True Odds Calculator
Calculate the bookmaker margin and true probability from offered betting odds. Enter values for instant results with step-by-step formulas.
Formula
True Probability = (1/Odds) / Sum(1/All Odds)
Each implied probability is 1 divided by the decimal odds. The sum of all implied probabilities gives the total overround (market percentage). Dividing each implied probability by the total normalizes them to true probabilities that sum to exactly 100%. Fair odds are then 1 divided by each true probability.
Worked Examples
Example 1: Two-Way Market Analysis
Problem: A sportsbook offers Team A at 1.90 and Team B at 2.00 in a basketball game. What is the bookmaker margin and what are the true probabilities?
Solution: Implied probability Team A = 1/1.90 = 52.63%\nImplied probability Team B = 1/2.00 = 50.00%\nTotal implied = 102.63%\nOverround = 102.63% - 100% = 2.63%\nTrue probability Team A = 52.63/102.63 = 51.29%\nTrue probability Team B = 50.00/102.63 = 48.71%\nFair odds Team A = 1/0.5129 = 1.950\nFair odds Team B = 1/0.4871 = 2.053
Result: Margin: 2.63% | True prob: 51.29% / 48.71% | Fair odds: 1.950 / 2.053
Example 2: Three-Way Soccer Market
Problem: A soccer match has odds: Home 2.10, Draw 3.40, Away 3.60. Calculate the margin and true probabilities.
Solution: Implied: Home = 1/2.10 = 47.62%, Draw = 1/3.40 = 29.41%, Away = 1/3.60 = 27.78%\nTotal = 104.81%\nOverround = 4.81%\nTrue prob: Home = 47.62/104.81 = 45.43%\nDraw = 29.41/104.81 = 28.06%\nAway = 27.78/104.81 = 26.51%\nFair odds: Home = 2.201, Draw = 3.564, Away = 3.772
Result: Margin: 4.81% | True prob: 45.4% / 28.1% / 26.5%
Frequently Asked Questions
What are true odds versus bookmaker odds in sports betting?
True odds represent the actual probability of an event occurring without any bookmaker margin added. Bookmaker odds, on the other hand, include a built-in profit margin known as the vig, juice, or overround. For instance, a fair coin flip has true odds of 2.00 on each side, but a bookmaker might offer 1.91 on both outcomes. The difference between 2.00 and 1.91 represents the bookmaker margin. Understanding this distinction helps bettors identify when offered odds represent good value compared to the actual likelihood of an outcome occurring.
How do I find value bets using true odds?
A value bet exists when the bookmaker odds are higher than the fair odds implied by the true probability. To find value, first estimate the true probability of each outcome using your own research, models, or statistical analysis. Then convert your estimated probability to fair odds by dividing 1 by the probability. If the bookmaker offers odds higher than your fair odds, you have a positive expected value bet. For example, if you estimate a team has a 45 percent chance of winning and the bookmaker offers 2.50 (implied 40 percent), the odds are offering value because 2.50 is higher than the fair odds of 2.22.
Why do different bookmakers offer different odds on the same event?
Different bookmakers offer varying odds because they use different models, have different customer bases, and apply different margin strategies. Some books are sharper, meaning they use sophisticated algorithms and quickly adjust to market information, resulting in tighter margins. Others cater to recreational bettors with wider margins but offer bonuses and promotions. Regional books may also have biases based on local fan bases. This variation creates opportunities for bettors who shop for the best lines across multiple sportsbooks, a practice known as line shopping, which is one of the most effective ways to improve long-term betting returns.
Can I use true odds to determine if a bet is worth taking?
Yes, comparing true odds to offered odds is one of the fundamental methods for evaluating bets. If the true probability of an outcome is lower than the implied probability from the offered odds, the bet has negative expected value and should generally be avoided. If the true probability is higher, the bet has positive expected value. However, determining the actual true probability is the challenging part, as it requires significant knowledge, research, or modeling expertise. Even professional bettors only find a small edge, typically 1 to 5 percent, but consistently exploiting this edge across hundreds or thousands of bets generates long-term profit.
What is the difference between odds and probability?
Probability is expressed as a number between 0 and 1 (or a percentage), representing the likelihood of an event. Odds compare favorable outcomes to unfavorable ones — odds of 3:1 means 3 wins for every 1 loss, which is a probability of 3/(3+1) = 75%. Casinos often express odds differently from true probability to build in their house edge.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.