How betting odds work: fractional, decimal and probability

Odds are a price. They tell you how much you are paid if you are right and, read backwards, how likely the bookmaker thinks the outcome is.

Fractional odds

British bookmakers quote fractions: 5/2 means you win £5 for every £2 staked and get your £2 back, so a £2 bet returns £7. Odds-on prices have the bigger number second: 1/2 wins £1 for every £2 staked. “Evens” is 1/1.

Decimal odds

Decimal odds show the total return per £1 staked, stake included. 5/2 is 3.50: a £10 bet returns £35. Convert fractions by dividing and adding one: 5 ÷ 2 + 1 = 3.5. Exchanges and most European sites use decimals, and multiplying decimals is how accumulator returns are worked out.

Implied probability

Divide 1 by the decimal odds: 3.50 implies 28.6 per cent. Add up the implied probabilities of every outcome in a market and you get more than 100 per cent; the excess is the bookmaker’s margin, or overround. A Premier League match priced at 2.10, 3.40, 3.60 adds to about 104.6 per cent, so the margin is 4.6 per cent. Lower is better for you.

Reading a price

Two questions decide whether a bet is good value: does the implied probability look lower than the true chance, and how much margin is in the market? The odds converter does the arithmetic.