How the conversions work
Every format describes the same thing: how much a winning bet returns. Decimal odds are the total return per 1 staked, stake included, so everything else can be derived from them.
Implied probability is the win rate the price needs to break even. It includes the sportsbook’s margin, so the two sides of a market add up to more than 100%.
- American +odds to decimal: 1 + odds ÷ 100. American -odds to decimal: 1 + 100 ÷ |odds|.
- Decimal to American: 2.00 or more is (decimal − 1) × 100; under 2.00 is −100 ÷ (decimal − 1).
- Fractional a/b to decimal: 1 + a ÷ b. Implied probability: 1 ÷ decimal.
- American odds are never between −100 and +100. +100 and −100 are the same even-money price.
Questions
What is the difference between American, decimal and fractional odds?
American odds show profit on $100 (+150) or the stake needed to win $100 (-150). Decimal odds show total return per $1 staked (2.50). Fractional odds show profit per stake (3/2). They are three ways to write the same price.
Why is there no American price between -100 and +100?
Plus odds start where the bet pays even money. A bet that pays less than even money is quoted as minus odds, whose size is the stake needed to win $100, so it is always at least 100. +100 and -100 are the same price.
Does implied probability include the vig?
Yes. A single price’s implied probability includes the sportsbook’s margin, which is why both sides of -110/-110 imply 52.38% (104.76% in total). Use the no-vig calculator to take the margin out.
Why does my converted American price differ by a point or two from the book’s?
Decimal and fractional prices are rounded, and American odds are whole numbers, so a round trip can move a price by a point or so. The probability shown is calculated from the exact price you typed.
Put it into practice: Sportsbook odds comparison. Livdy shows every book’s price side by side and the game logs behind every prop hit rate.