The Same-Game Parlay Trap: Standard multi-game parlay calculators multiply independent probabilities: P(A and B) = P(A) × P(B). However, in an NFL game, touchdowns are a zero-sum team resource.

If a team scores 3 total touchdowns, every touchdown scored by the RB1 reduces the remaining TD ceiling available for WR1 and TE1. Standard sportsbooks account for this with compounding hold percentages (often 25% to 40% vig on 4-leg TD slips).

Monte Carlo Red Zone Modeling: Each simulation trial first draws team total touchdowns from a Poisson distribution calibrated to team Vegas implied totals. Then each TD opportunity is probabilistically allocated via player-specific red zone target/rush shares.

This reveals the true joint probability of hitting all legs, quantifying the negative correlation between teammates and positive correlation between opposing offensive shootouts.