Odds

:For the alternative rock band, see Odds (band).

Related Topics:
Alternative rock - Odds (band)

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In probability theory and statistics the odds in favor of an event or a proposition are the quantity p / (1 − p), where p is the probability of the event or proposition. The logarithm of the odds is the logit of the probability.

Related Topics:
Probability theory - Statistics - Probability - Logarithm - Logit

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Odds have long been the standard way of representing probability used by bookmakers, though the method of presenting odds varies by location.

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Taking an event with a 1 in 5 probability of occurring (i.e. 0.2 or 20%), then the odds are 0.2/(1−0.2) = 0.2/0.8 = 0.25.

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If you bet 1 at fair odds and the event occurred, you would receive back 4 plus your original 1 stake. This would be presented by a British bookmaker as odds of 4 to 1 against (written as 4/1), by a continental European bookmaker as 5.0 to include the returned stake, and by an American bookmaker as +400 representing the gain from a 100 stake.

Related Topics:
Bet - British - Continental - Europe - American

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By contrast, for an event with a 4 in 5 probability of occurring (i.e. 0.8 or 80%), then the odds are 0.8/(1−0.8) = 4. If you bet 4 at fair odds and the event occurred, you would receive back 1 plus your original 4 stake. This would be presented by a British bookmaker as odds of 4 to 1 on (written as 1/4), by a continental bookmaker as 1.25 to include the returned stake, and by an American bookmaker as −400 representing the stake necessary to gain 100.

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The odds are a ratio of probabilities; an odds ratio is a ratio of odds, that is, a ratio of ratios of probabilities. Odds-ratios are often used in analysis of clinical trials.

Related Topics:
Ratio - Odds ratio - Clinical trial

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