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The odds strategy is the rule to observe the events one after the other and to stop on the first interesting event from index s onwards (if any), where s is the stopping threshold of output a. The importance of the odds strategy, and hence of the odds algorithm, lies in the following odds theorem.
Graphs of probability P of not observing independent events each of probability p after n Bernoulli trials vs np for various p.Three examples are shown: Blue curve: Throwing a 6-sided die 6 times gives a 33.5% chance that 6 (or any other given number) never turns up; it can be observed that as n increases, the probability of a 1/n-chance event never appearing after n tries rapidly converges to ...
For an event X that occurs with very low probability of 0.0000001%, or once in one billion trials, in any single sample (see also almost never), considering 1,000,000,000 as a "truly large" number of independent samples gives the probability of occurrence of X equal to 1 − 0.999999999 1000000000 ≈ 0.63 = 63% and a number of independent ...
In 1964 Sherman Kent, one of the first contributors to a formal discipline of intelligence analysis addressed the problem of misleading expressions of odds in National Intelligence Estimates (NIE). In Words of Estimative Probability, Kent distinguished between "poets" (those preferring wordy probabilistic statements) from "mathematicians ...
For example, if a weapon is expected to hit a target nine times out of ten with a representative set of ten engagements, one could say that this weapon has a P hit of 0.9. If the chance of hits is nine out of ten, but the probability of a kill with a hit is 0.5, then the P k becomes 0.45 or 45%.
The true odds against winning for each of the three horses are 1–1, 3–2 and 9–1, respectively. In order to generate a profit on the wagers accepted, the bookmaker may decide to increase the values to 60%, 50% and 20% for the three horses, respectively. This represents the odds against each, which are 4–6, 1–1 and 4–1, in order.
In statistics, this is called odds against. For instance, with a royal flush, there are 4 ways to draw one, and 2,598,956 ways to draw something else, so the odds against drawing a royal flush are 2,598,956 : 4, or 649,739 : 1. The formula for establishing the odds can also be stated as (1/p) - 1 : 1, where p is the aforementioned probability.
To find the likelihood of a certain point range, one simply subtracts the two relevant cumulative probabilities. So, the likelihood of being dealt a 12-19 HCP hand (ranges inclusive) is the probability of having at most 19 HCP minus the probability of having at most 11 HCP, or: 0.9855 − 0.6518 = 0.3337. [2]