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Collins English Dictionary avows:

To shorten the odds on something happening means to make it more likely to happen.
To lengthen the odds means to make it less likely to happen.
You can also say that the odds shorten or lengthen.

I use the definition of 'odds' from p. 4 of Confusion Between Odds and Probability, a Pandemic? (in Journal of Statistics Education Volume 20, Number 3 (2012)):

odds in favor of A $= \dfrac{n(A)}{n(A^C)} = \dfrac{P(A)}{1 - P(A)}$

$\implies$ Odd $∝ P(A).$

  1. What semantic notions underlie odds and the notion of being shortened/lengthened?

  2. The word choice of 'shorten/length' also feels the wrong way around. Why doesn't 'shorten the odds' signify make something more less likely? Vice versa for 'lengthen the odds'?

1 Answers1

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"Shorten" and "lengthen" here come from the adjectives "short" and "long" as applied to odds: long odds means an event of low probability. OED has a citation from 1764:

Hist. Miss Charlotte Seymour II. xxviii. 273 Presently news was brought that the favourite horse, on whose head Mr. Huntly had laid the long odds,..had fallen and broke his leg, within three yards of the goal.

It seems this may be related to "long shot", i.e. literally shooting a weapon at a target at the extreme end of the weapon's range. Such a shot would have a low probability of hitting the target. The phrase was then applied to any venture that had a low probability of success.

Robert Israel
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