Research Publications
Independent mathematical research, closed-form derivations, and empirical probability studies for sports wagering efficiency.
Pot Odds, Equity Fundamentals & The Rule of 2 and 4
Mathematical foundations of poker profitability. Explores the relationship between pot odds ratios, required equity calculations (Risk / (Risk + Reward)), and probabilistic outs estimation using hypergeometric distributions.
Pot Odds = Call / (Pot + Call) Expected Value (EV) Modeling & Decision Trees in Poker
Formal application of Expected Value: EV = (P(Win) × Win Amount) - (P(Loss) × Loss Amount). Demonstrates multi-street EV calculations, fold equity dynamics, and the exact mathematical thresholds for profitable bluffs and calls.
EV = (Win% × Pot Won) - (Lose% × Amount Risked) Kelly Criterion, Variance Analysis & Poker Bankroll Risk Models
Advanced application of the Kelly Criterion to poker bankroll management. Features risk-of-ruin equations, standard deviation modeling for win rates (bb/100), and probabilistic analysis of downswing duration.
f* = μ / σ² Combinatorics, Card Removal & Range Morphology
Quantitative breakdown of the 1,326 hole card combinations and 19,600 flop textures. Explores blocker effects on opponent frequencies and range-vs-range equity distribution mapping.
C(n,k) = n! / (k!(n-k)!) All Mathematical Publications
Browse and search our full curriculum of open-source derivations, staking proofs, and match models.
Pot Odds & Equity Fundamentals: The Mathematical Core of Poker
Master the foundational mathematics of poker. Learn how to calculate pot odds, determine required equity, and use the Rule of 2 and 4 to make profitable decisions at the table.
Expected Value in Poker Decisions
Bankroll Management & Kelly Criterion for Poker
Learn the rigorous mathematical foundation of poker bankroll management, including the Kelly Criterion adaptation for poker, Risk of Ruin formulas, and practical buy-in rules.
Combinatorics & Range Analysis in Poker
Advanced poker combinatorics framework for precise range construction, blocker effect quantification, and Nash equilibrium hand analysis.