Odds Converter
Convert between fractional, decimal, American, implied probability, and Hong Kong odds formats.
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All odds formats can be converted through decimal odds as an intermediary. Decimal odds represent total return per unit staked. Dividing 1 by decimal odds gives the implied probability, which is the foundation for all conversions.
Last reviewed: December 2025
Worked Examples
Example 1: Converting Decimal Odds to All Formats
Example 2: Converting American Odds (Favorite)
Background & Theory
The Odds Converter applies the following established principles and formulas. Statistics and probability provide the mathematical framework for drawing conclusions from data under uncertainty. The measures of central tendency describe where data cluster. The mean is the arithmetic average, computed as the sum of all values divided by the count. The median is the middle value of an ordered dataset, robust to extreme outliers. The mode is the most frequent value. Spread is quantified by variance, the average squared deviation from the mean, and by its square root, the standard deviation. For a sample, variance uses n minus one in the denominator to correct for bias in estimation. The normal distribution, defined by its mean and standard deviation, is the cornerstone of parametric statistics. Its bell-shaped probability density follows the formula f(x) = (1 / (sigma * sqrt(2*pi))) * exp(-0.5 * ((x - mu) / sigma)^2). The empirical rule states that approximately 68 percent of observations fall within one standard deviation of the mean, 95 percent within two, and 99.7 percent within three. A z-score standardizes a data point by subtracting the mean and dividing by the standard deviation, expressing how many standard deviations an observation lies from the mean. In hypothesis testing, the p-value is the probability of observing a result at least as extreme as the one obtained, assuming the null hypothesis is true. Confidence intervals express the range within which the true population parameter falls with a specified probability, typically 95 percent. Correlation measures linear association between two variables, with Pearson's r ranging from negative one to positive one. Correlation does not imply causation. Linear regression fits a line of the form y = a + bx to minimize the sum of squared residuals. Bayes' theorem relates conditional probabilities: P(A|B) = P(B|A) * P(A) / P(B), allowing prior beliefs to be updated on new evidence. The law of large numbers guarantees that the sample mean converges to the population mean as sample size grows. The central limit theorem states that the distribution of sample means approaches normality regardless of the population distribution, provided the sample size is sufficiently large, typically 30 or more.
History
The history behind the Odds Converter traces back through the following developments. The mathematical study of probability emerged in the 17th century from correspondence between Blaise Pascal and Pierre de Fermat in 1654. Their exchange, prompted by a gambling problem posed by the Chevalier de Mere, established the foundations of probability theory by calculating expected outcomes through systematic enumeration of cases. Jacob Bernoulli formalized the law of large numbers in his posthumously published Ars Conjectandi of 1713, proving rigorously that empirical frequencies converge to theoretical probabilities with increasing observations. His work laid the groundwork for inferential statistics by connecting mathematical probability to observed data. Carl Friedrich Gauss developed the method of least squares around 1795 while adjusting astronomical observations, and he recognized the bell-shaped error distribution that now bears his name. Pierre-Simon Laplace independently worked on the normal distribution and proved an early version of the central limit theorem around 1810, demonstrating why errors in measurement tend toward normality. The late 19th century saw statistics emerge as a distinct scientific discipline. Francis Galton introduced regression and correlation in the 1880s while studying heredity. Karl Pearson formalized these concepts, developed the chi-squared test, and founded the journal Biometrika in 1901, establishing statistics as a rigorous academic field. Ronald Fisher transformed statistical practice in the early 20th century. His 1925 book Statistical Methods for Research Workers introduced significance testing, analysis of variance, and the concept of the p-value as a decision threshold, establishing the framework still used in scientific research. Fisher and Jerzy Neyman engaged in a prolonged methodological dispute over the interpretation of hypothesis tests. The Bayesian approach, rooted in the 18th century work of Thomas Bayes and Laplace, was largely eclipsed by frequentist methods through much of the 20th century but experienced a revival after World War II and accelerated with computational advances. The late 20th and early 21st centuries brought statistics into every domain through big data, machine learning, and the routine availability of software capable of processing millions of observations.
Key Features
- Calculate team standings rankings including points, wins, losses, draws, goal or point differential, and games behind the leader, supporting multiple tiebreaker rules.
- Apply handicap strokes or adjusted scoring in golf and other sports so players of different skill levels can compete on equal footing, with automatic net score computation.
- Rank an athlete's performance metric against a reference population to produce a percentile score, showing exactly where the result stands relative to peers or historical records.
- Estimate real-time win probability for either team based on current score, time remaining, and sport-specific scoring rates using standard statistical game models.
- Aggregate season statistics including batting average, on-base percentage, ERA, WHIP, and QBR across any number of games, automatically updating running totals as new results are entered.
- Convert between fractional, decimal, American moneyline, and implied probability odds formats instantly, letting you compare lines across different sportsbooks or betting systems.
- Project fantasy sports weekly scores using per-game averages and remaining schedule, and calculate trade value comparisons based on positional scarcity and projected points.
- Generate tournament bracket seedings from win-loss records, calculate head-to-head and points-differential tiebreakers, and determine which teams advance under single or double elimination formats.
Frequently Asked Questions
Sources & References
Formula
Implied Probability = (1 / Decimal Odds) x 100
All odds formats can be converted through decimal odds as an intermediary. Decimal odds represent total return per unit staked. Dividing 1 by decimal odds gives the implied probability, which is the foundation for all conversions.
Worked Examples
Example 1: Converting Decimal Odds to All Formats
Problem: A bookmaker offers decimal odds of 3.25 on a football match. Convert to all formats and calculate payout on a $50 bet.
Solution: Decimal: 3.25\nAmerican: (3.25 - 1) x 100 = +225\nFractional: 2.25/1 = 9/4\nImplied Probability: (1/3.25) x 100 = 30.77%\nHong Kong: 3.25 - 1 = 2.25\nPayout: $50 x 3.25 = $162.50\nProfit: $162.50 - $50 = $112.50
Result: Decimal: 3.25 | American: +225 | Fractional: 9/4 | Implied: 30.77% | Profit: $112.50
Example 2: Converting American Odds (Favorite)
Problem: A tennis player is listed at -180 American odds. Convert and calculate payout on a $200 bet.
Solution: American: -180\nDecimal: (100/180) + 1 = 1.5556\nFractional: 0.5556/1 = 5/9\nImplied Probability: (1/1.5556) x 100 = 64.29%\nHong Kong: 0.5556\nPayout: $200 x 1.5556 = $311.11\nProfit: $311.11 - $200 = $111.11
Result: Decimal: 1.5556 | Fractional: 5/9 | Implied: 64.29% | Profit: $111.11
Frequently Asked Questions
What are the main odds formats used in sports betting worldwide?
The three primary odds formats are decimal (European), fractional (British), and American (moneyline). Decimal odds represent the total payout per unit staked, including your stake, so 2.50 means you receive $2.50 for every $1 wagered. Fractional odds show profit relative to stake, so 3/2 means $3 profit for every $2 staked. American odds use a baseline of $100: positive odds like +150 show profit on a $100 bet, while negative odds like -200 show how much you must bet to win $100. Beyond these, Hong Kong odds show profit per unit (similar to fractional but as a decimal), Indonesian odds work like American but based on 1 unit instead of 100, and Malay odds have their own inverted format popular in Southeast Asian markets.
How do you convert between decimal and American odds?
Converting between decimal and American odds follows two rules depending on whether the decimal odds are above or below 2.0 (even money). For decimal odds of 2.0 or higher (underdog), subtract 1 then multiply by 100 to get positive American odds. For example, decimal 3.50 becomes (3.50 - 1) x 100 = +250. For decimal odds below 2.0 (favorite), divide -100 by the decimal minus 1. For example, decimal 1.50 becomes -100 / (1.50 - 1) = -200. Going the other direction: positive American odds are divided by 100 then add 1 for decimal. So +250 becomes (250/100) + 1 = 3.50. Negative American odds use 100 divided by the absolute value then add 1. So -200 becomes (100/200) + 1 = 1.50.
What is implied probability and how does it relate to odds?
Implied probability converts odds into a percentage representing the likelihood of an outcome as suggested by the odds. It is calculated as 1 divided by the decimal odds, then multiplied by 100. Decimal odds of 2.00 imply a 50% probability. Odds of 4.00 imply 25%. Odds of 1.25 imply 80%. Understanding implied probability is crucial because it allows bettors to compare bookmaker odds against their own estimated probability of an outcome. If you believe a team has a 60% chance of winning but the odds imply only 45%, the bet offers positive expected value. However, bookmaker margins mean the sum of implied probabilities for all outcomes exceeds 100%, creating the overround or vigorish that represents the bookmaker profit margin.
What is the overround and how does it affect betting odds?
The overround, also called vigorish or juice, is the built-in profit margin that bookmakers embed in their odds. In a fair market, the implied probabilities of all possible outcomes sum to exactly 100%. Bookmakers set odds so this sum exceeds 100%, with the excess being their margin. For example, in a two-outcome event, a fair coin flip would be 2.00 on each side (50% + 50% = 100%). A bookmaker might offer 1.91 on each side, implying 52.4% each, totaling 104.7%. The 4.7% overround is the bookmaker margin. Lower overrounds indicate more competitive odds and better value for bettors. Sharp bettors always compare overrounds across bookmakers to find the best value and minimize the house edge on their wagers.
How do Hong Kong, Indonesian, and Malay odds formats work?
These three Asian odds formats each represent payouts differently and are widely used in their respective regional markets. Hong Kong odds show the net profit per unit staked, essentially the decimal odds minus 1. So Hong Kong odds of 1.50 equal decimal 2.50, meaning $1.50 profit per $1 bet. Indonesian odds work similarly to American odds but use 1 unit instead of 100 as the base. Positive Indonesian odds of 1.50 mean $1.50 profit per $1 bet (same as Hong Kong). Negative Indonesian odds of -1.50 mean you risk $1.50 to win $1. Malay odds are inverted from Indonesian: positive Malay odds below 1.0 represent underdogs showing your profit per unit, while negative Malay odds show what you risk to win one unit. These formats are standard across Asian sportsbooks and betting exchanges in the region.
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.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy