Volatility Lab
Three games, one RTP: an interactive look at how volatility shapes a session.
Game mathematics & prototyping
Slot maths, simulated before it ships.
Stellarbeast Studios designs slot game mathematics — RTP models, volatility and hit-frequency targets, bonus-feature maths and the simulations that prove them — from first concept to the PAR sheet a development team builds from.
Fig. 1 — Running RTP, 1,000,000 simulated spins per game
- Low
- Medium
- High
- Target RTP
- 96.00%
- Games
- 3, synthetic
- Spins per game
- 1,000,000
- Shaded band
- 95% range, High
§ 01 — Lab
Where the 96% comes from.
- Concept
- Synthetic data
Every game below returns 96% in the long run. What differs is which wins carry that return — and how rarely they land.
- 0.5× (below stake)
- 1–5×
- 10–50×
- 100× and up
In the high-volatility game, 26 of the 96 points come from wins of 100× or more. A 200-spin session sees even one of those only about 21% of the time.
| Game | RTP | Hit frequency | Std. dev. | Top win | Spins to ±1%* |
|---|---|---|---|---|---|
| Low | 96.00% | 1 in 2.65 | 3.37 | 50× | ≈ 437,000 |
| Medium | 96.00% | 1 in 3.55 | 8.35 | 500× | ≈ 2.7 million |
| High | 96.00% | 1 in 4.82 | 18.38 | 5,000× | ≈ 13 million |
*Spins needed before measured RTP sits within ±1 point of 96% at 95% confidence. Std. dev. is per spin, in multiples of the bet. All figures come from synthetic paytables.
Lab — one session, up close
Every star is a winning spin.
6,000 simulated spins of the high-volatility game. Angle is spin order; distance from the centre is win size, on a log scale. Wins of the same size line up on the same ring.
- Winning spins
- 1,255
- Session RTP
- 72.9%
- Biggest win
- 250×
- Long-run RTP
- 96.00%
The 1,000× and 5,000× rings stay empty this session. Together they carry 10 points of the long-run 96%.
§ 02 — Expertise
What the maths covers.
- 02.1
RTP & paytable design
Paytables, reel strips and symbol weights balanced to RTP, hit-rate and volatility targets, optimised with Excel Solver.
- 02.2
Volatility & hit frequency
Payout distributions shaped to the experience a game is meant to deliver — steady, spiky or in between.
- 02.3
Mechanics & bonus features
Hold & spin, cascades, cluster pays, Slingo and crash games, with buy bonus, ante bet and multiple RTP variants.
- 02.4
Simulation & verification
Monte Carlo simulation in C/C++, with variance analysis and confidence intervals to check every figure, including the development team's build against the model.
- 02.5
PAR sheets & certification
PAR sheets plus game design and maths documents for GLI, NSW, QLD and VLT certification.
- 02.6
Playable prototypes
Games prototyped and play-tested for balance and player experience, then the model fine-tuned.
§ 03 — Selected work
Case studies, cleared one at a time.
Each case study appears once its owner has approved publication. Professional work, original prototypes and concepts are always labelled as such.
§ 04 — Background
Experience.
The maths behind Stellarbeast Studios comes from designing slot games since 2021 — first for land-based casino machines, now for online casino games. Every game is handled end to end: concept, maths model, simulation, PAR sheet, certification documents and a playable prototype, with support through implementation.
- Experience
- Lead and senior game-mathematician roles · land-based and online casino games · since 2021
- Patent
- Co-inventor on a granted US patent for a slot game mechanic
- Mentoring
- Seven game mathematicians mentored; a training programme built for graduate hires
- Mathematics
- B.Sc. (Hons) and M.Sc. Mathematics, University of Delhi · CSIR NET qualified
- Before games
- Five years teaching and writing advanced mathematics
- Tools
- Excel (advanced, incl. Solver), C/C++, Git, Jira, Confluence
§ 05 — Contact
Start a conversation.
Collaborations, projects and roles in game mathematics.
hello@stellarbeaststudios.com LinkedIn