In probability theory, 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 is the probability of the outcome:
where 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 to 5 (abbreviated 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 different forms, explained later:
Fractional odds with a slash: 5 (5/1 against), 1/1 (Evens), 1/2 (on) (short priced horse). Fractional odds can also be written with a colon or a hyphen or dash.
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This course is neither an introduction to the mathematics of statistics nor an introduction to a statistics program such as R. The aim of the course is to understand statistics from its experimental d
Bayesian statistics (ˈbeɪziən or ˈbeɪʒən ) is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a degree of belief in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability, such as the frequentist interpretation that views probability as the limit of the relative frequency of an event after many trials.
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of A in the presence of B and the odds of A in the absence of B, or equivalently (due to symmetry), the ratio of the odds of B in the presence of A and the odds of B in the absence of A. Two events are independent if and only if the OR equals 1, i.e., the odds of one event are the same in either the presence or absence of the other event.
Spread betting is any of various types of wagering on the outcome of an event where the pay-off is based on the accuracy of the wager, rather than a simple "win or lose" outcome, such as fixed-odds (or money-line) betting or parimutuel betting. A point spread is a range of outcomes and the bet is whether the outcome will be above or below the spread. Spread betting has been a major growth market in the UK in recent years, with the number of gamblers heading towards one million.
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