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One can also speak of "almost all" integers having a property to mean "all except finitely many", despite the integers not admitting a measure for which this agrees with the previous usage. For example, "almost all prime numbers are odd". There is a more complicated meaning for integers as well, discussed in the main article.
Odds are particularly useful 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. The odds are a ratio of probabilities; an odds ratio is a ratio of odds, that is, a ratio of ratios of probabilities.
One of the widely used types of impossibility proof is proof by contradiction.In this type of proof, it is shown that if a proposition, such as a solution to a particular class of equations, is assumed to hold, then via deduction two mutually contradictory things can be shown to hold, such as a number being both even and odd or both negative and positive.
In decision theory, the odds algorithm (or Bruss algorithm) is a mathematical method for computing optimal strategies for a class of problems that belong to the domain of optimal stopping problems. Their solution follows from the odds strategy , and the importance of the odds strategy lies in its optimality, as explained below.
Against All Odds (Conflict album), 1989; Against All Odds (Curtis Lundy album), 1999; Against All Odds, a 2000 album by Take 5; Against All Odds (Tragedy Khadafi album), 2001; Against All Oddz (Lethal Bizzle album), 2005; Against All Oddz (Young Noble and E.D.I. album), 2006; Against All Odds (N-Dubz album), 2009; Against All Odds, a 2009 album ...
If the U.S. Congress passes a bill, the president's signing of the bill is sufficient to make it law. Note that the case whereby the president did not sign the bill, e.g. through exercising a presidential veto, does not mean that the bill has not become a law (for example, it could still have become a law through a congressional override ...
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The gambler's fallacy is a particular misapplication of the law of averages in which the gambler believes that a particular outcome is more likely because it has not happened recently, or (conversely) that because a particular outcome has recently occurred, it will be less likely in the immediate future.