The PokerMath Research Group is an independent quantitative research initiative affiliated with the Applied Probability Institute. We engineer deterministic mathematical models, open-access stochastic simulation engines, and game-theoretic benchmarks for imperfect information sequential games, with specialized focus on No-Limit Texas Hold'em and modern poker variant economies.
| Repository | Focus & Domain | Language / Stack | License |
|---|---|---|---|
poker-monte-carlo |
High-throughput stochastic Range vs Range Monte Carlo equity engine | Python 3.11 / Bitwise | MIT |
preflop-equity-matrix |
Academic dataset of 1,326 Texas Hold'em starting hand combinations (21 metrics) | CSV / Open Data | CC-BY-4.0 |
pot-odds-evaluator |
Zero-dependency TypeScript/JavaScript pot odds, break-even equity & Kelly criterion library | TypeScript / ESM | MIT |
research-papers |
Preprints, empirical whitepapers, reproducibility test suites, and BibTeX citations | Markdown / LaTeX | Open Access |
-
Stochastic Equity Convergence: Bitwise evaluation and Monte Carlo simulation scaling under the Law of Large Numbers (
$O(1/\sqrt{N})$ error convergence). - Game Theory Optimal (GTO) Equilibria: Combinatoric range morphology, blocker distribution shifts, and minimum defense frequencies (MDF).
- Capital Growth & Risk of Ruin: Application of the Kelly Criterion, fractional Kelly sizing, and submartingale downswing modeling in finite bankroll regimes.
- Market & Rake Microeconomics: Empirical decomposition of rake drag and player value preservation across global online gaming networks.
All research papers, interactive vanilla JavaScript calculators, and comprehensive glossaries are accessible open-access at pokermath.org:
- Interactive Pot Odds & Equity Calculator: pokermath.org/tools/pot-odds-calculator/
- Expected Value (+EV) Matrix Tool: pokermath.org/tools/ev-calculator/
- 1,326 Preflop Equity Monte Carlo Study: pokermath.org/research/poker-equity-distribution-study/
- Poker Rake & Value Preservation Benchmark: pokermath.org/benchmarks/poker-rake-comparison/
If you utilize our algorithms, simulation code, or datasets in your academic research, please cite:
@article{pokermath2026empirical,
title={Empirical Distribution of Preflop Equities and Multi-Street Variance in No-Limit Texas Hold'em: A 1,326-Combination Monte Carlo Study},
author={{PokerMath Research Group}},
journal={Applied Probability Institute Research Hub},
year={2026},
url={https://pokermath.org/research/poker-equity-distribution-study/}
}