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The following sentence comes from "Introduction to Algorithms, 3rd Edition By Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein"

A political candidate may want to determine where to spend money buying campaign advertising in order to maximize the chances of winning an election.

The sentence is talking about "a candidate" and "an election", why does it use the plural form "chances"?

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    Using chance would be fine as well. See also Why do we use the plural "chances" and "odds" to talk about probability?
    – Glorfindel
    Apr 10, 2022 at 12:29
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    Does this answer your question? "Chances of (doing) something" vs. "chances at (doing) something"? The answer to that earlier question addresses the singular/plural issue as well as the choice of preposition. Apr 10, 2022 at 13:48
  • Looking at it mathematically, assuming just 2 candidates running, they could win with 51% of the vote. Or 52%, 53%, all the way up to 100%. Each of these is a "chance". If you count non-integers, there's an infinite number of "chances" between 50% +1 vote and 100%. (Well, not infinite since there's a finite number of voters, but probably a lot more than 50.) Apr 11, 2022 at 14:55
  • There is one way of looking at it where there is one chance (win) out of 2 outcomes (win or lose) but Darrel Hoffman nicely pointed out the other way of looking at it where there are many chances (ways in which votes could be cast to determine a win) among many outcomes (ways in which votes could be cast at all.)
    – Wyck
    Apr 11, 2022 at 16:29

3 Answers 3

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While mathematicians consider probabilities to be absolute numbers (usually expressed as a fraction between 0 and 1, possibly converted to a percentage), non-mathematicians often think of it as a number of chances out of a total. For instance, a 75% probability may be described as 3 chances out of 4.

In this way of thinking, "chance" becomes a countable noun, and we can refer to it in the plural.

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Chances in American (and British) English can mean 'probability'.

The chances are that the train hasn't left yet

Chances (Collins Dictionary)

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  • Interestingly, M-W defines the plural form as "the more likely indications", with an example of "chances are he's already gone". But I think one could perfectly well say "his chances are slim"m even though the singular would be fine (finer? Dunno). Apr 11, 2022 at 7:01
  • @Peter-ReinstateMonica The chances of anyone coming from Mars are a million to one -- but still they come! Apr 11, 2022 at 21:48
  • Well, I wouldn't object to a singular there. But perhaps the "more likely" qualification is specifically attached to "chances are ...", not to any plural, even though the M-W entry doesn't say that. Apr 11, 2022 at 22:12
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I'm not sure whether there is any linguistic support for the mental image which the plural "chances" evokes in me: A multitude of possibilities branching out from the point at which we are right now. Some of the branches eventually lead to a certain outcome, others not. The sum of the probabilities for those that do are the chances, plural.

The idea is a bit like in this tweet, except that some of the branches come together again.

Maybe I'm influenced by my hobby, the game of backgammon which is an intriguing mixture of luck and skill, not unlike life itself. There is typically more than one way to win: You can roll high, you can contain a checker from your opponent, or you can hit one and get ahead. The sum of the probabilities for each distinct path to victory are the overall winning chances — plural.

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