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Is this a formal or informal expression?

He doesn't stand a chance.

If it's informal, what are some formal alternatives?

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This is quite informal, in my opinion.

More formal alternatives abound though...
1. He cannot possibly win.
2. He will not win.
3. There is no likelihood that he will succeed.
4. His chances of victory are minimal at best.
5. It is my considered opinion that, endeavor as he might, victory is beyond his capabilities.
... and many more!

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Personally, I'd consider the expression informal. The usage of "to stand" in this case is probably the main reason for that impression.

Very similar expressions like

He does not have a chance.

or perhaps

There is no possibility [e.g. of him/her winning].

of course, depending on context, would sound more formal to me.

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