Parlay Margin Calculator
Quantify the exponential compounding of sportsbook margins across multi-leg accumulators, parlays, and combined wagers.
Parlay Legs & Market Odds
Compounded Parlay Metrics
Accumulator Compounding Law
Because bookmaker payouts are multiplicative products of rounded odds, every leg compounds the hold rate geometrically: E[Return] = ∏(1 - M_i).
Frequently Asked Questions
What is parlay margin compounding?
When you place a multi-leg parlay, the bookmaker takes a theoretical cut on every single selection. Because odds multiply, the margins do not simply add up — they compound exponentially. A 4-leg accumulator with a standard 5% margin per leg carries an effective combined margin of 18.55%.
How is the compounded parlay margin calculated?
If leg i has a bookmaker margin M_i, the expected return on that leg is (1 - M_i). For n independent legs, the composite expected return is the product ∏(1 - M_i). The overall parlay margin is then M_parlay = 1 - ∏(1 - M_i).
What is a typical sportsbook margin per leg?
Pinnacle and sharp exchanges typically price major markets at 2% to 3.5% margin. Standard retail books (DraftKings, FanDuel, BetMGM, Bet365) operate at 4.5% to 7% on main lines, and up to 8% to 12% on prop bets.
Why are Same Game Parlays (SGPs) mathematically worse?
In Same Game Parlays, selections are correlated. Rather than pricing legs with standard multiplication, sportsbooks apply synthetic copula formulas that bake in severe correlation penalties, often pushing the effective house margin above 25% to 35%.
Can an accumulator or parlay ever be +EV?
Yes, but only if the individual selections possess sufficient positive expected value (+EV) to outpace the compounding margin penalty. If you combine legs with a 6% true mathematical edge, the compounded return can remain positive.
What is the difference between parlay margin and house edge?
Margin (overround) is the percentage of total implied probability exceeding 100%. House edge is the percentage difference between true fair odds and the actual payout offered by the sportsbook: House Edge = (O_fair / O_offered - 1) × 100%.