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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. Answer: The odds in favour of a blue marble are One can equivalently say, that the odds are against. 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 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. 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,  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 , Canada , and Singapore , decimal odds quote the ratio of the payout amount, including the original stake, to the stake itself.
Therefore, the decimal odds of an outcome are equivalent to the decimal value of the fractional odds plus one. 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. When looking at decimal odds in betting terms, the underdog has the higher of the two decimals, while the favorite has the lower of the two. Decimal odds are 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.
This profit is known as the 'over-round' on the 'book' the 'book' refers to the old-fashioned ledger in which wagers were recorded, and is the derivation of the term 'bookmaker' and relates to the sum of the 'odds' in the following way:. 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.
They reflect the balance of wagers on either side of the event, and include the deduction of a bookmaker's brokerage fee "vig" or vigorish. From Wikipedia, the free encyclopedia. This article is about the gambling and statistical term. For the alternative rock band, see Odds band. For playing chess with odds, i. For the documentary film, see The Odds Against. Main article: Moneyline odds. Main article: Mathematics of bookmaking. Retrieved 18 August Wolfram Research Inc.
Retrieved 16 May CRC Press. Multi-State Lottery Association. But there are a potential number of different outcomes so the betting odds need to reflect the probability of these different outcomes. Once we know what these odds are we can then work out the probability of an event outcome. The easiest thing to do is to provide a breakdown with some examples. So if we look at our real life example we can now work out the probability of what the bookmakers think the outcome will be.
Looking at our real life example and the probability of the outcome we can see that the bookmakers make Liverpool favourites to win this match. This is followed by the draw and an Everton win is the least likely outcome. Remember, that when you place a bet, if you win you get back your original stake.
To make a very easy way to calculate your profit you simply divide the first number by the second number. You can use this on any odds to calculate exactly how much you will win. There are some online sports betting sites that do you not offer traditional fractions to show their odds, but instead use decimals. Decimals do in fact make it easier for you to calculate your winnings.
The majority of betting sites will allow you to choose how you want the odds to be displayed, so you can decide whether you want fractions or decimals. But remember, have no fear if you do get stuck. When you click on a bet or outcome which takes you fancy, you then enter a stake.
All online betting sites will show you exactly how much you will win from your stake, so they automatically make it nice and easy for you to see exactly what your bet will return. Sports betting odds explained — A beginners guide to help you understand how sports betting odds work Placing a bet at an online bookmaker can be a bit of a daunting task especially if you are new to sports gambling.