Parlay Math: How Compounding Vig Destroys Your Edge
Parlay math broken down with 5 worked examples. A 3-leg parlay at standard juice carries 15% vig, not 4.5%. Here is exactly how the compounding works.
How a parlay works
A parlay (called an accumulator in Europe) combines multiple individual bets into a single wager. Every leg must win for the parlay to pay out. If any leg loses, the entire bet loses. The tradeoff: higher potential payout in exchange for lower probability of winning.
The payout calculation is straightforward. Convert each leg to decimal odds and multiply them together.
Three legs at -110 (1.909 decimal each):
Parlay decimal odds = 1.909 x 1.909 x 1.909 = 6.966
A $100 bet at 6.966 decimal returns $696.60 total ($596.60 profit). That looks attractive. The problem is not the payout. The problem is what you are actually paying for it.
How to calculate parlay odds step by step
The process works the same regardless of how many legs you add.
Worked example: 2-leg parlay
Leg 1: -110 (decimal 1.909, implied 52.4%) Leg 2: -150 (decimal 1.667, implied 60.0%)
Parlay odds = 1.909 x 1.667 = 3.182
A $100 bet pays $318.20 total ($218.20 profit).
Now calculate the fair price. De-vig each leg to find the true probability. Assuming standard vig, -110 on a 50/50 market de-vigs to 50.0%. The -150 leg (if the other side is +130) de-vigs to approximately 57.5%.
Fair probability of both winning = 0.50 x 0.575 = 0.2875 (28.75%)
Fair decimal odds = 1 / 0.2875 = 3.478
The book is paying 3.182 instead of 3.478. That gap is the compounded vig. Use the de-vig calculator to strip the margin from each leg before you evaluate any parlay.
Worked example: 3-leg parlay at even odds
Three legs, each a fair 50/50 priced at -110:
Fair probability = 0.50 x 0.50 x 0.50 = 0.125 (12.5%)
Fair decimal odds = 1 / 0.125 = 8.00
Parlay pays = 1.909 x 1.909 x 1.909 = 6.966
The implied probability of the parlay payout: 1 / 6.966 = 14.36%.
True hold = (14.36% minus 12.5%) / 12.5% = 14.9%
A 3-leg parlay at standard juice carries roughly 15% vig. Not 4.5%. Not 13.5%. The vig compounds multiplicatively, not additively.
Why vig compounds instead of adding
Each leg of a parlay slightly inflates the implied probability. When you multiply inflated probabilities together, the inflation compounds at each step.
Think of it this way. Each -110 leg charges approximately 4.5% vig on that individual market. But the parlay payout is calculated from the vigged odds, not the fair odds. So you are multiplying three numbers that are each about 4.5% too low (1.909 instead of 2.00). The shortfall grows geometrically.
Here is the compounding in action across 1 through 6 legs, all at -110 on fair 50/50 outcomes:
| Legs | Fair Odds | Parlay Pays | True Hold |
|---|---|---|---|
| 1 | 2.00 | 1.909 | 4.5% |
| 2 | 4.00 | 3.645 | 9.7% |
| 3 | 8.00 | 6.966 | 14.9% |
| 4 | 16.00 | 13.30 | 20.3% |
| 5 | 32.00 | 25.41 | 25.9% |
| 6 | 64.00 | 48.54 | 31.6% |
By five legs, the house is keeping more than a quarter of the expected value. By six legs, nearly a third. These are not bets. They are donations with extra steps.
Run any combination of legs through the parlay calculator to see the true hold and fair odds side by side.
Same-game parlays: the worst deal in sports betting
Standard parlays at least use transparent market odds. Same-game parlays (SGPs) remove even that transparency.
In a standard parlay, each leg comes from a separate event. The outcomes are independent (or close to it), so multiplying the probabilities is mathematically valid. In an SGP, the legs come from the same game. Player props, totals, and spreads within a single contest are correlated. If the game goes to overtime, multiple legs are affected simultaneously.
Sportsbooks price SGPs using proprietary correlation models. You cannot see the inputs. You cannot verify the assumptions. You have no independent market to benchmark against.
The result: SGP vig commonly runs 20 to 40%, and it can exceed 50% on complex constructions. A 4-leg SGP that looks like it pays 10-to-1 might have fair odds closer to 6-to-1. You would need to be dramatically better than the sportsbook's model to overcome that margin, and the book has more data than you do.
This is why SGPs are the most promoted product on every major sportsbook app. DraftKings, FanDuel, and BetMGM all push SGPs aggressively. The margin is enormous and the customer cannot verify it. If a sportsbook is advertising something heavily, ask yourself who benefits from that marketing spend.
When parlays can be +EV
There is one legitimate scenario where parlays make mathematical sense: correlated outcomes that the book prices as independent.
If event A happening makes event B more likely, and the sportsbook treats them as independent when calculating the parlay payout, the true probability of both hitting is higher than what the book assumes. That correlation gap can overcome the compounded vig.
Example: You believe an NFL team will win AND the game will go over the total. If your model says these outcomes are positively correlated (the team wins by scoring a lot), the true probability of both hitting is higher than the product of their individual probabilities.
Say the book prices each leg independently:
- Team wins: de-vigged probability 60%
- Game goes over: de-vigged probability 55%
- Book assumes joint probability: 0.60 x 0.55 = 33.0%
Your model says the correlation adds 4 percentage points:
- Your estimated joint probability: 37.0%
Book's parlay decimal odds (from their implied 33%): approximately 3.03
Your EV per $100 = (0.37 x $203) minus (0.63 x $100) = $75.11 minus $63.00 = +$12.11
That is a +EV parlay. But finding these requires two things: first, accurate de-vigged probabilities for each leg (the de-vig calculator handles this), and second, a reliable estimate of the correlation between outcomes. Without both, you are guessing. Run the numbers through the EV calculator to confirm the edge exists before placing the bet.
For more on how correlated bets interact, read correlated positions.
Cross-platform parlay comparison: sportsbook vs prediction market
Parlays exist on sportsbooks. Prediction markets do not offer parlays directly. But you can construct synthetic parlays on prediction markets by buying multiple contracts independently.
The math changes significantly when you do this.
Sportsbook parlay: 3 legs at -110
Each leg carries standard vig. The parlay pays 6.966x on fair 8.00x odds. True hold: 14.9%.
Synthetic prediction market parlay: 3 independent contracts
Buy three contracts on Kalshi at $0.50 each (equivalent to a fair 50/50). Kalshi charges 7% x p x (1-p) taker fee, which on a $0.50 contract is $0.0175 per contract.
Effective cost per contract: $0.5175 Combined probability of all three winning: 12.5% Total invested: $100 across the three positions (proportionally sized) Fee drag on $100 deployed: approximately 3.5%
Compare that to the sportsbook's 14.9% hold on the same 3-leg parlay. The prediction market "parlay" costs roughly one quarter of the sportsbook version in fees. The difference compounds further with more legs.
| Structure | 3-Leg Hold | 5-Leg Hold |
|---|---|---|
| Sportsbook parlay (-110 legs) | 14.9% | 25.9% |
| PM synthetic parlay (Kalshi, $0.50) | ~3.5% | ~5.8% |
| PM synthetic parlay (Polymarket, 2% profit) | ~2.0% | ~3.3% |
Polymarket charges only 2% on net profits, making the fee drag even lower. The tradeoff: prediction markets have independent settlement, so partial wins still return capital on the legs that hit. With a sportsbook parlay, one loss wipes the entire ticket.
This structural difference is why cross-platform strategies matter. Read cross-platform edge for more on exploiting pricing gaps between sportsbooks and prediction markets. The fee calculator shows exactly how platform fees affect your breakeven on any contract.
Worked example: 4-leg NFL Sunday parlay
Four NFL sides, all -110:
Sportsbook parlay odds: 1.909^4 = 13.30 Fair odds: 2.00^4 = 16.00 Hold: (1/13.30 - 1/16.00) / (1/16.00) = 20.3%
On $100, the sportsbook keeps $20.30 in expected value. The same four outcomes bought as individual Kalshi contracts would cost roughly $4.70 in fees on $100 deployed. That is a $15.60 difference in expected cost for the same set of outcomes.
Live parlay pricing: how in-play odds change the math
Live parlays add a layer of complexity that most bettors ignore. When you build a parlay with live legs, the vig on each leg is typically higher than pre-game because sportsbooks widen their margins during in-play betting to account for information asymmetry.
A standard pre-game NFL side at -110 carries 4.5% vig per leg. The same market live often prices at -115 to -120, bumping per-leg vig to 6.5-9.1%. That difference compounds fast across multiple legs.
Worked example: 3-leg parlay, pre-game vs live
Pre-game (all -110): Parlay odds: 1.909^3 = 6.966. Fair odds: 8.00. Hold: 14.9%.
Live (all -115): Decimal odds per leg: 1.870 Parlay odds: 1.870^3 = 6.539. Fair odds: 8.00. Hold: 22.3%.
Live (all -120): Decimal odds per leg: 1.833 Parlay odds: 1.833^3 = 6.161. Fair odds: 8.00. Hold: 29.8%.
The jump from 14.9% to 29.8% hold is the difference between a bad bet and a terrible one. Sportsbooks promote live parlays because the wider spreads generate even more margin than standard parlays.
One alternative: build synthetic parlays on prediction markets where the fee structure does not change based on timing. Kalshi charges the same 7% x p x (1-p) taker fee whether you trade pre-event or during the event. Read live arbitrage betting for strategies that exploit the pricing gap between live sportsbook odds and prediction market prices.
How to evaluate any parlay before placing it
Before placing any parlay, run through this 5-step process:
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De-vig each leg individually. Get the true implied probability of each outcome using the de-vig calculator. If you do not know the true probability, you cannot evaluate the parlay.
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Check for correlation. Are the legs from different events (independent) or the same event (correlated)? If independent, multiply the de-vigged probabilities. If correlated, you need a correlation estimate.
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Calculate fair odds. Fair parlay decimal odds = 1 / (product of true probabilities). This is what the parlay should pay with zero vig.
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Compare to actual payout. If the parlay pays less than fair odds (it almost always will), calculate the hold percentage. If the hold is 15%+, the math is working heavily against you.
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Calculate EV. Use the EV calculator with your probability estimate and the actual parlay odds. If EV is negative, do not place the bet. If EV is positive, size it with Kelly Criterion.
Most parlays fail at step 4. The compounded vig makes the payout too low relative to the true probability. The only parlays that survive the full evaluation are correlated legs where the book underestimates the correlation, or lines where you have a significant edge on the individual legs that survives the compounding.
Parlays are the most profitable product sportsbooks sell. The hold percentage is 2 to 5 times higher than straight bets. The marketing spend tells you everything: if books are giving you parlay boosts and parlay insurance, it is because the base product is so profitable for them that they can afford to give back a fraction and still come out ahead.
This does not mean every parlay is a bad bet. It means the default is a bad bet, and the burden of proof is on you to show why a specific parlay overcomes the compounded vig. That proof requires math: de-vigged probabilities, correlation estimates, and an EV calculation. Without those numbers, you are just multiplying hope.
For the foundation of everything above, read what is vig to understand how the house margin works at the single-bet level. Once the vig mechanics are clear, expected value explained shows you how to determine whether any bet, parlay or straight, is worth placing. If you find a +EV parlay, bankroll turnover explains why your sizing and frequency matter as much as the edge itself.
New to sports betting odds? Start with how to read odds for the fundamentals of American, decimal, and fractional formats. For a broader view of every formula you need, sports betting math ties the complete system together. And if you want to understand how the over/under total works as a parlay leg, read what does over/under mean for the math behind totals pricing.
Frequently asked questions
- How does a parlay work?
- A parlay combines multiple bets into one. All legs must win for the bet to pay out. The payout is calculated by multiplying the decimal odds of each leg together. Higher potential payout, but lower probability of winning and significantly more vig.
- How do you calculate parlay odds?
- Convert each leg to decimal odds and multiply them together. Three legs at -110 (1.909 decimal) produce parlay odds of 1.909 x 1.909 x 1.909 = 6.966. A $100 bet at those odds returns $696.60 total.
- Why is the vig on parlays so much higher than straight bets?
- Because vig compounds multiplicatively across legs. Each leg carries roughly 4.5% vig at -110. But a 3-leg parlay does not carry 13.5% vig. It carries approximately 15%. A 5-leg parlay carries about 26%. The compounding effect makes every additional leg disproportionately more expensive.
- Are same-game parlays a worse deal than regular parlays?
- Yes. Regular parlays use transparent market odds from independent events. Same-game parlays use proprietary correlation models where the sportsbook controls the assumptions. The embedded vig is typically 20 to 40%, sometimes higher, and you have no independent market to verify the pricing.
- Can a parlay ever be a good bet?
- Only if the legs are correlated in a way the sportsbook has not fully priced. If event A makes event B more likely and the book treats them as independent, the true joint probability exceeds the book's estimate. This can overcome the compounded vig. But finding and verifying these opportunities requires rigorous math.
- How much vig is on a 4-leg parlay?
- A 4-leg parlay at standard -110 odds carries approximately 20.3% vig. That is roughly 4.5 times the vig on a single straight bet, not 4 times, because the margin compounds multiplicatively at each leg.
- Is it cheaper to build a parlay on prediction markets?
- Yes. A synthetic 3-leg parlay built from individual prediction market contracts costs roughly 3.5% in fees on Kalshi and 2% on Polymarket. The same 3-leg sportsbook parlay at -110 carries 14.9% vig. The tradeoff is that prediction market legs settle independently, so partial wins return capital.