[ENTRY_game-as-math-model] 2025-04-01
Matrix, Systems, Numbers, and Data.

A game designer is not just a creative endeveour —it’s a role grounded in problem solving and methods that engineer an experience. A good model of reason is to think as a system builder and an architecture of emotions- deliberately synthesizing 'experience engines' filled with decisions and consequences for the player - much like a dungeon master would do in a tabletop RPG, how a writer would do in a story, or how a screenwriter would do in a movie. They are engineers of experience. Game designers simply engineers experience with interactivity, or the act of 'play' within a system. Over the months, I've been reading The Game Design Toolbox by Martin Annander, which treats the process of game design with wide varieties of tools - and throughout my readings, I've observed that many of the tools involves deconstructing a game in a mathematical and system sciences lenses. Thinking in numerics, matrices, and optimization within systems.

One of the interesting tools is the 'Cross-Matrix' method, which, the game designers construct matrices between ideas - from the theme, mechanics/systems, and player psychology. This way we can reveal synergy between the systems and player experiences, to reveal blidn spots and opportunities for the game. In fact, we utilize the same method when designing our game 'BRAINROT'. We deconstructed the experiences within our game revolving around 'ludodynamics' - the study of systems/mechannics and how they interact with the narrative, theme, and story. We seperated the events in our game between 'ludonarrtiive' and 'ludodissonance' - the two sides of the coin of game design. The former is the synergy between the mechanics and narrative, while the latter is the dissonance between the mechanics and narrative. We then constructed a matrix between these two sides, and we were able to reveal opportunities for our game to explore. We wanted our system to align with the overall game's core theme while also creating a sense of dissonance For example, many of our minigames deal with brainrot culture, thematically and systematically, while one notable instance of ludodissonance is the “Giga Grind Simulator” minigame. In this game, players are forced to mindlessly press a single button repeatedly to gain fake dopamine points, all while a motivational narrator praises them for being “productive.” The dissonance arises because the game systems reward monotony and fake progress, while the theme mocks hustle culture and digital burnout. This contrast between the glorified feedback and the shallow mechanics is intentional—it provokes players to question what it means to “grind” in games and in life. This way, we can create a game that is both cohesive and thought-provoking. As a game designer, I believe that the best way to create a game is to think of it as a matrix of systems and experiences. You simply encode the many components of a game into a matrix, and then you can use that matrix to create a game as a pillar of your design. From the core loop, core theme, ludodyanmics, emotions, colors, and even the monetization strategy. You can even construct a matrix with many dimensions and layers, and then you can use that matrix to create a game that is both cohesive and structurally elegant.

Another model of reasoning in game design is through data-driven thinking. This approach shifts focus from abstract narrative and emotional “feel” to concrete values—allowing designers to break systems down into components that can be measured, tracked, and manipulated. This is particularly important in fast-paced or chaotic games like BRAINROT, where maintaining engagement across many players and stimuli requires fine-tuning. For example, in BRAINROT, we applied this model by deconstructing each minigame into a parameter matrix, using axes such as duration, difficulty, and unique configurations (e.g., number of AIs, spawn delay, object count). One of our early minigames, “RUN FROM THE TRAIN,” initially caused player frustration due to unclear difficulty spikes and inconsistent engagement. By creating a matrix that mapped each configuration—like AI speed, warning time, and train frequency—we were able to systematically tweak values and A/B test versions during playtests. This method allowed us to introduce numerical success criteria, such as “time-to-fun,” average failure rate, and player density around escape zones. The result was a more balanced experience where tension was preserved, but players felt they had agency. Ultimately, this data-centric approach provides a clear framework for experimentation and iteration, helping us design gameplay that is both chaotic and refined. It reinforces our core design philosophy: embracing absurdity, but engineering it with intention.

Lastly, another valuable model of reasoning in game design is emergent or rather, the idea that player experiences can arise from simple, well-crafted rules interacting in unexpected ways. Rather than designing every possible outcome, the designer sets initial conditions that defines a space of possibility. You may of experienced this with games like Dwarf Fortress, Rimworld, or even Minecraft. These games are not about controlling every aspect of the experience, but rather about creating a system that allows for emergent gameplay to arise. The designer sets the stage, and the players fill in the gaps with their own creativity and ingenuity. This approach embraces systems thinking not to control, but to curate emergence, Once we create a Procedural Generation system, we can then create a fine-tune to satisfy the player’s experience. .In this model, elegance comes not from adding more content, but from optimizing the generative potential of the systems already in place, fully embracing how data and generation to create emergent experiences.

In conclusion, game design can be understood through structured creative reasoning. Whether it's encoding systems into a cross-matrix, fine-tuning parameters through data, or designing elegant systems that allow emergence, each model provides a unique lens through which to approach the complexity of play. We are not just crafting content, its building the engine that creates dynamic, reactive systems that invite players into expressive, often unpredictable experiences. The more we learn to think in matrices, models, and mechanics, the more we can create games that are elegantly designed within the web of complexity that is play.

Exercises

1. [🟢 Easy] Define Systems Thinking in Game Design
In your own words, what does it mean to “think in systems” when designing a game? How does this differ from designing based solely on narrative or feel?

2. [🟢 Easy] Matrix Mapping
Think of a game you’ve recently played. Choose one mechanic (e.g., combat, movement, puzzle-solving) and list at least 3 parameters you could represent in a matrix (e.g., difficulty, duration, number of enemies). What kinds of values or configurations might each parameter take?

3. [🔵 Medium] Analyze Ludonarrative Dynamics
Pick a moment from a game that you feel either aligns perfectly with the story (ludonarrative harmony) or clashes with it (ludonarrative dissonance). What mechanics were used, and how did they support or contradict the narrative? Why do you think the designers made that choice?

4. [🔵 Medium] Build a Mini Cross-Matrix
Create a simple 2x2 matrix. Choose two categories (e.g., Theme vs. Mechanic or Emotion vs. System). Populate the cells with examples or ideas from your own project or a game you admire. What patterns or opportunities do you notice?

5. [🔴 Hard] Design a Procedural System with Tunable Parameters
Imagine a procedural event system (e.g., enemy wave spawns, weather effects, dynamic story beats). Define at least 4 parameters you would need to tune for balance and variation. How would you measure player engagement or success using data from this system?

6. [🔴 Hard] Diagnose a Flawed System
Describe a system or mechanic you've designed or played that felt off. Use a systems-thinking lens: what parameters or values might have caused it to feel unbalanced, boring, or unclear? How might representing it as a matrix have revealed those issues sooner?

7. [🔴 Hard] Reflect on the Role of Emergence in Your Design
Think about a system you've built (or want to build) that could lead to emergent gameplay. How much control do you want over the player experience, and where do you want the game to surprise you? How might matrix-thinking and data-driven iteration help you maintain balance while still allowing for chaos?

8. [🔴 Hard] Construct Your Own Matrix-Based Design Document
If you had to design your entire game as a high-dimensional matrix—where each axis represents things like player emotions, systems interactions, visual style, monetization ethics, pacing, and theme—what would the structure look like? How could this "design matrix" help guide future updates or expansions?

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