Parlay Odds Calculator
A parlay (also called an accumulator, combo bet, or multi-bet) combines multiple selections into a single wager. While parlays offer tempting high payouts, they are mathematically one of the worst bets available because winning probability decreases exponentially while the house edge compounds with each added leg.
This calculator demonstrates the mathematics behind parlay betting, showing how combining bets drastically reduces your chances of winning. Understanding these probabilities is essential for anyone researching sports betting mathematics or evaluating legal betting options like Sports Toto in South Korea. For additional context on probability theory, see Encyclopedia Britannica's guide to probability theory.
Legal Notice for Korean Readers
In South Korea, only Sports Toto offers legal parlay-style betting for citizens. Private sports betting and offshore gambling are illegal under Articles 246-249 of the Criminal Act. This tool is for educational purposes to understand gambling mathematics, not to encourage illegal betting activity.
Build Your Parlay
Add legs to your parlay to see how the combined probability and house edge change. Each leg reduces your overall chances of winning.
Quick Add Common Bet Types:
Parlay Analysis
Win Probability
Parlay Odds
Potential Payout
House Edge Analysis
Common Parlay Scenarios
Click a scenario to see detailed probability analysis. These demonstrate why parlays become increasingly unfavorable as legs are added.
2-Leg "Easy" Parlay
Two -110 point spread bets. Common "beginner" parlay that seems safe but still has ~25% win rate.
4-Leg Standard Parlay
Four -110 bets on spreads/totals. Popular format but only ~6% chance of winning.
6-Leg Longshot Parlay
Six mixed bets including underdogs. Less than 2% win probability despite huge potential payout.
10-Leg "Sucker" Parlay
Ten -110 bets. Demonstrates how even "safe" bets compound to nearly impossible odds (~0.1%).
"Safe" Heavy Favorites Parlay
Four heavy favorites at -300. Shows why even "sure things" are risky in parlays.
Scenario Analysis
Win Probability
Parlay Decimal Odds
House Edge
Parlay Probability Reference
This table shows how win probability decreases as legs are added, assuming each leg has a 50% (even money) chance of winning.
| Legs | Win Probability | Odds Against | Typical Payout | Fair Payout | House Edge |
|---|---|---|---|---|---|
| 2 | 25.00% | 3 to 1 | +260 | +300 | ~10% |
| 3 | 12.50% | 7 to 1 | +600 | +700 | ~12.5% |
| 4 | 6.25% | 15 to 1 | +1200 | +1500 | ~15% |
| 5 | 3.13% | 31 to 1 | +2400 | +3100 | ~17.5% |
| 6 | 1.56% | 63 to 1 | +4500 | +6300 | ~20% |
| 7 | 0.78% | 127 to 1 | +9000 | +12700 | ~22% |
| 8 | 0.39% | 255 to 1 | +17500 | +25500 | ~24% |
| 10 | 0.10% | 1023 to 1 | +75000 | +102300 | ~27% |
Understanding American Odds
American odds are displayed as positive or negative numbers:
- Negative odds (-110): Amount you must bet to win $100. -110 means bet $110 to win $100.
- Positive odds (+150): Amount you win on a $100 bet. +150 means win $150 on a $100 bet.
Negative:
1 + (100 / |odds|) → -110 = 1.909Positive:
1 + (odds / 100) → +150 = 2.50
Negative:
|odds| / (|odds| + 100) → -110 = 52.38%Positive:
100 / (odds + 100) → +150 = 40.00%
Why Parlays Are Mathematically Unfavorable
Parlays compound the house edge from each individual leg. According to research from the UNLV International Gaming Institute, the effective house edge on parlays typically ranges from 10% for 2-leg parlays to over 25% for larger parlays.
The key insight is that while payouts increase linearly with risk, the probability of winning decreases exponentially. For comprehensive analysis of gambling mathematics, the National Council on Problem Gambling provides resources explaining why the house always maintains its mathematical edge.
The Compounding Problem
Consider this: A sportsbook might offer -110 odds on each leg (4.55% edge per bet). For a 4-leg parlay:
- Single bet EV: -4.55%
- 4-leg parlay EV: Not 4 × -4.55% = -18.2%, but actually worse due to how payouts are calculated
- The "vig" (house commission) is built into the parlay odds, compounding the disadvantage
How Parlay Mathematics Works
Understanding parlay mathematics reveals why bookmakers love offering these bets. The fundamental formula for parlay probability is straightforward multiplication of individual probabilities:
P(parlay) = P(leg₁) × P(leg₂) × P(leg₃) × ... × P(legₙ)
For example, if you have three bets each with a 50% chance of winning:
- Leg 1: 50% = 0.50
- Leg 2: 50% = 0.50
- Leg 3: 50% = 0.50
- Parlay probability: 0.50 × 0.50 × 0.50 = 0.125 (12.5%)
Your three "coin flip" bets now have only a 1-in-8 chance of winning. This exponential decrease in probability is why parlays are so profitable for bookmakers.
The Hidden House Edge in Parlays
Standard sports betting odds of -110 already include a 4.55% house edge. When these are combined in parlays, the edge compounds. Research published in the Journal of the American Statistical Association has demonstrated that parlay betting represents one of the highest-margin products offered by sportsbooks.
Here's a detailed breakdown:
| Bet Type | True Win Rate | Implied by Odds | Edge on Bet |
|---|---|---|---|
| Single -110 bet | 50.00% | 52.38% | 4.55% |
| 2-leg parlay (-110 each) | 25.00% | 27.44% | ~9% |
| 3-leg parlay (-110 each) | 12.50% | 14.37% | ~13% |
| 4-leg parlay (-110 each) | 6.25% | 7.53% | ~17% |
Why People Still Play Parlays
Despite the mathematics clearly favoring the house, parlays remain popular due to several psychological factors:
- Excitement of large payouts: The potential for a small bet to yield a large return is emotionally appealing
- Entertainment value: Following multiple games creates extended engagement
- Illusion of control: Bettors believe their "expertise" in picking multiple winners overcomes the math
- Near-miss effect: Coming close (hitting 4 of 5 legs) encourages continued play
- Confirmation bias: Remembering wins while forgetting the many losses
These cognitive biases are explained in detail in our Gambling Fallacy Analyzer tool. Understanding these psychological traps is crucial for making informed decisions about gambling.
Parlays in the Korean Context
In South Korea, Sports Toto offers legal multi-game betting options similar to parlays. The "Proto" product allows bettors to combine multiple game predictions. However, the same mathematical principles apply: more legs mean lower probability of winning and higher effective house edge.
Illegal offshore sportsbooks also target Korean bettors with parlay promotions, but participating in these violates Korean gambling law and can result in serious legal consequences including fines and imprisonment.
Responsible Gambling Considerations
If you choose to bet parlays legally, consider these guidelines:
- Treat parlay bets as entertainment with a known cost, not an investment
- Never bet more than you can afford to lose completely
- Understand that winning parlays are rare events, not expected outcomes
- Use our Budget Calculator to set limits before betting
- If gambling causes financial stress or relationship problems, seek help from the Korean Center on Gambling Problems (1336)
Related Tools
Explore other educational tools to understand gambling mathematics:
- Probability Calculator - Calculate true odds and expected value
- House Edge Calculator - Calculate expected losses from any casino game
- Odds Converter - Convert between decimal, fractional, and American odds
- Fallacy Analyzer - Identify cognitive biases in gambling decisions
- Betting System Analyzer - See why no betting system beats the house
- Variance Calculator - Understand short-term swings vs. long-term results
Frequently Asked Questions
What is a parlay bet?
A parlay (also called accumulator or combo bet) combines multiple individual bets into one wager. All selections must win for the parlay to pay out. While this offers higher potential payouts, the probability of winning decreases exponentially with each added leg because you must win every single selection.
Why are parlays mathematically worse than single bets?
Parlays compound the house edge from each individual bet. If a sportsbook has 4.5% edge on each leg, a 4-leg parlay has approximately 17% house edge (not 4 x 4.5% = 18% due to compounding). The more legs added, the higher the effective house edge, making parlays significantly worse value than placing individual bets.
How do I calculate parlay probability?
Multiply the win probability of each leg together. For example, if Leg 1 has 50% chance and Leg 2 has 50% chance, the parlay probability is 0.50 x 0.50 = 0.25 (25%). Three 50% legs would be 0.50 x 0.50 x 0.50 = 0.125 (12.5%). This is why parlays become extremely unlikely to win as legs increase.
Are parlays legal in South Korea?
In South Korea, only Sports Toto offers legal multi-bet options for Korean citizens. Private sports betting and offshore parlay betting are illegal under Articles 246-249 of the Criminal Act. This calculator is for educational purposes to understand the mathematics behind parlay bets, not to encourage illegal gambling.