How are parlay odds calculated?

Parlay odds are calculated by multiplying the decimal odds of each leg together. For example, a 3-leg parlay with legs at 1.91, 2.10, and 1.80 has combined decimal odds of 1.91 x 2.10 x 1.80 = 7.22. The payout is your stake multiplied by the combined decimal odds. This multiplicative structure is why parlays are high-risk, high-reward: one losing leg kills the entire bet.

What is a round robin bet?

A round robin is a set of parlays created from all possible combinations of your selected legs at a given parlay size. For example, with 4 legs and 2-leg parlays, you get C(4,2) = 6 separate parlays. Round robins provide insurance: you can still profit even if one or two legs lose, unlike a single parlay where one miss loses everything. The tradeoff is higher total cost since you're placing multiple bets.

What is a correlated parlay?

A correlated parlay combines outcomes that are statistically linked. For example, 'Team A wins' and 'Over 220.5 points' are positively correlated because a winning team often scores more. Sportsbooks typically price parlay legs as independent events, but correlated outcomes occur together more often than independence assumes. This mispricing creates potential +EV opportunities for bettors who can estimate the true correlation.

Why do sportsbooks limit same-game parlays (SGPs)?

Sportsbooks limit SGPs because correlated legs are hard to price accurately. When outcomes within the same game are combined, the true joint probability often differs from the product of individual probabilities. Books add extra margin to SGPs to compensate for model uncertainty, but sharp bettors who understand correlation can still find +EV spots, especially in prop-heavy markets where the book's correlation model is weakest.

What is the hold on a parlay?

Parlay hold (or vig) is the bookmaker's built-in margin. For a single bet, hold might be 4-5%. But parlay hold compounds multiplicatively with each leg. A 4-leg parlay at -110 each has about 18-20% total hold versus ~4.5% on a single -110 bet. This compounding vig is a major reason most parlays are -EV. To calculate parlay hold: find the implied probability from the combined odds, compare it to the true combined probability, and the difference is the hold.

Can you arbitrage parlays?

Yes, parlay arbitrage is possible but rare. It works by combining a parlay at one book with individual bets at other books to guarantee profit. For example, if Book A offers a boosted 2-leg parlay at +600 and the true combined odds are +450, you can hedge the individual legs at sharp books. Correlated parlay arbs are more common: if a book underprices an SGP relative to the true correlated probability, that is a positive expected value opportunity even without hedging.

Parlay Calculator: Free Parlay & SGP Calculator

TL;DR

Parlays multiply your legs' decimal odds together for a single high-risk payout. Round robins split your legs into every possible sub-combination so one missed leg doesn't kill everything. The real edge is in correlated same-game parlays (SGPs): when two outcomes in the same game are statistically linked (like "team wins" + "game goes over"), the true joint probability is higher than what most books price. Our SGP mode quantifies that gap so you can find +EV parlays that most bettors miss.

How Parlay Odds Work

A parlay is a single bet that chains multiple selections together. Every leg must win for the parlay to pay out. The combined decimal odds equal the product of each leg's decimal odds. A 3-leg parlay at 1.91, 2.10, and 1.80 gives you combined odds of 1.91 × 2.10 × 1.80 = 7.22, meaning a $100 stake pays $722.

The catch is compounding vig. A single -110 bet has about 4.5% hold. But a 4-leg parlay of -110 lines carries roughly 18-20% hold because the bookmaker's margin multiplies with each leg. This is why parlays are the most profitable product for sportsbooks and why sharp bettors generally avoid them unless they have a specific edge. Use our hold calculator to see exactly how much vig you're paying.

The Math Behind Round Robins

A round robin generates all C(N, K) combinations from N legs taken K at a time. With 5 legs and 3-leg parlays, you get C(5,3) = 10 separate parlays. If one leg loses, you lose only the parlays containing that leg rather than your entire stake.

The tradeoff is cost. Ten parlays at $10 each costs $100 total. If all 5 legs hit, every parlay pays, and you profit handsomely. If 4 of 5 hit, you still collect on the 4 parlays that don't include the losing leg. Round robins are a risk-management tool: they reduce variance at the cost of lower max payout per dollar risked. Use our Kelly criterion calculator to find optimal sizing.

Correlated Parlays: The Hidden Edge

Most sportsbooks price parlay legs as independent events, meaning P(A and B) = P(A) × P(B). But in same-game parlays, outcomes are often correlated. If you bet "Lakers win" and "LeBron over 28.5 points," those outcomes are positively correlated. When the Lakers win, LeBron is more likely to have scored heavily. The true joint probability is higher than independence assumes.

Our SGP mode uses the correlation formula: P(A∩B) = P(A)×P(B) + ρ × √(P(A)(1-P(A)) × P(B)(1-P(B))), where ρ is the correlation coefficient. A correlation of +0.4 between two 50% outcomes raises the joint probability from 25% to 35%, a massive difference the book might not fully account for.

The key insight: books know correlation exists, so they adjust SGP pricing. But their models are imperfect, especially in prop markets, player performance combos, and situational spots. If you can estimate the true correlation better than the book, you can find +EV SGPs consistently. The edge is in your correlation estimate.

SGP Strategy: Finding Mispriced Correlation

Start by identifying which outcomes in a game are naturally correlated. Some common patterns: a team's moneyline is positively correlated with their players' point totals; totals (over/under) are correlated with pace and opponent defensive rating; first-half results are correlated with full-game results. The stronger the correlation, the more the book's independent pricing model breaks down.

Use this calculator to plug in the book's offered SGP odds, your correlation estimate, and see if the edge is positive. Even a 3-5% edge on SGPs can be highly profitable because the payout multipliers are large. Compare with our EV calculator for individual legs and our odds converter to switch between formats.

Parlay Hold: Why the House Always Wins (Usually)

The hold on a parlay is the cumulative margin baked into the combined odds. For a fair 2-leg parlay of two 50/50 outcomes, fair decimal odds would be 4.00 (2.00 × 2.00). But at -110 each, the combined odds are only 3.65 (1.91 × 1.91), giving the book about 8.75% hold. Add more legs and the hold grows exponentially. A 10-leg parlay at -110 can have over 40% hold.

This is why serious bettors either avoid parlays or focus exclusively on correlated SGPs where the mispricing can overcome the vig. For deeper analysis on finding edges, see our guides on arbitrage betting calculators and what sports arbitrage is.

Examples

Example 1, simple parlay: You like three NBA sides at -110 (1.91 decimal) each. Combined odds: 1.91³ = 6.97. A $50 stake pays $348.36 if all three hit. The implied probability of all three hitting is (1/1.91)³ = 14.36%, but the true no-vig probability (at -105 fair each) would be (1/1.952)³ = 13.42%. The hold is about 6.5%.

Example 2, correlated SGP: You combine "Celtics ML" at 1.50 (implied 66.7%) with "Jayson Tatum over 27.5 pts" at 1.87 (implied 53.5%). Independent combined probability: 35.7%. But these are positively correlated at roughly +0.35. When Boston wins, Tatum usually goes off. True correlated probability: 43.4%. Fair odds: 2.30. If the book offers the SGP at 2.65, your edge is +15.0% and EV is +$15.02 per $100. That's a strong play.

Free Parlay & SGP Calculator

Parlay Results

Round Robin Summary

Correlation Analysis