Jump to navigation Jump to search This article is about the gambling and statistical term. For the 1966 documentary film, see The Odds Against. Look up odds in Wiktionary, the free dictionary. This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. Odds are a numerical expression, usually expressed as a pair of numbers, used in both gambling and statistics.

If you bet six times and win once, you win five times your wager while also losing your wager five times, thus the odds offered here by the bookmaker reflect the probabilities of the die. In gambling, odds represent the ratio between the amounts staked by parties to a wager or bet. In statistics, the odds for an event E are defined as a simple function of the probability of that possible event E. One drawback of expressing the uncertainty of this possible event as odds for is that to regain the probability requires a calculation. The gambling and statistical uses of odds are closely interlinked. If a bet is a fair one, then the odds offered to the gamblers will perfectly reflect relative probabilities. The language of odds, such as the use of phrases like “ten to one” for intuitively estimated risks, is found in the sixteenth century, well before the development of probability theory.

The sixteenth-century polymath Cardano demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes. Implied by this definition is the fact that the probability of an event is given by the ratio of favourable outcomes to the total number of possible outcomes. This section does not cite any sources. Usually, the word “to” is replaced by a symbol for ease of use. This is conventionally either a slash or hyphen, although a colon is sometimes seen. When the probability that the event will not happen is greater than the probability that it will, then the odds are “against” that event happening. Odds of 6 to 1, for example, are therefore sometimes said to be “6 to 1 against”. To a gambler, “odds against” means that the amount he or she will win is greater than the amount staked. Odds on” is the opposite of “odds against”.

It means that the event is more likely to happen than not. Note that the gambler who bets at “odds on” and wins will still be in profit, as his stake will be returned. Even odds” occur when the probability of an event happening is exactly the same as it not happening. In common parlance, this is a “50-50 chance”. Guessing heads or tails on a coin toss is the classic example of an event that has even odds. From the perspective of a gambler rather than a statistician, “better than evens” means “odds against”. 10 units would return 20 units for profit of 10 units. A successful gamble paying out at 4:1 would return 50 units for a profit of 40 units. However, in popular parlance surrounding uncertain events, the expression “better than evens” usually implies a greater than 50-percent chance of an event occurring, which is exactly the opposite of the meaning of the expression when used in a gaming context.

In statistics, odds are an expression of relative probabilities, generally quoted as the odds in favor. Conversely, the odds against is the opposite ratio. For example, the odds against a random day of the week being a weekend are 5:2. In probability theory and statistics, odds and similar ratios may be more natural or more convenient than probabilities. In some cases the log-odds are used, which is the logit of the probability. Bayesian statistics as the Bayes factor. Odds-ratios are often used in analysis of clinical trials. 1 There are 5 pink marbles, 2 blue marbles, and 8 purple marbles. What are the odds in favor of picking a blue marble? Answer: The odds in favour of a blue marble are 2:13.