odds (noun)

the likelihood of a thing occurring rather than not occurring

odds, betting odds (noun)

the ratio by which one better's wager is greater than that of another

"he offered odds of two to one"

odds (Noun)

The ratio of the probabilities of an event happening to that of it not happening.

odds (Noun)

The ratio of winnings to stake in betting situations.

Odds

The odds in favor of an event or a proposition is defined by the ratio of the probability that the event will happen to the probability that it will not happen. For example, the odds that a randomly chosen day of the week is a Sunday are one to six, which is sometimes written 1 : 6.; see section 1.5 of Gelman et al.. 'Odds' are an expression of relative probabilities. Often 'odds' are quoted as odds against, rather than as odds in favor. For example, the probability that a random day is a Sunday is one-seventh, hence the odds that a random day is a Sunday are 1 : 6. The odds against a random day being a Sunday are 6 : 1. The first figure represents the number of ways of failing to achieve the outcome and the second figure is the number of ways of achieving a favorable outcome. In probability theory and Bayesian statistics, odds may sometimes be more natural or more convenient than probabilities. This is often the case in problems of sequential decision making as for instance in problems of how to stop on a last specific event which is solved by the odds algorithm. Stating "odds against" is a convenient way to propose a bet. When a bookmaker offers betting odds of 6 : 1 against some event occurring, it means that he is prepared to pay out a prize of six times the stake, and return the stake as well, to anyone who places a bet, by making the stake, that the event will occur. If the event does not occur, then the bookmaker keeps the stake. For example, a winning bet of 10 at 6 : 1 against will win '6 × 10 = 60' with the original 10 stake also being returned. Betting odds are skewed to ensure that the bookmaker makes a profit — if true odds were offered the bookmaker would break even in the long run — so the numbers do not represent the bookmaker's true odds.

Odds

Odds provide a measure of the likelihood of a particular outcome. They are calculated as the ratio of the number of events that produce that outcome to the number that do not. Odds are commonly used in gambling and statistics. 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. In mathematical terms, where p {\displaystyle p} is the probability of the outcome: odds = p 1 − p {\displaystyle {\text{odds}}={\frac {p}{1-p}}} where 1 − p {\displaystyle 1-p} is the probability that the outcome does not occur. Odds can be demonstrated by examining rolling a six-sided die. The odds of rolling a 6 is 1:5. This is because there is 1 event (rolling a 6) that produces the specified outcome of "rolling a 6", and 5 events that do not (rolling a 1,2,3,4 or 5). The odds of rolling either a 5 or 6 is 2:4. This is because there are 2 events (rolling a 5 or 6) that produce the specified outcome of "rolling either a 5 or 6", and 4 events that do not (rolling a 1, 2, 3 or 4). The odds of not rolling a 5 or 6 is the inverse 4:2. This is because there are 4 events that produce the specified outcome of "not rolling a 5 or 6" (rolling a 1, 2, 3 or 4) and two that do not (rolling a 5 or 6). The probability of an event is different, but related, and can be calculated from the odds, and vice versa. The probability of rolling a 5 or 6 is the fraction of the number of events over total events or 2/(2+4), which is 1/3, 0.33 or 33%.When gambling, odds are often the ratio of winnings to the stake and you also get your wager returned. So wagering 1 at 1:5 pays out 6 (5 + 1). If you make 6 wagers of 1, and win once and lose 5 times, you will be paid 6 and finish square. Wagering 1 at 1:1 (Evens) pays out 2 (1 + 1) and wagering 1 at 1:2 pays out 3 (1 + 2). These examples may be displayed in many different forms: Fractional odds with a slash: 5 (5/1 against), 1/1 (Evens), 1/2 (on) (short priced horse). Tote boards use decimal or Continental odds (the ratio of total paid out to stake), e.g. 6.0, 2.0, 1.5 In the US Moneyline a positive number lists winnings per $100 wager; a negative number the amount to wager in order to win $100 on a short-priced horse: 500, 100/–100, –200.