CrashMath Labs is an independent quantitative research collective operating under the Applied Probability Institute. We engineer deterministic cryptographic verification suites, discrete probability models, stochastic ruin simulators, and empirical machine learning benchmarks for high-frequency crash game protocols and multiplier commitment schemes.
| Repository | Focus & Domain | Language / Stack | License |
|---|---|---|---|
provably-fair |
Cryptographic Provably Fair verification suite using W3C Web Crypto API (HMAC-SHA256) | JavaScript / TypeScript | MIT |
crash-predictor-benchmark |
Empirical ML benchmark evaluating LSTM, XGBoost, and Markov models against hash chains | Python 3.10+ / ML | MIT |
monte-carlo-sim |
High-throughput Monte Carlo risk simulator proving asymptotic Gambler's Ruin across 1M rounds | Python 3.10+ / NumPy | MIT |
research-papers |
Preprints, LaTeX sources, 50,000-round empirical hash datasets, and verification suites | LaTeX / Python / CSV | CC-BY-4.0 |
- Cryptographic Commitment & Provable Fairness: Deterministic verification of HMAC-SHA256 commitment schemes, 52-bit mantissa deconstruction, and hash-chain reverse preimage resistance ($\text{Hash}n = \text{SHA256}(\text{Hash}{n+1})$).
-
Serial Independence & Martingale Impossibility: Rigorous empirical proof via Ljung-Box autocorrelation (
$Q(20) = 18.42, p = 0.56$ ) and Wald-Wolfowitz runs tests ($Z = 0.42, p = 0.67$ ) establishing that multiplier sequences form memoryless white-noise processes. -
Empirical Refutation of Machine Learning Predictors: Benchmarking deep sequence architectures (LSTM, GRU) and gradient boosted trees (XGBoost) against 50,000 cryptographically confirmed rounds, demonstrating convergence to pure random walk baselines (
$\text{ROC-AUC} \in [0.4998, 0.5004]$ ). -
Stochastic Absorption & Asymptotic Capital Ruin: Application of Doob's Optional Stopping Theorem and Brownian motion with negative drift (
$\mathbb{E}[X] = -0.03$ ), proving that progressive staking systems (Martingale, Fibonacci, d'Alembert) yield asymptotic certainty of ruin ($P(\text{Ruin}) \to 1.00$ ).
All research papers, empirical verification datasets, and interactive zero-runtime JavaScript tools are accessible open-access at crashmath.org:
- Provably Fair Hash Verifier: crashmath.org/tools/hash-verifier/
- Predictor Bot Detector & ML Benchmark: crashmath.org/tools/predictor-detector/
- Expected Value (+EV) & House Edge Tool: crashmath.org/tools/ev-calculator/
- Bankroll & Monte Carlo Terminal: crashmath.org/tools/monte-carlo-terminal/
- 50,000-Round Empirical Study (PDF): crashmath.org/papers/provably-fair-empirical-study-2026.pdf
If you utilize our algorithms, cryptographic verification suites, or empirical datasets in your research or applications, please cite:
@techreport{crashmath2026empirical,
title={Empirical Evaluation of 50,000 Provably Fair Rounds: Autocorrelation, House Edge Invariance, and Resistance to Machine Learning Predictors},
author={{CrashMath Quantitative Research Labs}},
institution={CrashMath Quantitative Research Labs and Applied Probability Institute},
number={CRASHMATH-TECH-2026-04},
year={2026},
url={https://crashmath.org/papers/provably-fair-empirical-study-2026.pdf}
}