can find in any digital game, from puzzle games to casino favourites.

Types of Maths Used in Video Games

Mathematics refers to the science of dealing with logic, shape, quantity and arrangement. Maths is one of the few genuinely ubiquitous things, in that it appears in everything from the structure of our own bodies to the world around us.

While the maths you can find in a typical game is not exactly the same as the maths you’d use to calculate your weekly budget, for example, they’re not too dissimilar. Typically, the branches of mathematics that commonly power digital games include:

• Algebra and Linear Algebra – formulae and equations, including linear equations
• Applied Mathematics – combining maths with specialised knowledge, in this instance different aspects of designing and coding games
• Calculus – studying rates of change, used to create movement and gameplay
• Discrete Mathematics – graphs, integers and statements in logic
• Trigonometry – the function of angles and their application to calculations

Going further, some of the most important mathematical operations used in designing and developing games are:

• COS, SIN, TAN
• Cross Product and Dot Product
• Delta Time
• Domain and Range
• Matrices
• Reflection
• Scalar Manipulation
• Vectors including scaling and unit

How Maths is Applied in Game Development

There are several ways in which mathematical formulas and systems are applied in game design and development. All of those incredible things that you can do in video games that you just can’t in the real world are thanks to the application of the right formula or process.

Just take the environment you encounter in a digital game, for instance. Geometry is what’s responsible for every single gaming universe. When you enter the virtual world of your favourite game, everything you can see is comprised of polygons. 3D artists spend days creating landscapes, skies, objects and characters using polygons.

As you get on with playing the game, you’ll notice that somehow the game knows to take your character from their current position to a specific destination, and it does so in a linear fashion – i.e avoiding objects like trees or walls.

No gaming device is currently so advanced that it can think for itself. Therefore, game developers need to programme in specific sets of instructions called pathfinding, and pathfinding is only possible thanks to the area of maths called network theory.

Maths in the Wider Gaming Landscape

As well as being intentionally applied to create games, maths is also present in titles throughout the wider gaming landscape. For instance, there are several mathematical systems at the heart of the “most well-known casino game”, roulette.

Like many classic games of this nature, roulette is comprised of various different mathematical complexities that structure the rules of the game and how it plays out. Take odds, for example. Each of the numbers playable within the game all have their own applied odds. Additionally, if a player chooses more numbers or decides to straddle two numbers with their chip, the odds are changed yet again.

Chess, too, is a game founded on mathematical reasoning and logical plays. Meanwhile, the classic card game Bridge includes everything from simple addition and subtraction in its gameplay, to more complex percentage calculations.