Odds

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Opportunities are numerical expressions, usually expressed as pairs of numbers, used both in gambling and statistics. In statistics, the opportunity for or chance of multiple events reflects the possibility that the event will take place, while odds against reflects the possibility that the event will occur. will not. In gambling, the odds are the ratio of payments to the bet, and do not necessarily reflect the probability. Opportunities are expressed in several ways (see below), and sometimes they are used incorrectly to mean only the probability of an event. Conventionally, gambling opportunities are expressed in the form of "X to Y", where X and Y are numbers, and it is implied that opportunities are opportunities against events in which the gambler considers bets. Whether in gambling or statistics, 'odds' are numerical expressions of possible events.

In gambling, the opportunity represents the ratio between the amount at stake for betting or betting. Thus, the possibility of 6 to 1 means the first party (usually bet) has six times the amount at stake at the second party. In the simplest terms, 6 to 1 chance means if you bet one dollar ("1" in expression), and you win you paid six dollars ("6" in expression), or 6 x 1. If you bet your two dollars will be paid twelve dollars, or 6 x 2. If you bet three dollars and win, you will be paid eighteen dollars, or 6 x 3. If you bet a hundred dollars and win, you will be paid six hundred dollars, or 6 x 100 If you lose the bet, you will lose the dollar, or two dollars, or three dollars, or a hundred dollars.

In statistics, the odds for E events are defined as simple functions of the probability of possible events. E. One disadvantage of stating the uncertainty of the probability of this occurrence as an opportunity is that to regain probability requires calculation. The natural way to interpret opportunities for (without taking into account anything) is as the ratio of events to non-events in the long term. The simplest example is that the (statistical) opportunity to roll six with a fair die (one of a pair of dice) is 1 to 5. This is because, if someone rolls the dice over and over, and keeps the count of results, one expects 1 six events for each 5 times off does not show six. For example, if we roll up the fair as much as 600 times, we would really expect something around 100 points, and 500 out of five other possible outcomes. That is a ratio of 100 to 500, or just 1 to 5. To express the possibility (statistics) against, the order of pairs is reversed. Therefore the odds of rolling six with a fair die are 5 to 1. The probability of rolling six with a fair dice is a single number of 1/6, about 0.17.

The use of gambling and opportunity statistics is closely related. If the bet is fair, then the opportunities offered to the gamblers will perfectly reflect the relative probability. A fair bet that a fair dice will overthrow six people will pay a $ 5 gambler for a $ 1 bet (and return the bet bet) in case six and none in other cases. The betting requirements are fair, because on average, five rolls yield something other than six, at a cost of $ 5, for each roll resulting in six and net payouts of $ 5. The advantages and costs equally offset each other so there is no advantage to gamble in the long run. If the opportunities offered to gamblers do not match the probability in this way then one party to bet has an advantage over the other. Casinos, for example, offer opportunities that place themselves at an advantage, that is how they guarantee themselves to profit and survive as a business. A certain gambling fairness is more evident in games involving relatively pure possibilities, such as the ping-pong ball method used in state lotteries in the United States. It is much harder to judge the fairness of the opportunities offered in betting on sporting events like football matches.

Video Odds

Histori

Opportunity languages, such as the use of phrases like "ten to one" for intuitively expected risks, were discovered in the sixteenth century, well before the development of probability theory. Shakespeare writes:

Know that we are traveling in such a dangerous ocean That if we spend our lives' twenty-one to one

The sixteenth century Cardago polymath demonstrates the efficacy of defining opportunities as favorable and unfavorable yield ratios. Implied by this definition is the fact that the probability of an event is given by a favorable yield ratio with the total number of possible outcomes.

Maps Odds

Terminology

Peluang diekspresikan dalam bentuk ${\ displaystyle X}  ÂÂ$ untuk ${\ displaystyle Y}  ÂÂ$ , di mana ${\ displaystyle X}  ÂÂ$ dan ${\ displaystyle Y}  ÂÂ$ adalah angka. Biasanya, kata "ke" diganti dengan simbol untuk kemudahan penggunaan. Ini secara konvensional berupa garis miring atau tanda hubung, meskipun tanda titik dua kadang-kadang terlihat. Jadi, ${\ displaystyle 6/1}  ÂÂ$ , ${\ displaystyle 6-1}  ÂÂ$ , dan ${\ displaystyle 6: 1}  ÂÂ$ semuanya dapat dipertukarkan.

Odds terhadap

When the probability that the event will not occur is greater than the possibility that it will happen, then the chances are "against" the event occurred. Odds 6 to 1, for example, are therefore sometimes said to be "6 to 1 against ". For a gambler, "fighting chances" means that the amount he will win is greater than the amount at stake.

Odds on

"Odds on" is the opposite of "odds against". That means that the event is more likely than not to happen. This is sometimes expressed by smaller numbers first (1 to 2) but more often using the word "on" ("2 to 1 on "), which means that the event is twice more may occur as not. Note that gamblers who bet on "odds" and win will still make a profit, because the shares will be returned. For example, on a $ 2 bet, the gambler will be awarded $ 1 plus a $ 2 bets returned, earning $ 1 profit.

Even chance

"Even chance" occurs when the probability of an event occurs exactly the same as that did not happen. In common language, this is a "50-50 chance". Guessing a head or tail on a coin toss is a classic example of an event that even has an opportunity. In gambling, this is often referred to as "even money" or just "balanced" (1 to 1, or 2 for 1). "Evens" implies that payments will be a unit per unit at stake plus original shares; that is, "doubling your money".

Better than/worse than others

The meaning of the term "better than GENAP" (or "worse than GENAP") depends on the context. From the perspective of a gambler rather than a statistician, "better than others" means "opportunity to fight". If odds are evens (1: 1), bet 10 units will return 20 units for 10 units profit. Successful gambling pays 4: 1 will generate 50 units for profit 40 units. So, this bet is "better than average" from a gambler's perspective for paying more than one for one. If an event is more likely to occur than the same probability, it is likely to be "worse than it should be", and the bet will pay less than one for one.

However, in popular languages ​​surrounding uncertain events, the phrase "better than others" typically implies an opportunity of more than 50 percent of events, which is the opposite of the meaning of expression when used in the context of a game.

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Use of statistics

In statistics, odds are expressions of relative probability, commonly cited as opportunities in favor of . The chance (in favor) of an event or proposition is the probability ratio that the event will occur on the probability that the event will not occur. Mathematically, this is a Bernoulli test, because it has two results. In the case of a limited sample space of the same possible result, this is the ratio of the number of results in which the event occurred with the number of results in which the event did not occur; this can be represented as W and L (for Win and Loss) or S and F (for Success and Failure ). For example, the chances that a randomly chosen day of the week is a weekend is two to five (2: 5), since the days of the week form a sample space of seven results, and events occur for two results (Saturday and Sunday) and not for the other five. Instead, given the opportunity as an integer ratio, this can be represented by the probability space of a finite number of possible same results. This definition is equivalent, because dividing the two terms in ratio by the number of results yields probability: ${\ displaystyle 2: 5 = (2/7) :( 5/7).}$ Conversely, the opposite possibility is the opposite ratio. For example, the odds for a random day of the week were weekend: 5: 2.

Opportunities and probabilities can be expressed in prose through the preposition to and in: "so many possibilities to so much on (or against) [some events] "refers to the opportunity - the ratio of the number (possibly the same) favorable outcome and against (or vice versa); "so many possibilities, so many results" refers to the - the sum of (equal to) favorable results relative to the numbers for and against the combination. For example, "weekend opportunities are 2 to 5", while "weekend opportunities are 2 at 7". In ordinary use, the chance and possibly (or accidental ) are often used interchangeably to vaguely indicate some measure of opportunity or opportunity , although the intended meaning can be deduced by noting whether the preposition between two numbers is to or in .

Mathematical relationship

Opportunities can be expressed as two-digit ratios, in this case are not unique - scaling both terms with the same factor does not change the proportions: 1: 1 odds and 100: 100 opportunities are equal (even chance). Opportunities can also be expressed as numbers, dividing terms in ratios - in this case unique (different fractions can represent the same rational numbers). Odds as ratios, probabilities as numbers, and probabilities (as well as numbers) are related to simple formulas, and equal opportunities in support and contradiction, and the likelihood of success and probability of failure having a simple relationship. Odds range from 0 to infinity, while probabilities range from 0 to 1, and are therefore often represented as a percentage between 0% and 100%: reversing the chance switch ratio for with opposing opportunities, and also the likelihood of success with a probability of failure.

Diberikan odds (mendukung) sebagai rasio W: L (Wins: Kerugian), peluang yang menguntungkan (sebagai angka) ${\ displaystyle o_ {f}}  ÂÂ$ dan peluang terhadap (sebagai angka) ${\ displaystyle o_ {a}}  ÂÂ$ dapat dihitung dengan hanya membagi, dan merupakan pembalikan perkalian:

${\ displaystyle {\ begin {aligned} o_ {f} & amp; = W/L = 1/o_ {a} \\ o_ {a} & amp; = L/W = 1/o_ {f} \\ o_ {f} \ cdot o_ {a} & amp; = 1 \ end {aligned}}}  ÂÂ$

Analogously, the opportunity given as the ratio, the probability of success or failure can be calculated by dividing, and the probabilities of success and the probability of failure are summed to one, because they are the only possible outcome. In the case of a number of possible same results, this can be interpreted as the number of results in which an event occurs divided by the total number of events:

${\ displaystyle {\ begin {aligned} p & amp; = W/(W L) = 1-q \\ q & amp; = L/(W L) = 1- p \\ p q & amp; = 1 \ end {aligned}}}$

Dengan probabilitas p, peluang sebagai rasio adalah ${\ displaystyle p: q}  ÂÂ$ (kemungkinan keberhasilan terhadap probabilitas kegagalan), dan peluang sebagai angka dapat dihitung dengan membagi:

${\ displaystyle {\ begin {aligned} o_ {f} & amp; = p/q = p/(1-p) = (1-q)/q \\ o_ {a} & amp; = q/p = (1-p)/p = q/(1-q) \ end {aligned}}}  ÂÂ$

So if expressed as a fraction with the numerator 1, the probability and probability differs exactly 1 in the denominator: probability 1 in 100 (1/100 = 1%) equals 1 chance < 99 (1/99 = 0,0101... = 0. 01 ), while probability 1 to 100 (1/100 = 0.01) equals probability 1 at 101 (1/101 = 0.00990099... = 0, 0099 ). This is a small difference if the probability is small (near zero, or "long chance"), but the difference is large if the probability is large (approaching one).

This works for some simple opportunities:

This transformation has certain special geometric properties: the conversion between opportunity and probability (resp. Probability of success with probability of failure) and between probability and probability are all MÃÆ'¶bius transformations (linear fractional transformation). They are thus determined by three points (sharp 3-transitive). Swap odds and odds against swap 0 and infinity, fix 1, while swapping possible successes with probability of swap failures 0 and 1, fix.5; both are of order 2, because of that circular transformation. Convert opportunity to probability improvement 0, send infinity to 1, and send 1 to.5 (possibly even 50% chance), and vice versa; this is a parabolic transformation.

Apps

In probability theory and Bayesian statistics, opportunities are sometimes more natural or more comfortable than probabilities. This often happens in sequential decision-making issues such as in the case of how to stop online at the final-specific event that is solved by an opportunity algorithm. Similar ratios are used elsewhere in Bayesian statistics, such as the Bayes factor.

Chances are probability ratios; odds ratio is the probability ratio, that is the ratio of probability ratio. Odds-ratios are often used in clinical trial analysis. Although they possess useful mathematical properties, they can produce counter-intuitive results: an event with an 80% likelihood occurs four times more likely to occur than an event with a 20% probability, but the chance is 16 times higher on an event that is less likely (4-1 against , or 4) than on the more likely (1-4, or 4-1 at , or 0.25).

In some cases, log-odds are used, which is the logit of probability. Simply, opportunities are often multiplied or shared, and logs convert multiplication into sum and divide into subtraction.

Example # 1

There are 5 pink marbles, 2 blue marbles and 8 purple marbles. What is the chance to choose blue marble?

Answer: Opportunities that support blue marble are 2:13. One can equivalently say that the probability is 13: 2 against . There are 2 of 15 chances that support blue, 13 out of 15 against blue.

Dalam teori probabilitas dan statistik, di mana variabel p adalah probabilitas yang mendukung peristiwa biner, dan probabilitas terhadap peristiwa tersebut adalah 1- p , "peluang" acara adalah hasil bagi dari dua, atau ${\ displaystyle {\ frac {p} {1-p}}}  ÂÂ$ . Nilai tersebut dapat dianggap sebagai probabilitas relatif peristiwa akan terjadi, dinyatakan sebagai pecahan (jika kurang dari 1), atau kelipatan (jika sama atau lebih besar dari satu) dari kemungkinan bahwa peristiwa tersebut tidak akan terjadi.

In the first example above, say Sunday's opportunity is "one to six" or, less commonly, "one sixth" means randomly selecting Sunday's probability is a sixth chance of not selecting Sunday. While the mathematical probability of an event has values ​​in the range from zero to one, "opportunities" that support the same event are between zero and infinite. Opportunities to events with probabilities given as p are ${\ displaystyle {\ frac {1-p} {p}}}$ . Opportunity to Sunday is 6: 1 or 6/1 = 6. It is 6 times more likely that the random day is not Sunday.

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Gambling use

The use of opportunities in gambling facilitates bets on events where the relative probability of results varies. For example, on a coin toss or a match race between two equally horses, it makes sense for two men to bet the stakes. However, in more varied situations, such as multi-runner horse racing or football matches between the two unbalanced sides, betting on "disputes" provides a perspective on the relative possibilities of possible outcomes.

In the modern era, most of the odds of opportunity remain between betting organizations, such as bets, and individuals, rather than between individuals. Different traditions have grown in a way to express opportunities to customers, the older era comes with the odds of betting between people, these days being illegal in most countries, it is referred to as "odding", an underground slang with origin- suggestions based in the Bronx.

Fractional odds

Liked by the dealers in England and Ireland, and also common in horse races, the chances of a fraction cite the net total to be paid to the bettor, should he win, relative to the bet. Opportunities 4/1 will imply that the bettor will make a profit of £ 400 on a £ 100 stock. If the likelihood is 1/4, the bettor will make £ 25 on a stock of £ 100. In either case, after winning, always receive back the original bet; so if the odds are 4/1, bettor receives a total of Ã, Â £ 500 (Ã, Â £ 400 plus the original Ã, Â £ 100). Opportunities 1/1 are known as even or even money .

Counters and fray denominators are always integers, so if gambling payments should be à £ 1.25 for each à £  £ 1 share, this will be equivalent to à £ 5 for each à £ 4 installed, and will likely be expressed as 5/4. However, not all fractional chances are traditionally read using the lowest denominator. For example, given that there is a chance pattern of 5/4, 7/4, 9/4 onwards, a chance of being mathematically 3/2 easier than if expressed in equivalent form 6/4.

The possible fractions are also known as UK opportunities, UK opportunities, or, in that country, traditional opportunities . They are usually represented by "/" but can also be represented by "-", e.g. 4/1 or 4-1. Odds with denominator 1 are often presented in the list as a count only.

The fractional opportunity variation is known as the Hong Kong opportunity. Opportunity fractions and Hong Kong can actually be exchanged. The only difference is that the UK opportunity is presented as a fraction notation (eg 6/5) while Hong Kong's chances are decimal (eg 1.2). Both show net returns.

European opportunities also represent potential victories (net returns), but in addition they factor in bets (eg 6/5 or 1.2 plus 1 = 2.2).

Decimal Opportunity

Preferably in continental Europe, Australia, New Zealand and Canada, decimal opportunities cite the ratio of the payment amount, including the original stock, to the stake itself. Decimal opportunities are generally considered the easiest to handle because they reflect the inverse of the probability of results. Therefore, the decimal probability of a result is equivalent to the decimal value of the fractional probability plus one. So, even 1/1 chance is quoted in the decimal odds as 2.00. The 4/1 fractional opportunities discussed above are cited as 5.00, while the 1/4 odds are quoted as 1.25. This is considered ideal for parlay bets, since the odds to be paid are merely the product of the odds for each outcome at stake. Decimal opportunities are also favored by betting exchanges because they are easiest to work with trading.

Decimal opportunities are also known as European opportunities , digital opportunities or continental opportunities.

Moneyline Misfortune

Moneyline mischief is favored by American bookmakers. The quoted number is positive or negative.

• When the moneyline odds are positive, the figure shows how much money will be won on a $ 100 bet (this is done for results that are considered less likely than not). For example, a 4/1 net payment will be quoted as 400.
• When the moneyline odds are negative, that figure shows how much money should be put on winning $ 100 (this is done for results that are considered more likely than not). For example, a 1/4 net payment would be quoted as -400.

Moneyline possibilities are often referred to as American opportunities . A "moneyline" bet refers to odds on live game results without considering the spread point. In most cases, favorites will have a negative moneyline opportunity (fewer payments for safer bets) and underdogs will have a positive moneyline opportunity (more for risk bets). However, if the team is matched evenly, the second team can have a negative line at the same time (for example, -110 -110 or -105-115), due to home taking.

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Gambling Odds versus possibility

In gambling, the opportunities on display do not represent the true opportunity (as envisaged by the betting maker) that the event will or will not happen, but is the amount that the wager will pay on the winning bet, along with the required bet. In formulating an opportunity to display a bet will include a profit margin that effectively means that payments to successful bidders are less than those represented by the true opportunity of the event. This advantage is known as 'over-round' in 'book' ('book' refers to the ancient tome book in which bets are recorded, and is derived from the term 'bet') and corresponds to the sum of 'opportunities' in the following way:

In a 3-horse race, for example, the true probability of any winning horse based on their relative ability may be 50%, 40%, and 10%. The total of these three percentages is 100%, thus representing a fair 'book'. The real chances to win for each of the three horses are 1-1, 3-2 and 9-1 respectively.

To generate profit on the bets received, the bet can decide to increase the value to 60%, 50% and 20% for three horses, respectively. This represents their respective odds, ie 4-6, 1-1, and 4-1, respectively. These values ​​are now 130%, which means that the book has an excess of 30 (130-100). This value of 30 shows the amount of profit for the bet if he gets a bet in a good proportion for each horse. For example, if he took à £  £ 60, à £ 50 and à £ 20 each bet for three horses he received à £ 130 in the bet but only paid à £ 100 back including pegs), anybody who wins the horse. And the expected value of the benefits is positive even if everyone is betting on the same horse. Betting art is in setting a fairly low chance that it has the positive expected returns while maintaining a high enough chance to attract customers, and at the same time attracts enough bets for each outcome to reduce its risk exposure.

A study of football betting found that the probability for the home team to win is generally about 3.4% lower than the calculated value of the odds (eg, 46.6% for even chance). That's about 3.7% less to be won by visitors, and 5.7% less for the lottery.

Making a profit in gambling involves predicting a true probability relationship with a payout opportunity. Sports information services are often used by professional and semi-professional sports players to help achieve this goal.

The odds or the amount of bets to be paid are determined by the total amount already bet on all possible events. They reflect the balance of bets on both sides of the event, and include cutting brokerage fees ("vig" or spirit).

Also, depending on how the bet is affected by the jurisdiction, the tax may be involved for the bet and/or the winning player. This may be taken into account when offering opportunities and/or can reduce the amount won by a player.

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See also

• Galton box
• Math game
• Formal mathematical specification of logistic regression
• Optimum termination
• Associate football predictions statistics

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References

Source of the article : Wikipedia