Statistics Probability Odds Probability

Finding the odds
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clinacvirdapptho.ml/the-mermaids-tears.php I do not know if this interpretation would be correct. So, any guidance and more examples on interpreting odds would be greatly appreciated.

On another thread there is a much broader answer by gung that also deals with related technical issues such as the odds ratio, but I am going to stick to the topic at hand: As a beginner's question, it's worth thinking how "odds" are expressed in everyday speech especially in betting parlance as well as what odds mean to a statistician, because discrepancies between the two are problematic for learners. For odds as expressed by a statistician , your contention is correct.

The probability that the selected token is aquamarine is 3 out of 4, i. More generally, you could take the fraction of "favourable outcomes over unfavourable outcomes" and cancel divide both numerator and denominator by the total number of outcomes, to obtain "the probability of a favourable outcome over the probability of an unfavourable outcome", from which a little algebra gives:.

Odds as expressed by a bookmaker are usually quoted either as "odds against" or "odds on", and which way they are written seems to be a common cause of confusion.

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So far, so little discrepancy: Consider a race in which all four horses let's say F oinavon , G regalach , M on Mome and T ipperary Tim are equally likely to win: What would the fair odds be for a bet on, say, Foinavon? Sadly, "odds against" the usual form of odds does not correspond to a statistician's "odds in favour". If any layperson in your audience comes from a country where fractional odds are used by bookmakers, and regularly quoted in the media e.

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I've seen people try this, perhaps in the belief that "the general public is more familiar with odds than probabilities", but statisticians wise to the bookmaker's overround, and who have therefore never placed a bet in their lives, may be caught by surprise that the popular conception of odds is "the wrong way round". Before presenting statistical odds to such an audience, I would at least make them aware of the following points:.

Even this may not be sufficient to avoid confusion. Decimal odds , also known as continental odds or European odds , have become more prevalent in an era of online gambling, especially for in-play betting and betting exchanges where fractional odds are unwieldy for displaying small, rapid changes in implied probabilities.

Probability vs. odds

European odds quote the payout per unit staked, including the return of the stake. You may have noticed that the European odds are the reciprocal of the implied probability of success: European odds have several advantages to the gambler.

Implied Probability in Sports Betting

Small changes to the implied probability work "smoothly" for a decimal whereas the form of a fraction may have to completely change as a different denominator is required. Calculating the payout from a win is as simple as multiplying the stake by the European odds e.

Confidence Intervals

The reciprocal relationship with implied probability is especially useful for spotting "value bets": However, it's harder for a statistician to explain mathematical odds to a layperson accustomed to European odds! Even worse, the numbers are not simply the "wrong way round" but completely misleading: This key conceptual ratio is retained in the moneyline system used in US sports betting, even though it looks more complex at first sight. I appreciate much of this answer has concerned betting and pay-offs rather than statistics, but I've found the everyday usage of "odds" differs so markedly from the statistician's technical definition, that a thorough comparison might address some confusion both of non-technical gamblers, and non-gambling statisticians.

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The explanation for this is that if the outcome being studied is fairly uncommon, then the odds of disease in an exposure group will be similar to the probability of disease in the exposure group. Even worse, the numbers are not simply the "wrong way round" but completely misleading: Another key aspect to computing probability is factoring in the number of opportunities for something to occur. As another example, in rolling two dice there are 36 possible outcomes: Each event is independent and therefore the player can never predict what will come up next.