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Parlay Margin Calculator

Quantify the exponential compounding of sportsbook margins across multi-leg accumulators, parlays, and combined wagers.

Parlay Legs & Market Odds

Selections (Legs):
3
Range: 2 to 12 selections

Compounded Parlay Metrics

Modelled Expected Loss
14.26%
Heavy Margin Compounding
Offered Parlay Odds
6.86
Estimated Fair Parlay Odds
8.00
Compound Overround
+16.62%
Expected Return per $100
$85.74
Step-by-Step Margin Escalation Margin %
Read Parlay Compounding Research →

Accumulator Compounding Law

S_i = Σ_j(1/O_ij); E[Return] = ∏(1/S_i); Loss = 1 - ∏(1/S_i)

Assumes independent legs and proportional de-vig probabilities. Overround m_i=S_i-1 implies expected loss m_i/(1+m_i) per leg. These are model estimates, not known true probabilities.

Frequently Asked Questions

What is parlay margin compounding?

Independent legs compound their expected return. Four legs with 5% overround each have modelled expected loss 1 - 1/1.05^4 = 17.73% under proportional de-vig.

How is the compounded parlay margin calculated?

For each complete market, S_i is the sum of inverse odds. Under proportional de-vig and independence, expected return is ∏(1/S_i), expected loss is 1 - ∏(1/S_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. For independent legs, the product of their expected gross-return factors must exceed 1. Every leg being +EV is sufficient but not necessary: 1.20 × 0.95 - 1 = +14%.

What is the difference between parlay margin and house edge?

Compound overround is O_fair/O_offered - 1. Modelled expected loss is 1 - O_offered/O_fair. They use different denominators and are not interchangeable.