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The following sentence, from my grammar textbook, confused me:

What's the odds? (What does it matter?)

I looked up odds in some dictionaries. All say that odds is a plural noun. So, there are two questions:

1) Why can is be used after a plural noun?

2) Is there any singular form of odds? What exactly is an odd?

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I think you found a typo in your book! It should read: "What're (What are) the odds?"

Here are some other examples of plural nouns in English that don't have a singular equivalent but sometimes get conjugated as singular:

  • Scissors
  • Pants

Even though the singular conjugation is not correct it still shows up, especially in conversation. "Media" is a great example of this, since it is actually a plural of "medium" but almost never is used as a plural.

  • It is not uncommon in casual speech for people to contract "there are" to "there's", even though that's not a correct contraction. For example: "There's three books on the table." So it might not be a typo, but it is very sloppy to have this in a grammar book! – Canadian Yankee Mar 13 '18 at 13:58
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The Google definition is

odds, plural noun: the ratio between the amounts staked by the parties to a bet, based on the expected probability either way.

Notice that the definition is the ratio (as in, there is by definition only one ratio). So, even though the noun odds is plural, when you replace the word with it's definition, it would switch from "What are the odds?" to "What is the probability?"¹. While odd is a word with its own definition, you cannot use it as a singular form to odds. It's similar to the word clothes; you wear clothes, but you do not say that your pants or shirt are each a cloth.

¹ Odds (ratio) and probability are different but related terms in statistics, but when using them in a non-statistcal context, they are generally interchangeable.

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