Just a quick note: the original version of this text was written by me in Russian, and you’re currently reading its English translation. Because of that, a few phrases or ideas might s ound a bit awkward or unusual here and there. If you’re curious, you can find the Russian version here, and as always, I’ve done my best to preserve the original intent and tone.

— Enjoy the read! ;)

Reflections on chance, context, and controlled chaos.

You know, there’s an old joke about a mathematician who refuses to fly because he’s calculated the odds of a terrorist attack. His friends try to reassure him:

«Come on, the odds are practically zero!»

He replies,

«Yes, but the odds that there will be **two* bombs on board are orders of magnitude smaller. That’s why I always bring one myself!»*

Absurd as it is, that joke has always struck me as an uncanny reflection of the way we, as Game Designers, often handle randomness. We fear “bad” RNG, dread the possibility that a player might face something truly unforeseen, and so we lug around an entire arsenal of “bombs” — pity timers, smoothed drop tables, hidden chance tweaks. We try to tame chaos, to make it safe.

Before I continue, a funny aside: this text has already been through several reincarnations. It began as a much smaller fragment of another, heftier article, nearly morphed into an off-the-cuff rant, but that didn’t pan out either. Now, while squeezing these thoughts into a so-called “warm-up,” I suddenly find myself with a piece as long as my very first article. Yet I still can’t manage to pin down one central question around which to build a neat dialogue.

Even so, the urge to explore this topic — to articulate the concepts that land me in certain mental cul-de-sacs — hasn’t gone anywhere. That’s precisely why this material is, quite literally, an “essay”: you’ll find a fair amount of analysis and references to some not-so-obvious things, but also plenty of pure reflection and, perhaps, outright rhetoric.

So, fair warning: what follows may seem dense, maybe even overloaded or confusing — and that’s partly deliberate. These musings lie in the domain of specialised reading, and I understand many points might fly past or remain unclear at first, or even turn out to be wrong. But I have no wish to turn an already hefty text into a textbook that spoon-feeds every term — this isn’t a lecture. I’ll be more than happy, though, to dig into the details and debate them in the comments. If something strikes a chord or raises questions, you’re warmly invited to join the discussion there.

Now, to business. In my attempts to grasp exactly what we lose when we try to “defuse” randomness and bring chaos to heel, I keep stumbling over three fundamental pillars — three “whales” that, to my mind, hold up the entire issue. First, there’s Context — the way the player’s accumulated history of decisions shapes each subsequent event. Second, there’s Game Theory (and its close cousin, probability theory) as a tool for analysing strategic behaviour under uncertainty. And third is what I’d borrow from physicists as an Entropic Budget — a finite supply of “true” randomness every game possesses. All three pillars are inseparably tied together through the figure of the player and how he interacts with randomness, how his choices infuse the game with meaning, and how our designer “crutches” disturb that fragile balance. Let’s try turning each one over in our hands.

Context: decision density and the richness of experience

At the heart of replayability lies the idea that a game remains engaging on subsequent play-throughs. How can we achieve that? Years ago Sid Meier famously remarked:

«A game — is a series of interesting decisions»

Every decision a player makes adds a new brushstroke to the game state, creating fresh context for whatever comes next. The more of these meaningful branches appear, the richer the experience becomes: past choices reshape the current situation, and no session is ever an exact copy of the last.

Put simply, we can measure context by the density and depth of decisions. If a game keeps throwing the player into different circumstances, forcing adaptation — it provides a rich context, and therefore a reason to replay. Strategy titles and sandboxes excel at this: their abundance of possible states and outcomes ensures that two play-throughs are never identical. The player gains confidence that each new run will offer fresh impressions, because the space of potential situations is vast and every game ends unpredictably, just like the first time. That is what fuels replayability.

For clarity, let me introduce a little character of mine. Imagine our Slepok decides to bake a pie. The first time he follows the recipe to the letter — that’s his baseline behaviour, his “first play-through.” But then he bakes a second pie. If he enjoys freedom of choice (a different flour, berries instead of apples, a tweak to the baking time), each such decision creates new context. The pie may come out slightly different, perhaps better, perhaps worse, but it will be his pie, the result of his decisions. The more of these small yet meaningful choices Slepok can make, the more eager he is to experiment again and again, even though the tools (the core game mechanics) remain unchanged.

Randomness, however, is a double-edged way to create diverse context. RNG spawns unique situations, but if it dictates events too strongly it nullifies the weight of decisions. Ideally, player choices and chance complement one another: the game tosses up an unexpected scenario, and the player, drawing on experience and context, responds. That is how interesting decisions arise — the clearest, simplest example of this perfect balance is chess (and yes, within the frame of “context,” randomness is agent-driven, i.e. enacted by the players themselves). But let chaos slip its leash — and intrigue turns into frustration. This is precisely where the second pillar steps onto the stage.

Game probabilities: meddling with randomness

When we add random elements to a game, we are in fact letting chaos into the system. Game theory and its sibling, probability theory, remind us that probability distributions have an annoying habit — every so often they spit out extreme values.

For example, in purely theoretical terms a player can fail to obtain a rare drop ten times in a row even though the chance is high. The system considers that normal, while a human suspects foul play. Our brains do not get along with statistics: if a fair coin lands heads ten times straight, we start believing the coin is crazy-biased or that the next flip simply has to be tails. This well-known “gambler’s fallacy” makes us see patterns that are not there and feel cheated even when randomness is formally fair. Designers — myself included — therefore compromise. We meddle with the probabilities to tame the variance of outcomes.

Beyond distributions, game theory teaches us to analyse how players adapt their strategies in response to the situation, in our case to random elements. A player does not just passively accept good or bad luck; he shapes his behaviour around expectations, odds and potential gains, which becomes especially clear in competitive or asymmetric games. Thus, tinkering with chaos changes not only the math of drops but the very nature of the player’s choices.

Pity systems are a textbook illustration: after a set number of failures the success chance rises, or a guaranteed prize appears. Mathematically we trim the tail of the distribution — we chop off the extremely unlucky streaks. Diablo III, for instance, runs a hidden timer that gradually increases the legendary-drop chance if the player has gone too long without one. This safety net keeps RNG from drifting too far into the red: after roughly 90 minutes without a legendary the game starts tilting the odds toward the player. Designers say openly that the aim is to prevent randomness from ever becoming too negative. In effect we are doing exactly what gamblers are criticised for: after a string of losses we raise the stakes on luck, turning the illusion of a pattern into an actual rule.

That is why both theories matter here: probability explains why cold streaks occur, and game theory explains why players respond by reshaping their behaviour. For a Game Designer this is crucial, because one theory rolls the dice, while the other decides when and why to roll them.

Back to Slepok and his pie. The recipe calls for “a pinch of salt.” But what is “a pinch”? That is our randomness. Slepok may accidentally sprinkle a little too much or too little. If he oversalts several times in succession and the pie becomes inedible (an extremely negative outcome), he might get upset and stop baking. To prevent that, we — the recipe designers — can add a pity system: give him a special measuring spoon that makes it impossible to over-salt, or quietly swap his shaker for one that dispenses salt very slowly. We control the chaos of the pinch so he does not spoil the whole experience.

Pity timers are not the only “bombs against chaos.” In many single-player games randomness secretly backs the player up. XCOM, for example, is notorious for an optional hidden RNG compensator: if a soldier misses several shots in a row, the chance to hit the next one invisibly rises. The code embeds the unspoken principle “You can’t be that unlucky forever!”

Resident Evil offers a different case: resource positions are fixed, but the items themselves are dealt out randomly with a bias toward the player’s needs — the game is slightly more likely to spawn ammo when you are running low. All of this is game theory in service of UX. We meddle with randomness to balance pleasure and unpredictability.

RNG thus becomes controlled chaos: the player may flirt with risk, yet we almost never let him tumble into an abyss of bad luck. If you picture the spread of possible outcomes, our intervention compresses it. Players encounter truly awful (or absurdly good) rolls far less often — everything gravitates toward a pre-arranged experience curve. That solves the fairness issue: even the unluckiest protagonist, subjectively, will not walk away empty-handed. Yet for this predictability we pay by constricting the third pillar — the entropic budget.

Entropic budget: the limits of chaos for UX

By entropic budget I mean the notional amount of unpredictability a game can afford without shattering the user experience.

Every genre, every audience — has its own tolerance threshold for chaos. A pinch of randomness adds variety; too much — steals the player’s sense of control. Our task is to find the balance point.

Clumsy though it is, we can compare it to seasoning once again: a pinch of randomness adds flavour and makes each play-through special, but oversalting ruins the dish instantly. When we design a system, we literally allocate the entropic budget — deciding where the player may encounter the unexpected and where the experience must stay stable.

In an RPG, for instance, you might randomise loot stats but not the number of grind mobs. In a card game — shuffle the hand yet give everyone the same number of cards. We sprinkle chaos where it heightens intrigue and trim it where it wrecks the player’s plans without recourse.

If Slepok ends up with an identical pie every time thanks to our “controlled pinch of salt” and the “smart oven” that auto-adjusts the temperature, then yes, he will avoid disappointment. But he will also never learn that a touch more salt can offset the sweetness in an interesting way, or that a slightly charred crust adds zest. His entropic budget for culinary experiments will be exhausted not because he has tried everything, but because we pre-limited the range of outcomes. He will get a “safe” but perhaps less varied experience.

Intuitively, the goal is to stay in a zone where the game still challenges and surprises, yet never feels like a pure lottery. A good game always offers a solid core and clear rules, against which measured RNG creates controlled disorder. The player needs to understand the bounds of possibility: in XCOM we don’t know whether a shot will hit, but we know its percentage and damage; in Balatro we hope to assemble a flush, but can’t know exactly which suit cards will drop, though we can inspect how many of each suit remain. Such transparency sets the boundaries of the entropic budget — the player sees the range within which luck can swing.

As long as events stay within that declared range, the user experience holds. But if chaos bursts beyond those limits (say, a string of defeats with no apparent way to intervene) — the budget is spent, the player feels powerless, intrigue turns to frustration, and the game is abandoned.

Where are the dice?

So, we’ve walked the length of our three pillars — Context, Game Theory, and the Entropic Budget. What, then, do we conclude? On the one hand, we Game Designers must intervene. If we leave our Slepok completely unsupervised, he’ll botch things so badly the pie will turn into a weapon of mass destruction. After all, nobody likes to feel like a victim.

«When we choose our problems we feel empowered. When problems choose us against our will, we feel like miserable victims»
— Mark Manson, The Subtle Art of Not Giving a F#ck

Players want challenges, want surprises, but they want to opt into them voluntarily — which is exactly why we measure out this “chaos on demand” so carefully.

Yet a quiet voice in me pulls the other way: if we do decide to use randomness, even in small doses, is it really worth spending so much effort on meticulous control? The player’s decision-space is finite anyway, always bounded by our own vision, by a pre-set arsenal of mechanics and scenarios. And if we’ve already sprinkled in these spices, might we let them bloom a bit more freely?

I’m not saying we should turn a game into real life — that’s both absurd and unnecessary. Rather, I’m wondering how we might calculate that reserve of context. Can we transplant game theory, probability, equilibria, and variance onto pre-built game graphs to gauge, even roughly, how much more “chaos” a given mechanic can afford before it starts eroding context?

Pursuing such questions, I find that the “replayability ceiling” stops being an abstract notion and becomes a tangible metric — one we could not only monitor but extend through honest randomness that adds depth instead of merely sanding off edges.

Thus, at this crossroads I see no binary “control or not” dilemma (control is axiomatic) but a task: to learn to measure and dose randomness across an entire game as deliberately as we now manage economy or balance.

That is exactly what I want to discuss next: not so much the ethics of interference as the potential of chaos itself, treated as a resource we can quantify, budget, and apply consciously. I crave a clearer sense of freedom for unexplored branches, for rare stories that would feed the community. Hence I propose we move past “control / no control” toward the tougher question: How do we calculate how many unique situations a game offers, and how that reserve of “chaos energy” is spent within its genre?

Honestly, the idea of “counting chaos” and setting a “replayability cap” has been rattling in my head for years. Like many of you, I’ve abandoned games not because they were bad or I had “finished everything” in the traditional sense, but because a slow realisation crept in:

«That’s it. It can’t surprise me anymore»

Whether at the fifth hour, the tenth, or the two-hundred-and-fiftieth, once the internal counter of potential surprises hits zero, interest dies. It feels as though I’ve explored every combo, seen every “random” event, and what awaits me now is only a retread of familiar patterns, however freshly wrapped. That sense of exhaustion stems not just from the amount of content but from the quality of the randomness that was supposed to keep each run unique.

Trying to systematise that feeling led me to the notion of a provisional formula. A bid to decompose the ephemeral “wow factor” into components, to grasp what drives it and how our design choices, conscious or otherwise, drain it. This isn’t a quest for an “ideal game” with infinite replayability (though who among us hasn’t dreamed of that?) but an attempt to locate the levers that let us steward the resource more knowingly. If we can see precisely how a “tuned” RNG or a narrowed context affects the surprise reserve, perhaps we can craft games that astonish longer, deeper, and more meaningfully.

Before we dive into the formalisation attempt, one disclaimer. The next section, where I sketch this “replayability formula,” was developed with help from AI. Casting gut feelings into strict mathematical terms is no small feat. To avoid reinventing the wheel — or drowning in my own wording, which might prove still more mistaken — I used AI as a tool to structure thoughts into a formula, to hunt for suitable “calculations,” and to lend the passage below a touch of that “mathematical elegance” I may lack.

The entire concept, all variables and their relationships, stem from my own reflections. The AI merely helped package those ideas into a more formal shell. I employed it deliberately as an assistant to set boundaries and find direction. So if anything feels overly “academic-artificial,” know that it is a joint product of human intuition and machine logic — under my careful editorial eye.

A 5-minute “how-to” for the replayability formula

To keep our musings from floating off into abstraction, let’s package them in a simple mathematical model. This formula is not the last word on the subject — think of it as a sketch, a starting point for reflection and (with luck) future iterations. Its purpose is to estimate a game’s notional replayability ceiling R, factoring in both deterministic and stochastic influences on how unique each run feels.

At the core of our hybrid formula sit four key variables, each rated — for convenience — on a scale from 0 to 1 (0 = minimal presence, 1 = maximal):

1. C — Contextual Density. Reflects the depth and richness of meaningful decisions the player can make, and how those decisions shape subsequent game states. A high C means past choices weave a branching history full of unique situations.

Example: Chess scores extremely high — every move radically alters the board and available plans. A linear visual novel with one predetermined ending nears zero, because the player’s “decisions” (if any) create no new context for later events.

1. A — Player Agency. Measures how strongly the player’s own actions and skill generate unique situations and sway outcomes. A high A makes the player an active author of experience; mastery, tactics, or even random experiments lead to diverse results.

Example: Competitive titles like Dota 2 or arena shooters boast very high A, as live opponents spawn endless tactical permutations. Roguelikes such as Slay the Spire or Hades also rank high: constant build and combat choices heavily colour each run. A tightly scripted story game with little player influence scores low.

1. RNG — “True” Randomness. Captures the share and impact of pure, un-tamed chance inside core mechanics — how much the game relies on random outcomes for variety.

Example: A card game with a well-shuffled deck has a high RNG. A title where every event and reward is hard-scripted clocks in at zero.

1. I — Intervention (Control Tools). Indicates how aggressively the designer steps in to smooth RNG spikes and valleys, making the experience more predictable and less frustrating — and how many levers the player gets to observe or tweak that RNG. A high I means the system actively “helps,” suppressing extreme luck swings.

Example: Pity timers, “smart loot,” or hidden chance buffs (as in XCOM or Diablo III) push I upward. A game that leaves RNG untouched keeps I near zero.

With these variables in place, the hybrid formula for the replayability ceiling R looks like this:

R = C × A + (1 − C × A) × (RNG × (1 − I))

Let’s unpack it:

• C × A — replayability driven by deterministic factors: the depth of context plus the player’s agency. The higher this product, the more unique situations players forge without raw randomness. If C × A = 1 (max context and max agency — imagine a perfect sandbox with live players), the game already sits at peak replayability through emergent play alone.
• (1 − C × A) — the share of replayability not yet covered by deterministic factors. If C × A hits 1, this multiplier falls to zero, so randomness contributes nothing (logical: when players themselves supply endless variety, RNG matters less). If C × A hovers near zero — say, a very linear game — the whole replayability burden shifts to chance.
• RNG × (1 − I) — the contribution of pure randomness, tempered by designer control.
  • When I = 0 (no control), the formula taps the full RNG potential.
  • When I = 1 (complete control), the term vanishes — “rigged” randomness adds no true unpredictability.

How it plays out (roughly):

• High C and A — complex multiplayer strategies or deep sandbox RPGs: the first term dominates. RNG’s slice can be small, yet players still enjoy vast novelty.
• Roguelikes — Slay the Spire, Hades: balanced mix. C and A are solid, and RNG × (1 − I) remains hefty, since random drops, foes, and layouts define the genre while control tools stay moderate.
• Linear narrative games: C and A approach zero. Replayability (if any) relies on RNG × (1 − I). Should RNG be low or I high, R trends toward zero.

Again, this sketch makes no claim to scientific precision; it simply frames the slippery notion of replayability in a way that highlights which levers we, as designers, can pull.

The fun part is to try it yourself! I’ve set up a small interactive Google Sheet. All you need to do is follow the link:

🔗 Link: REPLAYABILITY CALCULATOR

Make a personal copy, then drop your own 0–10 ratings (0 = absent, 10 = max) for C, A, RNG, and I for any game you fancy. The sheet rescales the inputs to 0–1 and spits out the resulting R ceiling.

Most importantly, you can interpret R as the percentage likelihood that a player will:

• finish the game
• fire it up again
• decide to replay the story, or
• queue up “just one more round”

Compare different titles, tweak parameters, and you may spot surprising patterns. The score is still a rough approximation, of course, but I hope it nudges us to think harder about what sustains long-term interest.

Critique and common sense

Well, here it is — our attempt to measure the unmeasurable. And, to be frank, the moment the formula is born it already feels… shall we say, lifeless. Don’t get me wrong: I’m glad I managed to structure my thoughts at all. But let’s stay realistic. For all its tidy symmetry, the model comes with a laundry list of flaws. One of them, in the context of game-design-as-process, is especially glaring — but we’ll save that for last. First, the more obvious aches.

First, it is painfully linear. Games are living, breathing organisms that keep changing: patches, expansions, new seasons, shifting metas, evolving communities. Trying to squash that ocean of shifts into four static coefficients is like describing the sea with a single drop of water.

Second, scoring the coefficients themselves (C, A, RNG, I) is pure subjectivity, even when we lean on “objective” cues. Where’s the line between a moderate and a high context rating? How do you pin “player agency” to a number when it hinges on a million factors, mood and skill included? Deep down, each variable deserves its own nested formulas and subsystems. For now, the fairest R for any title would be an average of a dozen designers’ gut ratings.

Third, it almost entirely ignores the human factor. Emotion, social play, modding scenes, aesthetic pleasure, narrative immersion, personal taste, even plain fatigue — all of that sits outside the brackets. Yet those very things often decide whether someone comes back, even if every “mathematical” replayability index reads zero.

Fourth, the puzzle of pure randomness. While shaping the formula I hit a contradiction. Logic says chance without meaningful choice (that is, agency) is shallow variety and shouldn’t fuel lasting replayability. ***Yet millions keep returning to slot machines, lotteries, and the like precisely *because** of pure luck. The AI and I toyed with ways to “crop” RNG’s impact when agency is low, but every mathematical trick broke something else or opened new conceptual holes. In the end I left the simplest version, admitting: yes, unfiltered randomness can sustain replayability, even if it’s a different species from that born of deliberate decisions. Who are we to forbid the joy of watching unpredictable outcomes? It may not be the flavour of replayability we designers wish to cultivate, but it plainly exists.

Yet the flaw that, for me as someone who also makes games, outweighs all others is this: the formula — like any of its kin — is a tool of retrospective analysis. We stare at a finished product, at what has already happened, and ask “why does it work like that?” We’re judging from the end, already knowing its guts and the experience it yields.

But what about the development stage? These musings on replayability, on balancing chaos and control, bite hardest when you’re knee-deep in a prototype or a design doc, before anything is playable. How do you evaluate future “agency”? How do you predict “contextual density” when you only have two core mechanics? How do you tune “RNG control tools” when you have no idea how players will react to RNG? You could wield the formula during early iterations and milestones, but only with wild assumptions and hand-waving, which guts its practical value. We’re still checking the rear-view mirror while guessing the road ahead.

So was it all for nothing? Did we just play at mathematics and craft a pretty yet useless toy? Not quite. The act of formulating — of breaking the complex into parts — is valuable in itself. It forces us to think harder about what shapes game experience, which factors matter, and where hidden connections lurk. Even if the formula never becomes an everyday tool, it offers a shared language, a coordinate system for discussing these slippery matters.

And since the exercise has at least brought us somewhere —since we now possess an imperfect yard-stick — why not use it for illustration? Armed with the formula and a dash of designer instinct, let’s walk through a handful of landmark projects across genres. Not to deliver a final verdict on their “replayability,” but to see how the abstract variables surface in real games and what insights (or fresh questions) that sparks. Before we move to the final takeaways, then, I propose a small practical exercise.

Single-player: the art of a controlled symphony

Before she slices into individual titles, let’s pause and ask what single-player actually means in the context of randomness, context, and replayability. Solo games — especially those built around story and atmosphere — are, at heart, carefully staged performances, full-blown symphonies. Here the Game Designer acts not just as world architect but as director, leading the player along a deliberate emotional arc. The chief goal is rarely endless variety; it is the creation of one (or a few) powerful, memorable play-throughs.

In such games Context (C) comes less from procedural generation than from the interweaving of storylines, character growth, world-building, and the (often illusory yet emotionally weighty) choices the player makes along the way. Agency (A) is peculiar, too: it may be high within specific gameplay slices (combat, puzzles), yet globally submits to the narrative vector. RNG is a guest, not a host. Its job is to add a pinch of spice, to enliven the world and keep routine actions from feeling mechanical — never to wreck the main design. Intervention (I), meanwhile, usually hums at full power behind the curtain, smoothing everything into that coveted just-right experience.

The trouble, of course, is that any move to “disarm” randomness inevitably nibbles away at the entropic budget we discussed. Single-player titles often do this knowingly, preferring a guaranteed high-quality couple of runs to a potentially messy infinity.

The Witcher 3: Wild Hunt

A monumental work and a benchmark narrative RPG. The world is vast, the quests meticulously written, the characters alive. Yet let’s press our little formula against it:

• Context (C) – 4 / 10

The Witcher’s world is drenched in detail, branching dialogue, quest consequences. Each major decision really does shift the state of the world and people’s attitudes. That’s strong context. Still, the overarching plot rails are quite firm; truly game-changing branches are limited.

• Player Agency (A) – 4 / 10

Geralt is Geralt. You may flavour his dialogue, choose combat styles, but he remains a witcher with a set skill-tree and a moral compass. You wield agency in tactics, quest order, a handful of narrative forks, yet the game leads you down a well-paved road. You are more leading actor than true co-author.

• RNG (Randomness) – 2 / 10

Where is raw, untamed randomness? Loot exists, sure, but the drop tables are tuned. Combat crits add flair, not wholesale swings against equal foes. Random encounters form set dressing, not a systemic pillar. Globally, the game is highly deterministic.

• Intervention (I) – 8 / 10

Here The Witcher shines. Hidden crutches abound: loot systems (quietly massaged), dynamic difficulty tweaks (though unadvertised), scripted events masquerading as chance. All serve the epic yet non-frustrating adventure. The developers clearly refused to let “bad RNG” brick a player’s journey.

R = 0.19 (~ 19 %)

What does that tell her? The replayability of The Witcher 3 hinges first on a wish to witness alternate narrative outcomes (C × A), to replay with another build or a harsher difficulty. Pure randomness contributes almost nothing. Once you have seen the key branches, the game delivers essentially the same, exquisitely staged experience — an intentional trade-off favouring narrative quality over endless novelty.

Disco Elysium

A very different beast: dialogue-driven, skill-check-laden, and steeped in the protagonist’s inner monologue.

• Context (C) – 6 / 10

The main murder plot is linear at a glance, yet every dialogue choice, thought upgrade, success or failure on a skill roll nudges the next interaction into its own contour. The world flexibly reacts to which Harry you become. Those micro-shifts matter more than they first appear.

• Player Agency (A) – 6 / 10

Agency lies in deciding what kind of Harry you’ll be: communist, fascist, moralist, drunk, super-cop, amorphous… Each stance unlocks or bars dialogue, alters NPC perception, even spawns new thoughts. High narrative agency, indeed.

• RNG (Randomness) – 4 / 10

Virtual dice govern every skill check, seemingly central. Yet you influence odds via clothing, thoughts, substances, prior actions. It isn’t bare RNG.

• Intervention (I) – 6 / 10

The game won’t hesitate to punish failed rolls. Consequences can sting. On the other hand, you can “re-roll” some checks (after rest or new context), equip thoughts that boost stats, and certain actions are gated until the plot is ready. Chaos is allowed, but not entirely unchecked; failures often become story rather than simple dead ends.

R = 0.46 (~ 46 %)

A noticeably higher score, and it feels right. Disco Elysium invites replays to explore radically different Harry builds, dialogues, and narrative layers. Deterministic factors still weigh heavy, yet semi-controlled randomness meaningfully colours each run; botched rolls are narrative fuel, not mere bad luck.

So, what about single-player?

These two titans reveal that solo games always juggle the safety of a scripted journey against the intrigue of unpredictability (thank you, Captain Obvious!). The stronger the desire to tell a specific story and shepherd the player along it, the more we tighten, tune, and trim randomness.

That doesn’t make such games non-replayable. Their replay value more often lies in exploring alternate narrative branches or play styles, not in hoping that “pure RNG” will spin a wholly fresh tale. The entropic budget is spent sparingly, usually just enough to make the first — or second — run rich and unforgettable.

And, she repeats, this is not a flaw. It is a feature of a genre that prizes the quality of a single deep dive over a theoretically infinite, but rarely achievable, variety. Sometimes a story simply has to end.

Roguelike: chaos in the service of eternal life

If single-player titles resemble a flawlessly performed symphony, with every note in its place, roguelikes (and their lighter cousins, roguelites) are more like unbridled jazz improvisations. There is a core theme (the basic mechanics) and a set of instruments (characters, items, enemies), but the melody of each “jam session” (run) depends on the virtuosity of the performer (the player) and the random chords the universe decides to throw in. Here randomness (RNG) is not mere background noise; it is an active member of the ensemble, setting the rhythm and tossing out surprising harmonies. Context (C) may reset at the start of every set, yet it snowballs inside a single composition: every random element, every item drop, every chosen talent radically shifts the sound and direction of the improvisation. Agency (A) is the player’s ability to pick up those motifs, weave them into her solo, make bold on-the-fly decisions, and sculpt a unique piece from chaos. Intervention (I) over that RNG is usually minimal or so delicately woven into the structure that it feels more like choosing a key signature than obeying strict sheet music.

Roguelikes all but shout at the player:

«The world is unfair, full of chance, and luck will abandon you often. Get used to it and learn to survive!»

The famous motto “Losing is fun” is not bravado; it is the genre’s philosophy. Every defeat is a lesson — new knowledge about mechanics, foes, and items. Yet even in this realm of chaos there are limits: if a game devolves into a pure lottery where the player’s input means nothing, interest fades fast. The best roguelikes therefore hand the player levers to engage randomness, to manipulate or cleverly exploit it, if not outright control it. Let’s see how that plays out in two standout examples.

Hades

Supergiant’s masterpiece made the roguelike approachable to a broad audience without sacrificing depth.

• Context (C) – 7 / 10

Each run starts from zero, but new weapon aspects, god boons, and story lines unlock as you progress. Within a run, context builds rapidly — which god appears first, which boon is offered, how it meshes with your weapon and prior upgrades or narrative choices — all of it creates a unique situation. Still, after enough hours the main combinations and patterns become familiar.

• Player Agency (A) – 7 / 10

Zagreus handles responsively; combat demands skill. Choosing room paths, boons, and weapon upgrades are player decisions that directly affect success. You are no mere victim of RNG; you actively craft your build and tactics.

• RNG – 6 / 10

Boons, rooms, enemies, Daedalus upgrades — all are heavily RNG-driven. Each escape attempt feels genuinely distinct. But—

• Intervention (I) – 6 / 10

Here Hades shows its “lite” side. First, there is meta-progression (the Mirror of Night, resources for unlocks). Second, you can influence which gods appear more often via keepsakes. Third, the boon menu typically offers three choices, granting real control. Add second chances from Patroclus or healing from Eurydice, and the game never lets sheer bad luck bury you.

Calculated R ≈ 0.61 (~ 61 %)

A high score, mirroring Hades’ deserved popularity. Strong agency, sizeable yet not feral RNG, and smart control tools (plus narrative momentum) keep the game engaging for dozens — even hundreds — of hours. Still, as with any roguelite that relies on meta-progression, the entropic budget eventually drains: once you unlock everything and see most combos, the adventure ends and you log out for good.

Balatro

A card-based roguelike that rocked the indie scene with deceptive simplicity and staggering depth; poker hands are just the tip of the iceberg.

• Context (C) – 8 / 10

A single Joker, a Tarot or Planet card, a shop voucher — any of these can overhaul your strategy and deck potential. Context snowballs with every ante, every new blind modifier. You continually adapt to what the game deals, striving to build a scoring “engine.”

• Player Agency (A) – 8 / 10

Although draws are random, your decisions — what to buy, what to skip, which combo to play, when to risk a Tarot — matter enormously. Spotting synergies, gauging risk, and pivoting strategy at the right moment are all-important. Agency is sky-high within deck-building.

• RNG – 9 / 10

Card draws, Joker rolls in the shop, some Joker effects — almost unfiltered randomness. The tension never eases because you can’t predict the next turn.

• Intervention (I) – 4 / 10

Very little. Yes, you can skip blinds for cash, and certain Jokers let you tinker with the deck or shop, plus you may inspect remaining deck cards. But largely Balatro is about embracing and outplaying brutal, often “unfair” RNG. If luck deserts you, it really deserts you.

Calculated R ≈ 0.83 (~ 83 %)

Balatro’s sky-high replayability shows in practice. Nearly wild RNG, colossal synergy space, and high build-crafting agency lure players back run after run. Each game is a fresh puzzle, a new challenge. The entropic budget feels inexhaustible: the number of possible situations is astronomical, and safety nets are scarce. The game does not “protect” you — it hurls you into chaos and watches to see if you swim.

So, what about roguelikes?

Roguelikes live and breathe randomness; their entropic budget starts enormous. Yet even here we find a spectrum. Games like Hades nod to a wider audience, weaving in control elements and meta-progression. This tempers pure chaos, making long-term play more comfortable and predictable.

Titles such as Balatro rely almost wholly on raw — and often ruthless — RNG, offering near-endless replayability for those ready to accept its terms and unafraid to lose to misfortune. The trade-off flips: the less control and “help” the designer provides, the higher the potential for unique, unpredictable stories — and the longer the game can surprise. But the entry bar and the player’s resilience must rise as well. The replayability ceiling soars, yet it is not accessible to everyone.

Multiplayer: people as engines of unpredictability

If single-player is a meticulously scored symphony and the roguelike a burst of jazz improvisation, then multiplayer titles are, without doubt, a never-ending, swirling carnival. Here every participant is performer, spectator, and conductor at once. Music blares from every side, the costumes dazzle, and no one can tell which act will erupt around the next corner. The prime source of this festive chaos and boundless variety is the players themselves. A live opponent, an unpredictable ally, an entire feuding guild — they can spin stories and craft unique situations that no procedural generator could dream up.

In multiplayer, Context (C) is not only the current state of a match but the ever-shifting meta-game: player knowledge, accumulated experience, trending tactics, psychological mind-games, even the reputations of individual personalities or teams. Agency (A) hits its peak — every move, every decision, every shot or well-timed call can turn the tide not just for you but for dozens, even hundreds, of carnival-goers. RNG in its pure, algorithmic form often retreats to the background or is carefully calibrated, because the chief generator of unpredictability is the human mind. Designer Intervention (I), meanwhile, aims more at enforcing fair rules and preventing abuse than at “smoothing” the personal experience.

Developers of multiplayer titles tacitly strike a deal with their audience:

«We give you the stage, the props, and the ground rules. What kind of performance you put on is up to you. Astonish one another!»

Any randomness that grants an undeserved edge or wrecks competitive spirit usually sparks uproar. Hence in esports disciplines designers strive to minimise the die-roll’s sway over a match. Does that mean the entropic budget ceases to matter? Hardly — it is simply replenished from another source: the inexhaustible ingenuity, folly, brilliance, and unpredictability of people. Let’s examine two very different yet iconic entries in this “carnival” genre.

Counter-Strike (2 / Global Offensive / etc)

The legendary tactical shooter that has sat atop the esports Olympus for decades.

• Context (C) — 9 / 10

Each map, every round’s economy, previous plays by both teams — all combine to shape a unique decision space. Maps and modes stay constant, yet the micro-context mutates from round to round.

• Player Agency (A) — 9 / 10

Personal skill (aim, movement, grenade line-ups), tactical insight, communication, opponent reads — all directly affect victory. Yes, you’re bound to a role and a weapon pool, but within those limits your impact is enormous. She shaves off one point only because there’s virtually no “character play” — actions decide everything.

• RNG — 1 / 10

Competitive CS chases maximal determinism. Bullet spread exists, but follows learnable patterns. Spawn points vary slightly — nothing drastic. No random events flip a round. The chief “randomness” is the enemy’s choices.

• Intervention (I) — 1 / 10

Essentially none. The game sets its bounds; within them there’s no dynamic handicap. Weapon and map balance come from long tuning, not real-time adjustments. With near-zero RNG, there is little to control.

Calculated R ≈ 0.83 (≈ 83 %)

Despite minimal RNG, Counter-Strike boasts huge replayability. Its entire entropic budget flows from live player interaction. Each match is a fresh chess game where the pieces are people, complete with weaknesses, strengths, and unpredictable tactics. The formula shows that even with vanishing randomness, soaring agency and deep context sustain long-term interest.

World of Warcraft

A monumental MMORPG that has weathered many eras and still gathers millions. She admits her own hands-on time was long ago, so details may have shifted, yet the broad principles stand.

• Context (C) — 8 / 10

Azeroth is vast. Your character’s story, faction, profession, guild, world events, reputation grinds, cleared dungeons and raids — all weave a dense, ever-changing context.

• Player Agency (A) — 7 / 10 (heavily aspect-dependent)

During levelling or questing, agency may feel modest (often you follow set routes). But in PvP, high-end raiding, the economy, and social life, your decisions matter enormously. You might become a raid leader, a market mogul, a famed duelist, or simply the guild clown. Not every slice offers equal freedom, yet the ceiling is high.

• RNG — 8 / 10

Boss loot, craft procs, rare mobs or herbs — chance is everywhere. Some legendary drops come at vanishing odds, pulling players into month-long farms.

• Intervention (I) — 6 / 10

Blizzard has long tamed extremes: bad-luck protection on certain drops, tokens convertible to gear, mechanisms curbing too-rapid or too-slow progress. PvP uses rating queues. Chaos exists, but under watch to keep the economy and power curve intact.

Calculated R ≈ 0.68 (≈ 68 %)

WoW shows high replay potential. As in CS, human factors (social ties, guilds, shared hurdles) carry huge weight — our formula folds them indirectly into Context and Agency. The living world, its lore, and constant updates further contribute. Randomness is important, yet only one pillar of engagement.

So, what about multiplayer?

Multiplayer games are a special case where the entropic budget practically self-replenishes through human unpredictability. Designers often needn’t craft intricate RNG systems — providing a compelling playground and clear rules suffices; players will fill it with unique events and plot twists. The replayability ceiling can be the highest of all genres because the carnival of interaction never stops.

Yet nuances remain: if rules grow too rigid or the meta settles too fast, freshness evaporates. Thus developers keep stoking the carnival — patches, new content, events — injecting their own “controlled chaos” at the meta level. The trick is ensuring the carnival stays fair and thrilling for everyone beneath the masks.

When does the compass lose its bearing?

Our formula, as we’ve seen, copes nicely with typical representatives of each genre. Yet the gamescape is far more diverse, and some projects either break the logic outright or expose its limits. Let’s glance at a few such extremes — some real, some hypothetical — to understand where our tool begins to fray.

• Outer Wilds – The formula might hand it a rather high R (≈ 41 %), which feels odd for a game you “can’t really replay.” If, however, we treat replayability as the urge to keep exploring until the finale, the number starts to make sense: the game keeps surprising you for the duration of that one, singular journey. It’s all about interpretation. Personally, I suspect this is more of a modelling error than a feature.
• Dwarf Fortress / RimWorld – Here the formula cheers, spitting out an off-the-charts R (≈ 93 %), and deservedly so. Sky-high Context and Agency plus nearly feral RNG create an inexhaustible well of unique stories. These titles are living proof that well-tuned chaos breeds depth.
• A linear visual novel – Fairly earns an R close to zero (≈ 3 %). Minimal Context, almost no Agency, and zero RNG leave little reason to return after one read-through. The formula nails this case.
• “The perfect casino” (hypothetical) – Minimal Context and Agency, but maximum “honest” RNG with no control tools. The formula spits out R = 100 %. Absurd? Undeniably — yet, as noted earlier, that may not be a bug. Plenty of people roll the dice for the tenth, the hundredth time; addiction is powerful.
• “One-button sandbox” (hypothetical) – Maximal Context, almost no Agency, zero RNG. Result: a very low R (≈ 10 %). A deep world is useless if you can’t interact with it and it never surprises you.
• “Procedural forest walking sim” (hypothetical) – Endlessly, beautifully generated landscapes. High Context (every corner unique) and maximal RNG (constant generation), but minuscule Agency (you only walk and look). The formula may grant it a healthy R (≈ 10 %), yet in practice the game grows dull fast for lack of meaningful interaction — a clear mismatch.

These examples remind us that every model simplifies reality. Our formula is just one lens through which to view the thorny problem of replayability. It can be a helpful thinking tool, but it will never replace a designer’s intuition — or her sense of what truly hooks players.

Instead of a conclusion — an honest question

So here we are, at the finish line of this — let me risk the word — marathon of thought. I know perfectly well how much has been thrown on the table, how many concepts have intertwined, how many questions remain not merely unanswered but barely articulated. That, I confess, is not an accident. Had this been a classic article I would probably feel obliged to deliver neat take-aways, offer solutions, dot every “i”. Yet the point of this text — its long-suffering history of multiple iterations and ever-growing layers — is the process of searching, of asking questions of myself.

The longer she works in game design, the more a certain feeling hardens inside her, one that might be phrased — Socrates-style, but twisted for a designer’s tongue as:

«All I truly know is that I know nothing about this bottomless well we call player experience»

Not out of false modesty; rather a sober appraisal of the task’s scale. All around are people who claim they can teach you “how to make games that sell” or “how to keep players hooked,” building courses and careers on that certainty. She, by contrast, is certain only of her uncertainty. The deeper she digs, the clearer it becomes how provisional everything is — how every “success story” is a unique confluence of circumstance, talent, luck, and that unruly chaos we can never cage.

«Most revolutionary game designs are not created deliberately; they’re discovered by accident.»
— Tynan Sylvester, Designing Games

Remember the mathematician from the opening joke, the one who carried a bomb onto the plane? At first he was just a vivid symbol of our designerly fear of “bad RNG,” our urge to tame chaos. But the more I mused, the more layered that image became. He stopped being a mere metaphor for control and turned into the embodiment of conscious bias in the systems we craft.

The mathematician was not merely scared of randomness — he tried to game it, injecting his own, absurd yet deterministic, variable into the probability equation. He refused to leave matters to chance, actively shaping them according to his risk logic. He believed in his method even when it mocked common sense.

That’s when it struck me: how many such “bombs,” such deeply rooted yet dubious notions of “the right way,” do we lug around in our profession? How often do we make design choices not on data or deep player psychology but on ossified “best practices,” personal prejudices, or fear of doing things differently? Like that mathematician, we create our own local “truths,” our own “loaded dice,” and live by them.

Why, then, spill so many words and so much effort if there are no ready answers or universal fixes? Perhaps because the very act of untangling, of trying to understand, is the point. It’s my way of thinking aloud. Maybe, for some of you, this stream of consciousness — this attempt to stretch a mathematical owl over the globe of game design — will spark your own reflections. Perhaps you’ll find something that resonates, or you’ll want to argue, brandish your own “bomb,” your own formula, your own angle. Wonderful! Game design is not frozen dogma; it thrives on inquiry, dialogue, doubt, discovery.

If this text has nudged even a few of your neurons, made you ponder how the worlds we play in are built and how we, their makers, try (or refuse) to balance order and chaos, then none of it was in vain. Take it simply as an invitation to ask a timeless, slightly unsettling, yet crucial question for anyone who shapes interactive worlds:

«Is life still a game if the dice are loaded?»

See you where the secrets are hidden → t.me/slepokNTe 👀