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Twenty20 International Women 4. Bantamweight - UFC Men 3. Featherweight - UFC Men 1. Lightweight - UFC Men 1. In statistics, odds are an expression of relative probabilities, generally quoted as the odds in favor.

The odds in favor of an event or a proposition is the ratio of the probability that the event will happen to the probability that the event will not happen.

Mathematically, this is a Bernoulli trial , as it has exactly two outcomes. In case of a finite sample space of equally likely outcomes , this is the ratio of the number of outcomes where the event occurs to the number of outcomes where the event does not occur; these can be represented as W and L for Wins and Losses or S and F for Success and Failure.

For example, the odds that a randomly chosen day of the week is a weekend are two to five 2: These definitions are equivalent, since dividing both terms in the ratio by the number of outcomes yields the probabilities: For example, the odds against a random day of the week being a weekend are 5: Odds and probability can be expressed in prose via the prepositions to and in: For example, "odds of a weekend are 2 to 5", while "chances of a weekend are 2 in 7".

In casual use, the words odds and chances or chance are often used interchangeably to vaguely indicate some measure of odds or probability, though the intended meaning can be deduced by noting whether the preposition between the two numbers is to or in.

Odds can be expressed as a ratio of two numbers, in which case it is not unique — scaling both terms by the same factor does not change the proportions: Odds can also be expressed as a number, by dividing the terms in the ratio — in this case it is unique different fractions can represent the same rational number.

Odds as a ratio, odds as a number, and probability also a number are related by simple formulas, and similarly odds in favor and odds against, and probability of success and probability of failure have simple relations.

Given odds in favor as the ratio W: Analogously, given odds as a ratio, the probability of success or failure can be computed by dividing, and the probability of success and probability of failure sum to unity one , as they are the only possible outcomes.

In case of a finite number of equally likely outcomes, this can be interpreted as the number of outcomes where the event occurs divided by the total number of events:.

Given a probability p, the odds as a ratio is p: Thus if expressed as a fraction with a numerator of 1, probability and odds differ by exactly 1 in the denominator: 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.

These transforms have certain special geometric properties: They are thus specified by three points sharply 3-transitive. 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.

Converting odds to probability fixes 0, sends infinity to 1, and sends 1 to. 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 online on a last specific event which is solved by the odds algorithm.

Similar ratios are used elsewhere in Bayesian statistics, such as the Bayes factor. 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. While they have useful mathematical properties, they can produce counter- intuitive results: In some cases the log-odds are used, which is the logit of the probability.

Most simply, odds are frequently multiplied or divided, and log converts multiplication to addition and division to subtractions.

The odds in favour of a blue marble are 2: One can equivalently say, that the odds are There are 2 out of 15 chances in favour of blue, 13 out of 15 against blue.

That value may be regarded as the relative probability the event will happen, expressed as a fraction if it is less than 1 , or a multiple if it is equal to or greater than one of the likelihood that the event will not happen.

In the very first example at top, saying the odds of a Sunday are "one to six" or, less commonly, "one-sixth" means the probability of picking a Sunday randomly is one-sixth the probability of not picking a Sunday.

While the mathematical probability of an event has a value in the range from zero to one, "the odds" in favor of that same event lie between zero and infinity.

The odds against Sunday are 6: It is 6 times as likely that a random day is not a Sunday. The use of odds in gambling facilitates betting on events where the relative probabilities of outcomes varied.

For example, on a coin toss or a match race between two evenly matched horses, it is reasonable for two people to wager level stakes.

However, in more variable situations, such as a multi-runner horse race or a football match between two unequally matched sides, betting "at odds" provides a perspective on the relative likelihoods of the possible outcomes.

In the modern era, most fixed odds betting takes place between a betting organisation, such as a bookmaker , and an individual, rather than between individuals.

Different traditions have grown up in how to express odds to customers, older eras came with betting odds between people, today which is illegal in most countries, it was referred as "odding", an underground slang word with origins based in the Bronx.

Favoured by bookmakers in the United Kingdom and Ireland , and also common in horse racing , fractional odds quote the net total that will be paid out to the bettor, should he or she win, relative to the stake.

However, not all fractional odds are traditionally read using the lowest common denominator. Fractional odds are also known as British odds, UK odds, [12] or, in that country, traditional odds.

Odds with a denominator of 1 are often presented in listings as the numerator only. A variation of fractional odds is known as Hong Kong odds.

Fractional and Hong Kong odds are actually exchangeable. The only difference is that the UK odds are presented as a fractional notation e.

Both exhibit the net return. The European odds also represent the potential winnings net returns , but in addition they factor in the stake e.

Favoured in continental Europe , Australia , New Zealand and Canada , decimal odds quote the ratio of the payout amount, including the original stake, to the stake itself.

This is considered to be ideal for parlay betting, because the odds to be paid out are simply the product of the odds for each outcome wagered on.

Decimal odds are also favoured by betting exchanges because they are the easiest to work with for trading, as they reflect the inverse of the probability of an outcome.

Decimal odds are also known as European odds , digital odds or continental odds. Moneyline odds are favoured by American bookmakers.

The figure quoted is either positive or negative. Moneyline odds are often referred to as American odds. A "moneyline" wager refers to odds on the straight-up outcome of a game with no consideration to a point spread.

In most cases, the favorite will have negative moneyline odds less payoff for a safer bet and the underdog will have positive moneyline odds more payoff for a risky bet.

However, if the teams are evenly matched, both teams can have a negative line at the same time e. In gambling, the odds on display do not represent the true chances as imagined by the bookmaker that the event will or will not occur, but are the amount that the bookmaker will pay out on a winning bet, together with the required stake.

In formulating the odds to display the bookmaker will have included a profit margin which effectively means that the payout to a successful bettor is less than that represented by the true chance of the event occurring.

The true odds against winning for each of the three horses are , and respectively. This represents the odds against each, which are , and , in order.

This value of 30 represents the amount of profit for the bookmaker if he gets bets in good proportions on each of the horses.

And the expected value of his profit is positive even if everybody bets on the same horse. The art of bookmaking is in setting the odds low enough so as to have a positive expected value of profit while keeping the odds high enough to attract customers, and at the same time attracting enough bets for each outcome to reduce his risk exposure.

A study on soccer betting found that the probability for the home team to win was generally about 3. It was about 3. Making a profit in gambling involves predicting the relationship of the true probabilities to the payout odds.

Sports information services are often used by professional and semi-professional sports bettors to help achieve this goal. The odds or amounts the bookmaker will pay are determined by the total amount that has been bet on all of the possible events.

From Wikipedia, the free encyclopedia. Redirected from Fractional odds. This article is about the gambling and statistical term.

For the alternative rock band, see Odds band. For playing chess with odds, i.

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