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In probability theory, odds provide a measure of the probability of a particular outcome. Odds are commonly used in gambling and statistics.For example for an event that is 40% probable, one could say that the odds are "2 in 5", "2 to 3 in favor", or "3 to 2 against".
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of event A taking place in the presence of B, and the odds of A in the absence of B. Due to symmetry, odds ratio reciprocally calculates the ratio of the odds of B occurring in the presence of A, and the odds of B in the absence of A.
If p is a probability, then p/(1 − p) is the corresponding odds; the logit of the probability is the logarithm of the odds, i.e.: = = = = (). The base of the logarithm function used is of little importance in the present article, as long as it is greater than 1, but the natural logarithm with base e is the one most often used.
Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...
The values given for Probability, Cumulative probability, and Odds are rounded off for simplicity; the Distinct hands and Frequency values are exact. The nCr function on most scientific calculators can be used to calculate hand frequencies; entering nCr with 52 and 5 , for example, yields ( 52 5 ) = 2 , 598 , 960 {\textstyle {52 \choose 5 ...
The corresponding probability of the value labeled "1" can vary between 0 (certainly the value "0") and 1 (certainly the value "1"), hence the labeling; [2] the function that converts log-odds to probability is the logistic function, hence the name.
The odds strategy is optimal, that is, it maximizes the probability of stopping on the last 1. The win probability of the odds strategy equals = If , the win probability is always at least 1/e = 0.367879..., and this lower bound is best possible.
E.g. £100 each-way fivefold accumulator with winners at Evens ( 1 ⁄ 4 odds a place), 11-8 ( 1 ⁄ 5 odds), 5-4 ( 1 ⁄ 4 odds), 1-2 (all up to win) and 3-1 ( 1 ⁄ 5 odds); total staked = £200 Note: 'All up to win' means there are insufficient participants in the event for place odds to be given (e.g. 4 or fewer runners in a horse race).
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