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Parlay bets: why the margin grows with each selection
In a parlay, the odds are multiplied, and so is what the house keeps. With one selection from the example, the house keeps 5.6% of the amount bet; with 6 selections, 32.2%. The total odds grow much faster than the average return.
The math
total odds = o₁ × o₂ × … × oₙ
return = d₁ × d₂ × … × dₙ
dᵢ is the theoretical payout for each match (1 / the sum of its implied probabilities). House keeps = 1 − return.
The parlay's margin, measured as in the margin calculator, is s₁ × s₂ × … × sₙ − 1 (sᵢ: sum for each match): with the 6 selections, 47.5%. Both figures grow together.
The margin ladder
each row adds one selection
- 1
River - Talleres · home at 1.72
- Total odds
- 1.72
- All correct
- 1 in 1.8
- House keeps
- 5.6%
- Return from $ 1,000
- $ 944
- 2
Boca - Lanús · home at 1.95
- Total odds
- 3.35
- All correct
- 1 in 3.8
- House keeps
- 11.3%
- Return from $ 1,000
- $ 887
- 3
Estudiantes - Vélez · home at 2.30
- Total odds
- 7.71
- All correct
- 1 in 9.3
- House keeps
- 17.1%
- Return from $ 1,000
- $ 829
- 4
Rosario Central - Newell's · draw at 3.00
- Total odds
- 23.14
- All correct
- 1 in 29.9
- House keeps
- 22.7%
- Return from $ 1,000
- $ 773
- 5
San Lorenzo - Huracán · away at 2.95
- Total odds
- 68.27
- All correct
- 1 in 94.4
- House keeps
- 27.7%
- Return from $ 1,000
- $ 723
- 6
Belgrano - Instituto · home at 2.05
- Total odds
- 139.95
- All correct
- 1 in 206.4
- House keeps
- 32.2%
- Return from $ 1,000
- $ 678
Six example Liga Profesional matches with made-up odds, not from a real site. The bar is what the house keeps, cumulative; “return” is the long-run average if the odds without margin were the true probabilities.
Calculate your parlay
decimal odds, from 1 to 8 selections
How it is calculated, step by step (with the three example selections)
- Total odds: 1.72 × 1.95 × 2.30 = 7.71; with $ 1,000 you collect $ 7,714 if all three win
- Selection 1: 1 / 1.72 + 1 / 3.60 + 1 / 5.00 = 1.0592; payout 1 / 1.0592 = 94.41%
- Selection 2: 1 / 1.95 + 1 / 3.25 + 1 / 4.10 = 1.0644; payout 1 / 1.0644 = 93.95%
- Selection 3: 1 / 2.30 + 1 / 3.10 + 1 / 3.20 = 1.0699; payout 1 / 1.0699 = 93.47%
- Return: 94.41% × 93.95% × 93.47% = 82.91%; the house keeps 1 − 82.91% = 17.09%
- All three correct, no margin: 54.89% × 48.18% × 40.64% = 10.75%, or 1 in 9.3
What to know
High odds are not an opportunity
With the 6 selections in the example, the total odds are 139.95: $ 1,000 would pay $ 139,955. But getting all of them right happens 1 time in 206, and in the long run $ 678 comes back for every $ 1,000.
What the calculation assumes
That the matches are independent and that the odds without margin are the true probabilities. Neither is always true; that is why the result is a long-run average, not a prediction. If gambling has stopped being a game, the helpline is below.
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