The Mathematics of Same Game Parlays (SGPs)

The **Same Game Parlay (SGP)** emerged by solving the historical problem of **correlated parlays**, which were previously banned because standard probability models ($P(A \cap B) = P(A) \times P(B)$) could not account for the interdependence of events within a single match. **Key Mathematical Mechanisms:** * **Copula Functions:** Adapted from financial derivatives pricing, Copulas allow bookmakers to map separate marginal distributions (e.g., a player's yardage prop) into a joint probability distribution based on historical correlation matrices. * **Monte Carlo Simulations:** Advanced engines simulate a match thousands of times to determine the frequency of specific combinations (e.g., Team A wins + Player B scores), allowing for granular pricing of complex, multi-variable scenarios. **Economic Impact:** SGPs represent a shift from **price discovery** to **model-based pricing**. Because the correlation coefficients are proprietary and opaque, operators can extract significantly higher margins (20%+) compared to traditional markets, making SGPs the most profitable vertical in modern sports betting.