Implied Probability Calculator - Vig, Fair Odds, Edge

An implied probability calculator turns a sportsbook price into the chance the market is implying, and it removes the bookmaker's overround (vig) to surface the fair probability a sharp bettor compares to their own estimate. The same tool works for a single price, a two-way market, or a three-way market.

• • Convert a single price: Paste a decimal, American, or fractional price and read the chance the bookmaker is implying for that single outcome.
• • Remove the vig from a two-way market: Paste the two prices from a head-to-head market and read the no-vig fair probability per side plus the overround.
• • Remove the vig from a three-way market: Paste home, draw, and away prices from a soccer or outright winner market and read the no-vig fair probabilities plus the overround.
• • Compare prices across sportsbooks: Use the overround percentage to see which book offers the sharpest line, since a lower overround means more of each dollar returned to bettors.

If the book you usually read lists prices in fractional format, the Fractional Odds Calculator handles the same kind of conversion between fractional, decimal, and American odds that this calculator uses in reverse.

Parse the price to a decimal odds value, take one divided by the decimal odds to get the raw implied probability, sum those raw probabilities across the market to get the overround, and divide each raw probability by the overround to get the no-vig fair value.

• Odds format: Decimal is a multiplier like 2.10, American is a signed number like +150 or -200, and fractional is a profit-to-stake ratio like 4 for 4/1.
• Raw implied probability: One divided by the decimal odds for the outcome. For decimal this is 1 / 2.10, for American +150 this is 100 / 250.
• Overround: The sum of the raw implied probabilities across the active outcomes. A value of 1.0471 means a 4.71 percent bookmaker margin.
• Fair probability: The raw implied probability for one outcome divided by the overround. A two-way market at 1.91 and 1.91 gives each side a fair probability of 50.00 percent.

American moneyline odds need one extra step. A positive line like +150 means a 100 dollar profit on a 100 dollar stake, which is the same as decimal odds of 2.50 and an implied probability of 100 / 250 = 0.40.

According to Wikipedia Betting odds article, the decimal odds implied probability is 1 divided by the decimal price, the American moneyline formula is 100 / (positive odds + 100) or |negative odds| / (|negative odds| + 100), and the fractional formula is the denominator divided by the sum of the numerator and denominator.

Once the no-vig fair probability is in hand, the Binomial Distribution Calculator uses the same kind of probability per trial to size a series of bets or count a streak of wins at a given edge.

Four ideas cover what you need to read a sportsbook price and compare it to your own model.

The overround is a single number that describes the whole market, the fair probabilities sum to 100 percent, and the fair decimal odds are the reciprocal of the fair probability.

The no-vig fair probability is a single-event probability in the same sense the Probability Calculator handles, so the rules of complements, independent events, and conditional probability apply to a fair price the same way they apply to a coin flip.

Six steps take you from a sportsbook screenshot to a no-vig fair probability and the matching fair odds.

1. 1 Pick the market type: Choose single, two-way, or three-way. The result panel re-renders to show the right number of outcomes.
2. 2 Pick the odds format: Match the format to the sportsbook you are reading.
3. 3 Enter the outcome 1 odds: Type the price for the first outcome. For decimal enter 2.10, for American enter 150 or -200, for fractional enter 4 for 4/1.
4. 4 Enter the outcome 2 odds: Type the price for the opposing outcome when the market is two-way.
5. 5 Enter the outcome 3 odds when needed: For three-way markets such as soccer, add the third price to give the overround.
6. 6 Read the result panel: Use the implied probability, the overround, the fair probability, and the fair decimal odds to compare the price to your own estimate.

A two-way market at decimal odds 1.91 and 1.91 prints a 4.71 percent overround, a 50.00 percent fair probability per side, and a 2.00 fair decimal price per side. If your own model gives the home side a 52 percent chance, the 2.00 fair price is below your 1 / 0.52 = 1.92 fair value, so the listed price is the value side.

Before sizing a bet on a no-vig edge, the Standard Deviation Calculator is the right tool to estimate the variance of the bettor's bankroll so the bet size is consistent with the user's risk tolerance.

Using an implied probability calculator instead of trusting the listed price changes how you read a sportsbook.

• • Read the overround at a glance: The overround is the single best read on whether a book is sharp or recreational.
• • Compare prices to your own model: Compare the fair probability to your own estimate. If the gap is positive, the listed price is the value side.
• • Convert between odds formats: The same calculation works for decimal, American, and fractional odds, so a US bettor can read a European price and vice versa.
• • Check three-way markets cleanly: Soccer and outright winner markets have three outcomes, and the calculator surfaces the overround and the fair probabilities for all three.
• • Catch mispriced markets: A two-way market with a sum under 1.00 is a mispriced book that the calculator flags as a zero or near-zero overround.
• • Use a single workflow for any sport: The same workflow works for NFL, NBA, Premier League, and outright winner markets.

When the fair probability is reported as a percent, the Probability Fraction Calculator converts the same number to a fraction or a decimal so it can be dropped into a Kelly criterion or a bankroll model that expects a fraction.

Five variables move the no-vig fair value the most, and two caveats tell you when the calculator output needs a second look.

• • The calculator assumes the market is a clean two- or three-way event with no push, dead heat, or refund rules, so it does not capture niche markets such as Asian handicap or each-way betting.
• • The no-vig fair value is a market-level number and does not adjust for the time value of money, line movement, or steam moves that a sharp bettor would also factor in.

If the listed price is much lower than the no-vig fair value, the gap is usually a sign that the price is stale or that the market is rounding against the bettor.

According to American Gaming Association industry resources, US sportsbook hold percentages typically run between 4% and 7% on major leagues, which is the same overround range the no-vig output of the calculator is designed to detect.

According to Wikipedia Bookmaker article, a bookmaker builds the profit margin into the implied probabilities rather than the listed odds, which is why the implied probabilities of all outcomes sum to more than 100% in most markets.

A line move larger than a few cents is a standard-deviations event, and the Z-Score Calculator turns a no-vig fair price plus an observed line into a z-score so the bettor can decide whether a steam move is a real signal or noise.