In some cases the log-odds are used, which is the logit of the probability. In probability theory and statistics, odds and similar ratios may be more natural or more convenient than probabilities. 5 (even odds are 50% likely), and conversely this is a parabolic transform. Converting odds to probability fixes 0, sends infinity to 1, and sends 1 to. 5 these are both order 2, hence circular transforms. Swapping odds for and odds against swaps 0 and infinity, fixing 1, while swapping probability of success with probability of failure swaps 0 and 1, fixing. They are thus specified by three points ( sharply 3-transitive). probability of success with probability of failure) and between odds and probability are all Möbius transformations (fractional linear transformations). These transforms have certain special geometric properties: the conversions between odds for and odds against (resp. These are worked out for some simple odds: This is a minor difference if the probability is small (close to zero, or 'long odds'), but is a major difference if the probability is large (close to one). Thus if expressed as a fraction with a numerator of 1, probability and odds differ by exactly 1 in the denominator: a probability of 1 in 100 (1/100 = 1%) is the same as odds of 1 to 99 (1/99 = 0.0101. In mathematical terms, where p is the probability of the outcome: Odds also have a simple relation with probability: the odds of an outcome are the ratio of the probability that the outcome occurs to the probability that the outcome does not occur. Odds are commonly used in gambling and statistics. They are calculated as the ratio of the number of events that produce that outcome to the number that do not.

In probability theory, odds provide a measure of the likelihood of a particular outcome. Look up odds in Wiktionary, the free dictionary.

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