SlotMath Labs is an independent quantitative research collective operating under the Applied Probability Institute. We engineer deterministic combinatorial models, open-access stochastic simulation engines, and discrete probability benchmarks for modern slot architectures, configurable RTP profiles, and virtual reel mechanics.
| Repository | Focus & Domain | Language / Stack | License |
|---|---|---|---|
slot-rtp-monte-carlo-simulator |
High-throughput Monte Carlo simulation engine (up to 100M spins), Central Limit Theorem convergence, and standard error decay | TypeScript / Python | MIT |
slot-volatility-index-calculator |
Volatility Index ( |
TypeScript / ESM | MIT |
bonus-buy-ev-evaluator |
Mathematical expectation evaluator, Pareto right-skewed payout modeling, dud frequency analysis ( |
TypeScript / ESM | MIT |
research-papers |
Preprints, 100M-spin empirical convergence datasets, commercial operator RTP audit matrices, and verification suites | Markdown / CSV / Python | CC-BY-4.0 |
-
RTP Mechanics & Virtual Reel Strip Invariants: Discrete probability mass functions across virtual strips (
$L_1 \times L_2 \times \dots \times L_k$ ), theoretical vs actual RTP convergence, and turnover velocity capital depletion models. -
Volatility Indices & Dispersion Dynamics: Statistical modeling of slot variance, 90%/95%/99% confidence intervals, standard deviation contraction (
$\sigma / \sqrt{N}$ ), and Gambler's Fallacy refutations. - Feature Buy Economics & Fat-Tail Distortion: Closed-form mathematical derivations of Bonus Buy expected value, variance multiplier acceleration, and absorption barrier ruin probability.
- Bankroll Algorithms & Regulatory Standards: Markov chain ruin models, Doob's Optional Stopping Theorem proofs on negative expectation invariance, and GLI-19/BMM Dieharder CSPRNG certification standards.
All research papers, interactive zero-runtime client-side calculators, and quantitative glossaries are accessible open-access at slotmath.org:
- RTP & Confidence Interval Inspector: slotmath.org/tools/rtp-inspector/
- Slot Volatility & Drawdown Simulator: slotmath.org/tools/volatility-simulator/
- Bonus Buy EV & Variance Distortion Analyzer: slotmath.org/tools/bonus-buy-analyzer/
- Bankroll Decay & Spin Survival Calculator: slotmath.org/tools/bankroll-decay/
- Commercial Operator RTP Audit: slotmath.org/benchmarks/operator-rtp-audit/
If you utilize our algorithms, simulation suites, or datasets in your academic research or applications, please cite:
@article{slotmath2026empirical,
title={Empirical Distribution of Slot RTP, Volatility Indices, and Tail Win Probabilities Across 100 Million Simulated Spins},
author={{SlotMath Labs} and {Applied Probability Institute}},
journal={Applied Probability Institute Research Hub},
year={2026},
url={https://slotmath.org/en/research/slot-volatility-100m-simulation-study/}
}