poker MATH APPLIED PROBABILITY INSTITUTE
APPLIED PROBABILITY INSTITUTE // RESEARCH ARCHIVE

Research Publications

Independent mathematical research, closed-form derivations, and empirical probability studies for sports wagering efficiency.

PILLAR 01 // POT ODDS & EQUITY ANALYSIS
5 DOSSIERS

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.

Core Derivation: Pot Odds = Call / (Pot + Call)
Specialized Spoke Papers (4):
PILLAR 02 // EXPECTED VALUE & DECISION THEORY
5 DOSSIERS

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.

Core Derivation: EV = (Win% × Pot Won) - (Lose% × Amount Risked)
Specialized Spoke Papers (4):
PILLAR 03 // KELLY CRITERION & BANKROLL OPTIMIZATION
5 DOSSIERS

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.

Core Derivation: f* = μ / σ²
Specialized Spoke Papers (4):
PILLAR 04 // COMBINATORICS & RANGE MODELING
5 DOSSIERS

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.

Core Derivation: C(n,k) = n! / (k!(n-k)!)
Specialized Spoke Papers (4):
COMPLETE REPOSITORY // 20 PEER-REVIEWED DOSSIERS

All Mathematical Publications

Browse and search our full curriculum of open-source derivations, staking proofs, and match models.

Pot Odds & Equity Beginner

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.

PM Game Theory Division
30 min read
Expected Value Intermediate

Expected Value in Poker Decisions

PM Game Theory Division
Kelly & Bankroll Intermediate

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.

PM Stochastic & Risk Lab
25 min
Combinatorics Advanced

Combinatorics & Range Analysis in Poker

Advanced poker combinatorics framework for precise range construction, blocker effect quantification, and Nash equilibrium hand analysis.

PM Game Theory Division
45 min
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