Parlay Calculator

How Parlay Odds Are Calculated

Parlay odds are computed by multiplying the decimal odds of each leg. This multiplication reflects the compounding probability requirement: all legs must win.

Parlay Decimal Odds = Leg₁ × Leg₂ × Leg₃ × ... × Legₙ

Example: 3-leg parlay
- Leg 1: +110 (decimal 2.10)
- Leg 2: -120 (decimal 1.83)
- Leg 3: +150 (decimal 2.50)

Parlay Odds = 2.10 × 1.83 × 2.50 = 9.61
American Odds = +861

$100 wager pays out $961 ($861 profit)

Why multiplication?

• Each leg's outcome is independent (in theory)
• Probability of all events occurring = P₁ × P₂ × ... × Pₙ
• Since odds = 1/probability, multiplying odds compounds the requirement

True Probability vs Parlay Pricing

The fundamental problem with parlays: bookmaker vig compounds on every leg. Each individual bet typically has 4-5% vig, and this disadvantage multiplies across legs.

Example: 3-leg parlay, all at -110 odds
Individual leg implied probability: 52.38%
Individual leg true probability (no-vig): 50%

Parlay implied probability: 52.38%³ = 14.37%
True probability (if fair 50/50): 50%³ = 12.50%

Fair parlay odds: 1/0.125 = 8.00 (decimal) = +700
Book offers: 1/0.1437 = 6.96 (decimal) = +596

Edge lost to vig: +700 vs +596 = 14.9% house edge!

As you add more legs, the vig compounds exponentially. A 5-leg parlay at -110 odds carries approximately 25% house edge.

Expected Value of Parlays

Unless you have identified a +EV edge on every single leg, parlays are almost always -EV. The math is unforgiving:

Scenario 1: No edge (50% true win rate on -110 legs)
3-leg parlay EV = (0.50³ × $596) - (0.875 × $100) = -$12.50
Single bets EV = (0.50 × $91) - (0.50 × $100) = -$4.50 each, -$13.50 total

→ Parlay is slightly better than 3 separate -110 bets, but both are -EV

Scenario 2: Small +EV edge (55% true win rate, -110 odds)
3-leg parlay EV = (0.55³ × $596) - (0.834 × $100) = +$16.41
Single bets EV = (0.55 × $91) - (0.45 × $100) = +$5.05 each, +$15.15 total

→ Parlay is +EV but LESS profitable and HIGHER variance

Key insight: Parlays magnify variance while typically reducing EV. Even with edges on every leg, parlays underperform sequential betting due to Kelly Criterion principles.

Correlation: The Parlay Killer

Standard parlay calculations assume independence—the outcome of one leg doesn't affect others. This assumption breaks down in same-game parlays (SGPs) and correlated markets.

Positive correlation (SGP example):

Parlay: "Team A wins" + "Team A covers -7.5 spread"

Standard calculation assumes independence:
- P(Team A wins) = 70%
- P(Team A -7.5) = 50%
- Combined = 70% × 50% = 35%

Reality with correlation:
- If Team A wins, they're more likely to cover
- True combined probability ≈ 45-48%

Sportsbook prices SGP at ~38% implied (less favorable than 35%!), knowing:
1. You're overestimating the true probability using independence
2. Correlation makes the bet less valuable than it appears

Negative correlation example:

Parlay: "Over 220 total points" + "Underdog +10.5"

These outcomes are negatively correlated:
- High-scoring games favor favorites (they pull away)
- Close games (underdog covers) tend to be lower-scoring

Standard odds overvalue this parlay because correlation works against you

Rule of thumb: Any parlay involving the same game, same team, or related markets (e.g., team total + game total) has significant correlation. Standard multiplication doesn't apply.

When Parlays Make Sense

Despite the mathematical disadvantages, there are legitimate use cases for parlays:

1. Entertainment Value

If you're betting for fun rather than profit, parlays offer excitement. A $10 parlay can turn into $500, providing hours of entertainment across multiple games. Just recognize it as -EV entertainment spending, not investing.

2. Promotional Offers

Example: "Parlay insurance" promo
- Book refunds your stake (as bonus) if exactly 1 leg loses
- This dramatically improves parlay EV
- 3-leg parlay at -110 becomes +EV with 1-leg insurance

Original 3-leg EV (50% each leg): -$12.50
With insurance (refund if 2/3 hit): +$8.75

Strategy: Use insurance on 3-4 leg parlays with moderate odds (-120 to +120)

3. Correlated Edges

If you've identified a correlated betting opportunity where outcomes aren't independent, parlays can capture value books misprice:

Example: NFL game script correlation
Research suggests: When Team A's defense is elite AND opponent has weak run game,
games tend to be low-scoring AND favorites cover

Parlay: Favorite -7 + Under 42.5
- Standard pricing assumes independence
- Correlation actually makes this MORE likely than independent odds suggest
- Book prices as independent → you have +EV

4. Bankroll Constraints

If you have a small bankroll but want exposure to multiple +EV opportunities, a parlay lets you bet less per leg while maintaining action. This is suboptimal from a Kelly perspective, but practical for recreational bettors.

Common Parlay Mistakes

Mistake 1: Parlaying -EV legs

"If I parlay three -110 bets, I get better odds than betting them separately." Technically true, but you're still -EV on all three. Compounding -EV doesn't create +EV—it just increases variance while losing money slower than three separate bets.

Mistake 2: Treating SGPs like independent parlays

Same-game parlays are priced by sportsbooks using correlation models. The odds offered already account for correlation (and then some). You're not "outsmarting the book" by identifying correlation—they priced it in and then shaded it further against you.

Mistake 3: Chasing losses with parlays

Scenario: Down $500, need to "get back to even"
Bad reasoning: "$50 on a 10-leg parlay at +10000 can win $5000"
Reality:
- 10-leg parlay (even at +EV per leg) has <1% hit rate
- This is essentially throwing away $50
- Better: Make disciplined +EV bets and slowly grind back

Bankroll recovery should be systematic, not lottery-style

Mistake 4: Adding "safe" legs to boost odds

"I'll add -500 favorite to my parlay for a little extra juice." Each leg compounds vig. That -500 leg (83.3% implied, ~80% true) reduces your parlay EV more than it increases payout. Every leg must be +EV or you're sacrificing expected value for variance.

Practical Examples

Example 1: NFL 3-Team Parlay

Legs:
1. Patriots -3.5 at -110 (you estimate 58% win probability)
2. Cowboys +7 at -105 (you estimate 52% win probability)
3. Over 47.5 in Packers/Lions at -115 (you estimate 51% win probability)

Individual leg EV:
1. (0.58 × $91) - (0.42 × $100) = +$10.78
2. (0.52 × $95) - (0.48 × $100) = +$1.40
3. (0.51 × $87) - (0.49 × $100) = -$4.63

Problem: Leg 3 is -EV! Parlaying it destroys your edge.

Parlay odds: 2.10 × 2.05 × 2.13 = 9.17 (+817 American)
True combined probability: 0.58 × 0.52 × 0.51 = 15.37%
Parlay EV: (0.1537 × $817) - (0.8463 × $100) = +$41.08

Separate bets EV: $10.78 + $1.40 - $4.63 = +$7.55

→ Skip leg 3, bet legs 1 & 2 separately for +$12.18 EV

Example 2: NBA 5-Leg Parlay with Insurance

Promo: "Parlay insurance up to $50—if exactly 1 leg loses, get refund"

5 legs, all -110 (you estimate 52% on each):
Standard 5-leg EV: (0.52⁵ × $2496) - (1 - 0.52⁵) × $50 = +$16.53

With insurance:
- Hit all 5: 0.52⁵ = 3.8% → win $2496
- Hit 4/5: 5 × (0.52⁴ × 0.48) = 33.5% → refund $50
- Hit 3 or fewer: 62.7% → lose $50

EV = (0.038 × $2496) + (0.335 × $0) - (0.627 × $50) = +$63.45

→ Promo turns -EV parlay into strong +EV bet!

Parlay Strategy Recommendations

• Default to separate bets: Unless you have a specific reason (promo, correlation edge), individual bets are superior
• Never parlay -EV legs: If you wouldn't bet it alone, don't add it to a parlay
• Limit parlay size: 2-3 legs maximum for +EV parlays; house edge explodes beyond that
• Exploit promotions: Parlay insurance, odds boosts, and risk-free bets can flip parlays to +EV
• Avoid same-game parlays: Books are sophisticated with correlation pricing; you're unlikely to find edges
• Calculate true probability: Always multiply your estimated win probabilities to see real combined chance
• Track results separately: Don't let one big parlay win bias you toward -EV betting patterns

Bottom line: Parlays are fun but mathematically inferior to sequential betting in almost all scenarios. If you do parlay, make sure every leg is +EV and keep parlay size small.