Scattered magenta and violet data points settling toward a distribution curve on a dark plane
Game math & RNG · Vitória, Brazil

Stop guessing at randomness. Start modeling it.

Varianta is a learning portal for the numbers under your game systems — how RNG actually behaves, how drop rates and loot tables get balanced, and what variance does to the way a run feels. We break each one down into formulas you can run in a spreadsheet.

6 modules · video + spreadsheets E[X] worked by hand, not hand-waved
distribution · one drop table peak → μ = 0.14
What you'll learn

Four ideas, run end to end with real numbers.

No prior probability background assumed — we build intuition first, then hand you the formula and the spreadsheet that proves it.

01

How RNG actually worksseeds · PRNGs · uniform → weighted

What a pseudo-random generator really produces, why a fixed seed reproduces a run, and how a flat 0–1 value becomes a weighted pick. You'll build a small weighted picker and see where naive code quietly skews the result.

02

Drop rates & loot tablesweights · expected tries · pity timers

Turn a wish (“this should feel rare, but not cruel”) into weights. We compute expected tries to a first drop, model the long tail, and design a pity timer that guarantees a result by attempt n without breaking the economy.

03

Variance & player experiencespread · streaks · perceived fairness

Two systems can share the same average and feel completely different. We measure spread, model unlucky streaks, and connect variance to the emotional shape of a session — when players read a system as “fair” versus “rigged.”

04

Modeling & simulationMonte Carlo · histograms · sanity checks

Prove a design before it ships. You'll run thousands of simulated runs in a spreadsheet, read the histogram, and sanity-check the math against the sim so a balancing decision rests on evidence, not a hunch.

Var band · ±1σ μ drops / 100 kills
Sample lesson

“Why does 5% feel like 1%?”

A designer sets a boss to drop an item at five percent. Playtesters swear it's broken — most never see it in twenty kills. The math says both sides are right.

At p = 0.05, the chance of seeing nothing in 20 kills is (1 − 0.05)²⁰ ≈ 0.36 — more than a third of players. The average is fine; the spread is what people actually experience. In this lesson we plot that spread, watch the variance band widen, then add a soft pity curve so the unlucky tail gets pulled back in without touching the headline rate.

expected tries to first drop = 1 / p = 1 / 0.05 = 20 · but half of players need > 14, and 1 in 8 needs > 40.

You leave with the spreadsheet that drew this curve, so you can drop your own rate in and watch the shape change.

Tools you'll use

Everything runs in a spreadsheet you already know how to open.

No new engine, no custom app to install. The whole course is built so you can follow along in a spreadsheet and a text editor, then reuse the files on your own game the same afternoon.

/ 01 sheets

Modeling spreadsheets

Pre-built workbooks for weighted tables, expected-tries curves and variance bands. Editable cells, no locked formulas — change a weight and watch every chart recompute.

/ 02 sheets

Monte-Carlo simulator

A spreadsheet that runs ten thousand simulated sessions and plots the histogram, so you can compare your closed-form math against a brute-force result and catch the mistake before players do.

/ 03 ebook

Formula & worksheet ebook

A downloadable reference: every formula from the course with a plain-language sidebar, plus printable worksheets to practice on. It's the thing you'll keep open in a second monitor while you balance.

/ 04 exercises

Practical modeling exercises

Short, real prompts — “make this reward feel rare but reachable,” “tighten this streak” — with a worked solution to check yourself against once you've had a genuine go.

A dark study workspace lit magenta and violet, with monitors showing charts and math sketches
Who teaches it

Built by people who balance systems for a living.

Varianta comes out of a small systems-design practice on the Vitória waterfront. The people behind it have spent years tuning economies and reward tables for live games — and watching designers and engineers talk past each other because one side speaks in feelings and the other in code.

This course is the bridge we wished existed: the intuition a designer needs, in the same language an engineer can implement, grounded in numbers both can check. Every example is one we've actually had to solve on a real build.

6modules, self-paced
40+worked examples
10ksims per exercise
From the field

Designers and devs who now argue with numbers.

Each of these came in balancing systems by feel. They left plotting the spread — and reading their own drop tables like a chart.

I used to set a boss drop to “feels rare” and pray. Now I open the sheet, compute expected tries, and watch the unlucky tail before a single player ever sees it. The pity-timer lesson alone paid for the course — our worst outlier went from 60+ kills to a hard floor at 30.

Flat geometric avatar in magenta and violet on a dark background Mateus Ferreira Systems designer, mid-size studio @mferreira.rolls

Break it down: our designers spoke in vibes, I spoke in code, and nobody could check the other. This course gave us one shared language — weights, variance, a histogram we both trust. First time a balance meeting ended in a number instead of a shrug.

Flat geometric avatar of a person with short hair in violet and magenta on a dark background Valentina Rojas Gameplay engineer, live-ops team @vrojas_dev

The Monte-Carlo sheet caught a bug in my loot table I'd have shipped. My closed-form math said one thing, ten thousand simulated runs said another — turns out I was double-counting a weight. Ran the sim, saw the histogram lean wrong, fixed it in an afternoon.

Flat geometric avatar of a person with round glasses in magenta and violet on a dark background Diego Salazar Indie developer & solo dev @dsalazar.rng

What stuck with me was the variance module. Two reward tables, same average, one that felt fair and one that felt broken — and now I can point at exactly why. I model the spread first, then design the pacing around it. No more guessing at how a run will feel.

Flat geometric avatar of a person with curly hair in violet and magenta on a dark background Camila Andrade Reward & economy designer @camila.variance
Pricing

One clear price. The ebook, or the ebook bundled in.

Lifetime access to the videos, spreadsheets and every update. Pay once — no subscription, no recurring charge.

Course

Game Math & RNG

R$ 590 once
lifetime access · self-paced
  • 6 video modules, watch any time
  • All modeling spreadsheets & the simulator
  • 40+ worked examples and exercises
  • Free updates as the course grows
Start the course
Course + Ebook · best value

Course + Formula Ebook

R$ 740 once
everything above, plus the reference
  • Everything in the course plan
  • The formula-and-worksheet ebook (PDF)
  • Printable practice worksheets
  • Plain-language sidebar for every formula
Get the bundle
Questions

Fair things to ask before you start.

Straight answers, read like a log. Query on the left, resolved value below.

ask[01] Do I need a maths background?

No. We assume you can add, multiply and open a spreadsheet — nothing more. Every idea is built from intuition first, and the notation is introduced slowly, always tied to a concrete game example. If a formula shows up, there's a plain-language version right beside it.

ask[02] Is this for designers or programmers?

Both, and that's the point. Designers get the intuition and the vocabulary to argue for a change with evidence; developers get the models and the spreadsheets to implement it correctly. The examples are chosen so a mixed team can finally reason about the same system in the same terms.

ask[03] What software do I need?

Any spreadsheet app — Google Sheets, Excel or LibreOffice all work. The workbooks are provided in an open format. Nothing else is required; you don't need a game engine or a coding environment to follow along.

ask[04] Is the ebook sold on its own?

For now the ebook comes with the Course + Ebook bundle rather than separately — it's designed to sit next to the lessons, referencing the same examples. If you already own the course, you can add the ebook later; just email us and we'll sort out the upgrade.

ask[05] Is this about anything to do with real-money games?

No. Varianta is strictly educational material about how video-game systems behave — drop tables, reward pacing and variance in the design sense. It is not about money changing hands on a result, and nothing here teaches or promotes that. See our disclaimer for the full note.

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