Odds

Odds are a way of expressing the likelihood of an event by comparing the number of favorable outcomes to the number of unfavorable outcomes. They differ from probability, which expresses likelihood as a single fraction or percentage; odds express a ratio. For an event with a favorable count a and an unfavorable count b, the odds in favor are a:b and the probability is a/(a+b). If the probability is p, the odds in favor are p/(1−p); odds against are (1−p)/p.

Common formats include fractional odds, decimal odds, and American (moneyline) odds. Fractional odds, such as 3/1, express the profit relative to stake (you win 3 for every 1 staked). Decimal odds show the total return per unit stake, for example 2.50 means you receive 2.50 units back for each 1 unit staked. American odds present either a profit on a 100 stake (positive odds, e.g., +150) or the stake required to win 100 (negative odds, e.g., −200).

In statistics, the odds ratio is a measure of association between an exposure and an outcome, defined as the odds in one group divided by the odds in another (OR = (a/c) / (b/d) in a 2×2 table). In betting markets, odds reflect both the estimated probability of an outcome and a bookmaker margin, so offered odds may differ from the fair odds implied by the underlying probabilities.