Here are 6 core formulas hedge funds use to systematically extract alpha - with live charts so you can feel the math, not just read it. Formula 1: LMSR Pricing Model Price_i = e^(q_i/b) / Σ e^(q_j/b) The AMM engine powering every Polymarket contract. The key variable is b - liquidity depth. When b < 50, buying 10 shares moves price by 5%+. That is your arb window before the market corrects. Formula 2: Kelly Criterion f* = (p × odds − (1−p)) / odds Never size a bet on gut feel. Kelly maximizes geometric growth and tells you exactly what fraction of bankroll to risk. One rule: always use half-Kelly in practice. Full Kelly is theoretically optimal and practically ruins you. Formula 3: EV Gap EV = (p_true − price) × (1/price) Only enter when your model beats the market by more than fees. EV > 0.05 is the minimum threshold. Below that, you are paying the spread to feel smart. Formula 4: KL-Divergence D_KL(P‖Q) = Σ P_i × log(P_i / Q_i) Scan correlated markets for probability inconsistencies. Vance at 21% and a correlated candidate at 17% - high KL signals a hedge opportunity. Threshold: > 0.20 is actionable. Formula 5: Kelly Bankroll Simulation B_n = B_0 × ∏ (1 + f×odds)^wins × (1−f)^losses 100 bets. Same edge. Three strategies: full Kelly, half Kelly, quarter Kelly. The difference in drawdown is not linear - it is catastrophic. This chart is why fractional Kelly exists. Formula 6: Bayesian Update P(H|E) = P(E|H) × P(H) / P(E) Update your probability in real time as evidence arrives - a tweet, a poll, a news headline. Static models lose to dynamic ones in fast markets. Start with a prior, update on signal strength, re-evaluate position size via Kelly. The stack that actually works:Data → EV scan → Kelly sizing → Bayesian updates → repeat. Start with $500, backtest 3 months, scale when Sharpe > 1.5