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| {{For|the [[alternative rock]] band|Odds (band)}}
| | It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>In case you have any concerns about where along with tips on how to employ [http://www.youtube.com/watch?v=90z1mmiwNS8 dentist DC], you can e mail us from the web page. |
| {{Redirect|Odds against|the 1966 documentary film|The Odds Against}}
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| {{One source|date=May 2012}}
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| The '''odds''' in favor of an [[event (probability theory)|event]] or a [[proposition]] is the ratio of the probability that the event will happen to the probability that the event will not happen. For example, the odds that a [[random variable|randomly chosen]] day of the week is a Sunday are one to six, which is sometimes written 1 : 6.;<ref>{{cite web |url=http://mathworld.wolfram.com/Odds.html
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| |title=Wolfram MathWorld (Odds) |author=Wolfram MathWorld |publisher=Wolfram Research Inc. |accessdate=16 May 2012}}</ref> see section 1.5 of Gelman et al. (2003).
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| '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 (1/7), 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.
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| 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]].
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| 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.
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| "Odds on" means that the event is more likely to happen than not. This is sometimes expressed with the smaller number first (1 : 2) but more often using the word "on" (2 : 1 on) meaning that the event is twice as likely to happen as not.
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| ==Examples==
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| Example #1: There are 5 pink marbles, 2 blue marbles, and 8 purple marbles. What are the odds in favor of picking a blue marble?
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| Answer: The odds in favour of a blue marble are 2 : 13. One can equivalently say, that the odds are 13:2 ''against''. There are 2 out of 15 chances in favour of blue, 13 out of 15 against blue.
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| In [[probability theory]] and [[statistics]], where the variable ''p'' is the [[probability]] in favor of a binary event, and the probability against the event is therefore 1-''p'', "the odds" of the event are the quotient of the two, or <math>\frac{p}{1-p}</math>. That value may be regarded as the relative likelihood 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 above, 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 the event with probability given as ''p'' are <math>\frac{1-p}{p}</math>.
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| The '''odds against''' Sunday are 6:1 or 6/1 = 6. It is 6 times as likely that a random day is not a Sunday.
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| Example #2: There are 5 red marbles, 2 green marbles, and 8 yellow marbles. What are the odds against picking a yellow marble?
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| Answer: 7 : 8
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| ==Chances versus odds==
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| ''Odds of so many to so many on (or against)'' some event refers to the ratio of numbers of (equal) chances in favor and against (or vice-versa); ''chances of so many, in so many'' refers to the number of (equal) chances in favour relative to the number for and against combined. For example, example #1 above, the "chance of picking a blue marble is 2 '''in''' 15", the "odds on picking a blue marble are 2 '''to''' 13", "the odds '''against''' picking a blue marble are 13 to 2". Odds of 1 ''to'' 5 corresponds to 1 chance ''in'' 6. The words ''odds'' and ''chances'' are often interchangeably used to vaguely indicate some measure of probability; the intended meaning of the writer has to be deduced by noting whether the preposition between the two numbers is ''to'' or ''in''.<ref>{{cite web |url=http://www.powerball.com/powerball/pb_prizes.asp |title=Welcome to Powerball - Prizes |author=Multi-State Lottery Association |date= |work= |publisher=Multi-State Lottery Association |accessdate=16 May 2012}}</ref><ref>{{cite news |title=Odds of Finding Earth-Size Exoplanets Are 1-in-4 |author=Lisa Grossman |url=http://www.wired.com/wiredscience/2010/10/exoplanet-stats/ |newspaper=Wired |date=October 28, 2010 |accessdate=16 May 2012}}</ref><ref>{{cite web |url=http://www.wolframalpha.com/input/?i=Poker+Probabilities |title=Wolfram Alpha (Poker Probabilities) |author=Wolfram Alpha |date= |work= |publisher=Wolfram Alpha |accessdate=16 May 2012}}</ref>
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| ==Presentation of odds==
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| ===Decimal presentation===
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| Taking an event with a 1 in 5 probability of occurring (i.e. a probability of 1/5, 0.2 or 20%), then the odds are 0.2 / (1 − 0.2) = 0.2 / 0.8 = '''0.25'''. This figure (0.25) represents the monetary stake necessary for a person to gain one (monetary) unit on a successful wager when offered fair odds. This may be scaled up by any convenient factor to give whole number values. For example, if a stake of 0.25 wins 1 unit, then scaling by a factor of four means a stake of 1 wins 4 units.
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| ===Ratio presentation===
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| [[Fixed odds gambling]] tends to represent the probability as [[Fixed-odds gambling#Fractional odds|fractional odds]], and excludes the stake. For example, a probability 0.20 is represented as "4 to 1 ''against''" (written as 4-1, 4:1, or 4/1), since there are five outcomes of which four are unsuccessful. Thus the stake returned must be added to the odds to compute the entire return of a successful bet. In [[craps]] the payout would be represented as "5 for 1", and in [[Fixed-odds gambling#Moneyline odds|moneyline odds]] as +400 representing the ''gain'' from a 100 stake.
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| By contrast, for an event with a 4 in 5 probability of occurring (i.e. a probability of 4/5, 0.8 or 80%), then the odds are 0.8 / (1 − 0.8) = 4. If one bets 4 units at these odds and the event occurs, one receives back 1 unit plus the original unit 4 units stake. This would be presented in fractional odds of "4 to 1 ''on'''' (written as 1/4 or 1–4), in decimal odds as 1.25 to include the returned stake, in craps as "5 for 4", and in moneyline odds as −400 representing the stake necessary to gain 100.
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| Fixed odds are not necessarily presented in the lowest possible terms; if there is a pattern of odds of 5–4, 7–4 and so on, odds which are mathematically 3–2 are more easily compared if expressed in the mathematically equivalent form 6–4. Similarly, 10–3 may be stated as 100–30.
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| ==Gambling odds versus probabilities==
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| {{Main|Sports betting#Odds}}
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| 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. For instance, if the bookmaker offers odds of 4:6 against a certain horse winning a race, this means that he'll accept a $6 stake in return for a payoff of $4, plus return of the stake, if the horse wins. If the horse loses, the bookmaker keeps the stake. In formulating his odds to display the bookmaker will have included a profit margin which effectively means that the payout to a successful [[gambler|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:
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| In a 3-horse race, for example, the true probabilities of each of the horses winning based on their relative abilities may be 50%, 40% and 10%. The total of these three percentages is 100%, thus representing a fair 'book'. The true odds against winning for each of the three horses are 1-1, 3-2 and 9-1 respectively.
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| In order to generate a profit on the wagers accepted by the bookmaker he may decide to increase the values to 60%, 50% and 20% for the three horses, representing odds against of 4-6, 1-1 and 4-1. These values now total 130%, meaning that the book has an [[Mathematics of bookmaking|overround]] of 30 (130 − 100). This value of 30 represents the amount of profit for the bookmaker if he accepts bets in the correct proportions on each of the horses. The art of bookmaking is that he will take in, for example, $130 in wagers and only pay $100 back (including stakes) no matter which horse wins.
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| Profiting in [[gambling]] involves predicting the relationship of the true probabilities to the payout odds. [[Sports information service]]s are often used by professional and semi-professional sports bettors to help achieve this goal.
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| 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]]).
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| Also, depending on how the betting is affected by jurisdiction, taxes may be involved for the bookmaker and/or the winning player. This may be taken into account when offering the odds and/or may reduce the amount won by a player.
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| ==Even odds==
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| The terms "even odds", "even money" or simply "evens" (1 to 1, or 2 for 1) imply that the payout will be one unit per unit wagered plus the original stake, that is, 'double-your-money'. Assuming there is no bookmaker fee or built-in profit margin, the actual probability of winning is 50%. The term "better than even odds" (or "better than evens") looks at it from the perspective of a gambler rather than a statistician. If the odds are Evens (1–1), and one bets 10 units, one would be returned 20 units, profiting 10 units. If the gamble was paying 4-1 and the event occurred, one would make 50 units, or a profit of 40 units. So, it is "better than evens" from the gambler's perspective because it pays out more than one-for-one. If an event is more likely to occur than an even chance, then the odds will be "worse than evens", and the bookmaker will pay out less than one-for-one.
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| In popular parlance surrounding uncertain events, the expression "better than evens" usually implies a better than (greater than) 50% chance of the event occurring, which is exactly the opposite of the meaning of the expression when used in a gaming context.
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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 trial]]s. While they have useful mathematical properties, they can produce counter-[[Intuition (knowledge)|intuitive]] results: an event with an 80% probability of occurring is four times ''more likely'' to happen than an event with a 20% probability, but the ''odds'' are 16 times higher on the less likely event (4–1 ''against'', or 4) than on the more likely one (1–4, or 4–1 ''on'', or 0.25).
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| The [[logarithm]] of the odds is the [[logit]] of the probability. | |
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| ==Historical==
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| The language of odds such as "ten to one" for intuitively estimated risks is found in the sixteenth century, well before the discovery of mathematical [[probability]].<ref>{{Cite book |title=The Science of Conjecture: Evidence and Probability Before Pascal |first=Franklin |last=James |publisher=The Johns Hopkins University Press |location=Baltimore |year=2001 |pages=280–281 }}</ref> Shakespeare wrote:
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| {{quote|
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| Knew that we ventured on such dangerous seas<br />
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| That if we wrought out life 'twas ten to one
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| |[[William Shakespeare]]|[[Henry IV, Part II]], Act I, Scene 1 lines 181–2.
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| }}
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| ==See also==
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| *[[Galton box]]
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| *[[Gambling]]
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| *[[Gaming mathematics]]
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| *[[Logistic regression#Formal mathematical specification|Formal mathematical specification of logistic regression]]
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| *[[Mathematics of bookmaking]]
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| *[[Odds algorithm]]
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| *[[Optimal stopping]]
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| *[[Statistical Soccer (Football) Predictions]]
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| ==References==
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| * Andrew Gelman, John B. Carlin, Hal S. Stern, and Donald B. Rubin (2003), "Bayesian Data Analysis", Second Edition, CRC Press.
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| {{Reflist}}
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| {{Use dmy dates|date=September 2010}}
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| [[Category:Probability theory]]
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| [[Category:Statistical ratios]]
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| [[Category:Statistical terminology]]
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| [[Category:Wagering]]
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It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.
Here are some common dental emergencies:
Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.
At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.
Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.
Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.
Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.
Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.
Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.
In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.
In case you have any concerns about where along with tips on how to employ dentist DC, you can e mail us from the web page.