How to Calculate Parlay Odds (Manual Formula + Examples)
- Greg Kajewski
- 1 day ago
- 11 min read
Parlay bets combine multiple wagers into one, offering higher payouts but requiring all selections to win. Understanding how to manually calculate parlay odds can help you better evaluate potential returns and risks. Here's how it works:
Step 1: Convert American odds (-110, +150, etc.) into decimal format for easier math.
Positive odds:
Negative odds:
Step 2: Multiply decimal odds of all legs to find total parlay odds.
Example: For decimal odds 1.91, 2.30, and 3.00, multiply: .
Step 3: Convert decimal odds back to American odds for a clearer view of potential profit.
If decimal odds > 2.00:
If decimal odds < 2.00:
This method highlights how sportsbooks include a "vig" (commission) in odds, reducing payouts compared to true probabilities. While manual calculations improve understanding, tools like parlay calculators simplify the process and avoid errors.
The Math Behind Parlays | NFL Week 7 Example
Step 1: Converting American Odds to Decimal Odds
To start, you'll need to convert American odds into decimal format. American odds, commonly used in U.S. sportsbooks, are expressed as positive numbers (like +150) for underdogs and negative numbers (like -110) for favorites. Decimal odds, on the other hand, represent your total return per dollar wagered, including your original stake. This format makes it easier to handle the calculations required for parlays.
How to Convert Positive and Negative American Odds
The method for converting American odds to decimal format depends on whether the odds are positive or negative. Here's how it works:
For positive American odds (underdogs), use this formula: Decimal Odds = (American Odds ÷ 100) + 1
For negative American odds (favorites), use this formula: Decimal Odds = 1 + (100 ÷ |American Odds|)
The "+1" in both formulas accounts for your initial stake. For example, with +150 odds, you risk $100 to win $150, giving you a total return of $250 (or 2.50 in decimal odds). For -110 odds, you risk $110 to win $100, resulting in a total return of about $210 (or 1.91 in decimal odds).
Examples of Converting American Odds
Here are a few examples to illustrate the process:
Converting +200 to Decimal Odds: Apply the formula: (200 ÷ 100) + 1 = 3.00. This means a $100 bet at +200 odds returns $300 total - your $100 stake plus $200 in profit.
Converting -110 to Decimal Odds: Use the formula: 1 + (100 ÷ 110) = 1 + 0.909 ≈ 1.91. A $110 wager at -110 odds gives a total return of about $210.
Converting +150 to Decimal Odds: Calculate: (150 ÷ 100) + 1 = 2.50. A $100 bet at +150 odds returns $250 total.
Converting -160 to Decimal Odds: Follow the formula: 1 + (100 ÷ 160) = 1 + 0.625 = 1.625. This means a $1 wager returns $1.625, including your initial stake.
Quick Reference Table for Common Conversions
Having a quick reference for commonly used odds can save you time and help verify your calculations. Here's a handy table:
American Odds | Decimal Odds | American Odds | Decimal Odds |
+100 | 2.00 | -100 | 2.00 |
+120 | 2.20 | -110 | 1.91 |
+150 | 2.50 | -120 | 1.83 |
+200 | 3.00 | -150 | 1.67 |
+300 | 4.00 | -160 | 1.625 |
+400 | 5.00 | -200 | 1.50 |
+500 | 6.00 | -300 | 1.33 |
Key Patterns to Remember
Negative odds always convert to decimal values between 1.00 and 2.00.
Positive odds always convert to decimal values above 2.00.
These patterns can serve as a quick check for accuracy. A common mistake is forgetting to add 1 when converting positive odds, which can significantly skew your parlay calculations. Once your decimal odds are confirmed, you're ready to move on to the next step - multiplying the decimal values across your parlay legs to calculate your overall odds.
Step 2: Multiplying Decimal Odds Across Parlay Legs
The Multiplication Formula
Once you've converted American odds into decimal format, the next step is to multiply them together to calculate the total parlay odds. This gives you the overall payout multiplier, which includes both your potential profit and your original stake. The formula looks like this:
Total Parlay Odds = Decimal Odds (Leg 1) × Decimal Odds (Leg 2) × Decimal Odds (Leg 3)
By multiplying these odds, you're compounding both the risk and the potential reward.
For instance, if your parlay includes two legs with decimal odds of 1.91 and 2.30, the calculation would be: 1.91 × 2.30 = 4.39 This means a $100 bet would return $439 in total - $339 in profit plus your original $100 stake.
Examples: 2-Leg, 3-Leg, and 4-Leg Parlays
2-Leg Parlay: Imagine you’re betting on a two-leg parlay with odds of -110 (1.91) and +150 (2.50): 1.91 × 2.50 = 4.775 A $100 bet would return $477.50 in total. Subtract your $100 stake to find the profit: $477.50 - $100 = $377.50 profit.
3-Leg Parlay: Now, consider a three-leg parlay with all bets at -110, which converts to 1.91 in decimal odds. Multiply the odds for all three legs: 1.91 × 1.91 × 1.91 = 6.97. A $100 wager would return $697 in total, leaving you with $597 in profit. Keep in mind, while adding more legs increases the potential payout, it also significantly reduces the likelihood of winning.
4-Leg Parlay with Mixed Odds: Let’s look at a four-leg parlay with a mix of odds:
Sacramento Kings at +120 (decimal odds = 2.20)
Golden State Warriors at -110 (decimal odds = 1.91)
Chicago Bulls at +145 (decimal odds = 2.45)
Houston Rockets at +200 (decimal odds = 3.00)
To calculate the total parlay odds, multiply all the decimal values: 2.20 × 1.91 × 2.45 × 3.00 ≈ 30.89 A $100 bet would return approximately $3,089 in total, meaning a profit of about $2,989. The higher positive odds, like +200, significantly boost the payout since they translate to larger decimal values.
For a faster and more accurate way to calculate parlay odds, check out our parlay odds calculator. It’s a handy tool to save time and avoid errors!
Step 3: Converting Decimal Odds Back to American Odds
Formula for Decimal-to-American Odds Conversion
Once you've calculated the combined decimal odds, the next step is to convert them into American odds. This format often makes it easier to see your potential profit at a glance. The method for conversion depends on whether the decimal odds are above or below 2.00, which represents the break-even point.
For decimal odds 2.00 or higher, use this formula:
American Odds = (Decimal Odds − 1) × 100
Here's why this works: Decimal odds already include your stake. Subtracting 1 isolates the profit per dollar wagered, and multiplying by 100 converts it into the American odds format.
For decimal odds below 2.00, use this formula:
American Odds = −100 ÷ (Decimal Odds − 1)
This formula aligns with the convention for favorites, showing how much you need to bet to win $100.
Want to skip the math? Use our parlay odds calculator for instant results.
Conversion Examples
Let’s break it down with some examples:
Example 1: Converting Decimal 4.00 to American Odds
Calculation: 4.00 − 1 = 3.00
Multiply: 3.00 × 100 = 300
Result: American odds are +300, meaning a $100 wager returns $400 total ($300 profit plus your $100 stake).
Example 2: Converting Decimal 3.64 to American Odds Imagine a two-leg parlay at -110 and -110, resulting in combined odds of 3.64:
Calculation: 3.64 − 1 = 2.64
Multiply: 2.64 × 100 = 264
Result: American odds are +264, so a $100 bet would return $364 total.
Example 3: Mixed Odds Parlay (Decimal 4.77) For a parlay with legs such as -110 and +150, producing decimal odds of 4.77:
Calculation: 4.77 − 1 = 3.77
Multiply: 3.77 × 100 = 377
Result: American odds are +377, meaning a $100 stake would return $477 total.
Sportsbooks may round to the nearest whole number, so you might notice slight variations (e.g., +263 instead of +264). For the most accurate conversion that aligns with sportsbook pricing, try our parlay odds calculator.
These examples wrap up the manual conversion process. Next, you'll dive into understanding true probabilities and how sportsbooks adjust odds.
True Probability vs. Sportsbook-Adjusted Odds
Understanding Vig and Adjusted Odds
When you look at sportsbook odds, you're not seeing pure probabilities. Instead, you're seeing numbers that include the sportsbook's built-in commission, often called the vig. This adjustment means the odds reflect probabilities skewed in the sportsbook's favor.
Take a simple example: a fair coin flip. With a true 50% chance, the odds should be even money, or +100. But sportsbooks typically price both sides at -110. This adjustment implies a win probability of about 52.4% for each side. Add those together, and you get a total of approximately 104.8% - that extra 4.8% is the sportsbook's edge. For a single -110 bet, the vig works out to roughly 4.54%.
Now, things get trickier with parlays. The vig compounds with each leg you add. For instance, imagine a two-leg parlay where both bets are priced at -110. If these were truly 50/50 bets, the fair probability of winning both would be 25% (0.50 × 0.50), which corresponds to fair odds of +300. But because each leg is priced at -110 (implying a 52.4% probability), the parlay's implied probability becomes about 27.5% (0.524 × 0.524). This means the payout drops to +264, even though the true win probability hasn’t changed. Add more legs, and the gap between fair odds and actual payout widens. For example, a three-leg parlay at -110 pays around +597, but the fair odds would be +700 if each leg were truly 50/50.
This compounding effect is a major reason why many bettors misunderstand how parlay payouts work.
Why Bettors Misunderstand Parlay Math
The way sportsbooks calculate parlay payouts often leads to confusion. Many bettors see a four-leg parlay with a flashy +1200 payout and think it’s a great deal, not realizing that the odds already include the compounded vig. On the surface, the potential payout might seem appealing, but in reality, the sportsbook is stacking odds that already account for their edge - not the true probabilities.
Another common oversight is failing to account for correlations between parlay legs. For example, if you bet on a quarterback’s passing yards to go over and his team to win, those outcomes are positively correlated. A bettor might mistakenly multiply the posted odds as if the events were independent, but sportsbooks adjust for correlations by reducing potential payouts. This ensures they maintain their edge, even when bettors think they’ve spotted a clever angle.
Sportsbooks actively promote parlays because they know many bettors don’t fully understand these mechanics. The enticing payouts often hide the reality: parlays are typically negative expected value (EV) unless every leg offers positive EV on its own. To properly evaluate a parlay, you need to strip out the vig, calculate the no-vig probability, and compare it to the sportsbook's pricing. For more details on this process, check out our guide on parlay math, EV and no-vig betting concepts.
Why Use a Parlay Calculator?
Benefits of Automated Calculations
While understanding the math behind parlay bets is a great skill, using a parlay calculator is a far more practical option for real-world betting. Manual calculations, especially for parlays with four or more legs, can take several minutes and leave room for mistakes at every step. A parlay calculator eliminates this hassle by handling all conversions instantly, allowing you to focus on choosing your bets rather than crunching numbers. This combination of speed and precision is invaluable, particularly for more intricate parlay setups.
One major issue with manual calculations is the risk of rounding errors. For instance, converting -110 to decimal gives you 1.909090… (a repeating number). If rounding is done incorrectly across multiple legs, the final payout can be way off. A calculator avoids these cumulative errors, ensuring accurate results every time.
Another advantage is the ability to quickly compare different betting scenarios. Want to see how adding an extra leg or swapping a bet impacts your total odds? A calculator can give you an answer in seconds. This is especially helpful during live betting, where odds can change rapidly, and quick decisions are key.
Recommended Tool: Parlay Odds Calculator
For instant and accurate results, the BettorEdge Parlay Calculator is a fantastic tool. Simply input your stake and the odds for each leg - whether it’s a straightforward 2-leg parlay or a complex 12-leg combination - and you'll immediately see your parlay odds, total payout, total profit, and implied probability.
For example, if you place a $20 wager on a 4-leg parlay with odds of -110, -110, +105, and -110, the calculator will instantly compute +1326 odds, a 7.01% probability, a $285.27 total payout, and a $265.27 profit.
The tool also supports multiple odds formats, saving you from repetitive conversions. Whether you’re just starting to learn parlay math or fine-tuning your next bet, this calculator ensures accuracy and helps you avoid costly errors. Try it out and calculate parlay odds instantly to streamline your betting process.
Conclusion
Figuring out parlay odds boils down to three main steps: converting American odds to decimal, multiplying those decimals across all legs, and then converting the result back to American odds. These are straightforward formulas in action. For instance, as shown earlier, a 2-leg parlay with -110 odds translates to roughly +264, while a 4-leg parlay combining favorites and underdogs can skyrocket to +2987.
What’s also clear from this process is how the vig (the sportsbook’s built-in commission) affects your payouts. Each leg in a parlay includes its own vig, and when combined, this compounds significantly. That’s why a 2-leg parlay of -110 bets has an implied winning probability of only 27.5%, far from the 50% that many casual bettors might expect. By understanding this, you can spot where the vig eats into your potential returns and focus on constructing parlays that provide better value rather than just increasing the house’s edge.
Once you grasp the system, you’re already ahead of many bettors who skip the math entirely. This knowledge also allows you to make the most of technology. Tools like a parlay odds calculator can save time, eliminate rounding errors, and give you instant insights into odds, probabilities, and payouts for any combination you’re considering.
For more details on the math behind parlays, check out this guide. If you’re looking to refine your strategy, explore best practices for building parlays. Ready to take the next step? Use the BettorEdge Parlay Calculator to plan your bets and get precise results in seconds.
FAQs
How does the sportsbook's vig impact my parlay payouts?
The vig - short for vigorish - is essentially the sportsbook's way of ensuring they profit, no matter the outcome. It’s baked into the odds you see, reducing your potential payouts compared to the true odds. So, even if you’ve nailed the implied probabilities and calculated your parlay correctly, your payout will still take a hit because the sportsbook adjusts the odds to include their cut.
When it comes to parlays, the impact of the vig grows with each additional leg you add. This compounding effect makes it crucial to understand how the vig influences your potential winnings. By factoring it in, you can make smarter decisions about whether a parlay bet is worth the risk.
Why do you need to convert odds when calculating parlay payouts?
Converting odds plays a key role in figuring out both the overall probability and potential payout of a parlay. When you convert American odds into implied probabilities, you can gauge how likely each individual leg is to win. To calculate the total probability of the parlay succeeding, you simply multiply these probabilities together.
Once you've got the combined probability, you can convert it back into American odds to estimate the parlay's potential payout. This step-by-step approach gives you a clearer picture of the actual value of your bet, helping you make smarter wagering choices.
What are the most common mistakes when manually calculating parlay odds?
One common mistake bettors make is overlooking the sportsbook's vig - the built-in fee that inflates odds and lowers the actual value of your wagers. This can significantly skew your expectations and reduce potential returns.
Another frequent error involves misunderstanding correlated events. In these cases, the outcome of one leg directly affects another, leading to flawed calculations and unrealistic predictions.
Many also fail to correctly convert American odds to implied probabilities, or they miscalculate how probabilities interact across multiple legs. This often results in bettors underestimating how quickly the overall probability drops as more legs are added, creating overly optimistic expectations.
To avoid these traps, it’s crucial to focus on accurate odds conversions, ensure fair pricing, and grasp the math driving your bets. A solid understanding of these fundamentals can make a big difference in your success.
